exametrika 2.0.0

The version number was raised to 2.0.0 because the EM convergence fix below changes the estimates of every EM-based model: the same code on the same data now returns different numbers, and no longer the numbers printed in Shojima (2022). A minor bump would have understated that. The deprecation removals planned for 2.0.0 ride along, so that the break happens once.

Removals (breaking)

The names deprecated in earlier releases are gone. Each carried a deprecation warning for several releases: the function renames since 1.7.0, the field-name aliases since 1.8.0.

Functions removed, with their replacements:

Field aliases removed from returned objects. The snake_case names have been present alongside them since 1.8.0, so code that already reads the new names is unaffected:

GridSearch() still accepts "LogLik" as a value for its index argument; that is an input alias for the criterion name, not a field on the result.

Bug Fixes

• Biclustering() ignored maxiter on binary data. The binary branch set its own iteration cap to 1000 outright, so the argument was accepted and discarded; the polytomous branches always passed it through. The default is now 1000 to match what the function has actually been doing, so results do not change for anyone who left the argument alone, and the help says 1000 rather than 100.

• LRA(method = "GTM") ignored maxiter. The GTM branch called the EM loop without passing the argument on, so it always stopped at emclus()’s default of 100 cycles no matter what the caller asked for – while the help said the default was 1000. The SOM and isotonic branches were unaffected. Fits that needed more than 100 cycles returned with converge = FALSE and estimates short of the maximum; on the packaged datasets 100 was enough, which is why it went unnoticed. Found while building a small cross-validation dataset that needs 113 cycles, where the log-likelihood came out 7.2e-4 away from the reference and lands on it exactly once the argument is honoured.

• Posterior memberships were normalised by subtracting the row minimum, and polytomous biclustering silently merged fields once the sample passed roughly 700 respondents. The E-steps turn a matrix of log-likelihoods into memberships. Doing that safely means subtracting the row maximum before exponentiating, so every exponent is at most zero. Several E-steps subtracted the row minimum instead, which pushes every exponent positive, and then clipped at exp(700) to stop the overflow. Everything above the clip lands on the same value: two fields differing by a factor of exp(400) came out equally likely.

  How far a row spreads depends on what is being summed over. A class posterior sums over items, so it stays small and the clip is rarely reached. A field posterior sums over respondents, so it grows with the sample – which is why the visible symptom was backwards, more data giving a worse answer. Measured on ordinal data with 24 items in 3 true fields: fields recovered exactly up to 500 respondents, degrading at 700, and by 1000 two of the three fields had merged and one came out empty (adjusted Rand index 1.00 falling to 0.55). The class side was almost unaffected in the same runs, which is what made it look like a field-clustering quirk rather than a normalisation bug.

  Affected: Biclustering() and Ranklustering() on ordinal and nominal data (both the class and field steps), LCA() on nominal and rated data, and LDB(). Binary biclustering was already correct. Fixed by routing all of them through one row_softmax() helper.

  The same helper replaces the unstabilised exp(ll) / rowSums(exp(ll)) in binary LCA()/LRA(), LDLRA(), and LRA() on ordinal and rated data. Those subtract nothing at all, so their exponents are negative and they underflow rather than overflow – reachable only on very long tests, and loud (NaN) rather than silent when reached. The returned values are unchanged wherever the old code did not overflow or underflow.

  No test in the suite caught this: the biclustering reference fixtures top out at 515 respondents, below where the clip starts to bite. Regression tests over a range of sample sizes were added.

  BINET() uses the same unstabilised form but is deliberately left alone: it pins boundary-class respondents by writing a literal 1 next to the raw likelihoods, so rescaling the rows would change how hard that pin holds. That the strength of the pin depends on the test length looks unintended and is being reviewed separately.

• Order-restricted biclustering returned no field assignments at all on tests longer than about 40 items. The E-step needs the log of a category probability, formed as the difference of two upper-cumulative probabilities. That difference cannot be negative in exact arithmetic, but the order-restricted M-step pools adjacent categories, so exact ties are the norm rather than the exception (11 of 30 differences on a 72-item fit), and a tie computed as a subtraction lands anywhere within a few ulp of zero.

  The guard against that was + const, and const is exp(-nitems). It therefore shrinks as the test grows – exp(-72) is 5e-32 against rounding errors of 1e-14 – while the errors it has to absorb do not. Past roughly 37 items the guard stops working: log() of a negative difference gave NaN, the NaN reached the field posterior through the softmax, and max.col() returned NA for every item, so the fit came back with all fields empty and converge = FALSE. The cost was visible too, since a fit that never stabilises runs to the iteration cap: 72 items in 6 fields now converges in 5 cycles and 0.2 seconds.

  Fixed by clamping the difference at zero before adding const. Only the rounding is repaired: a genuinely tied pair still becomes log(const) exactly as before, and every already-positive value is unchanged to the bit, so no previously-working fit moves. Ordinal LRA() is unaffected – its isotonic path works with the probabilities themselves rather than a difference.

  const = exp(-nitems) is doing two jobs that pull apart as tests get longer: a modelling penalty for an impossible response, which should scale with the test, and a numerical floor, which should not. Separating them is left for a later release.

• M2() says how much memory it needs, and refuses a size the machine cannot hold. The margin covariance is a dense m x m matrix and m grows with the square of the test length: 35 items over 5 categories is 0.7 GB, 40 items is 1.2 GB, 72 items is 32 GB. Allocating tens of gigabytes unannounced is not something a user can recover from – the operating system kills the process, taking the session and everything in it – so M2() and add_M2() now report the size before starting whenever the computation needs 2 GB or more, and stop with an explicit error when the projected peak exceeds four fifths of physical memory. No question is asked: a prompt would have to be limited to interactive() to keep scripts and R CMD check from waiting on input, which would make the behaviour depend on how the code was started.

  options(exametrika.m2_max_gb = ) replaces the memory-derived ceiling with an explicit one, and Inf removes the check for anyone who wants the old behaviour back.

• M2() on a rank-deficient margin covariance is roughly 300x faster. When the Cholesky factorisation of Xi fails, the fallback was an eigendecomposition – an order of magnitude more arithmetic than the factorisation it replaces, and it needs room for the full eigenvector matrix beside Xi itself. It is now a pivoted Cholesky, which costs the same m^3/3 and reports the rank directly. On the largest margin set met so far (biclustering, 40 items x 5 categories, m = 12,640, Xi at 1.2 GB) that is 16 seconds against about 80 minutes. Both are generalised inverses of Xi and the statistic only uses the residual’s component in the column space, so the value is unchanged; the equivalence is pinned by tests.

  This mattered most for biclustering, where Xi is rank-deficient at any useful size, so the slow path was the normal path rather than the exception.

• The order-restricted solver no longer inherits the EM’s iteration cap. Biclustering() and LRA() on ordinal data passed their own maxiter straight into iso_dual_map(), so raising the EM cap from 100 to 1000 for the convergence fix silently raised the inner solver’s cap tenfold as well. Two unrelated loops shared one knob. The solver now uses its own budget. No results change – it converges well inside either cap, and the fit is identical for every EM cap from 100 to 1000 – but the coupling was not intended.

• maxiter documentation corrected for ordinal and nominal Biclustering(), which said 100 after the default became 1000.

• LRA() on ordinal or rated data could die on a lumpy score distribution. The EM starting values come from grouping respondents by total score at the score quantiles. When the scores pile up – few categories with a strong floor or ceiling is enough – a quantile group comes out empty, its mean is 0/0, and the NaN propagates until sort() drops it and an array assignment fails with a message about replacement lengths that says nothing about scores. Measured instance: 20 items, 3 categories, 6 ranks, 300 respondents, with 66 people at the lowest possible score and 77 at the highest.

  The grouping rule is unchanged – it is the reference implementation’s – and only the undefined values are repaired: an empty group borrows from the nearest group that has respondents, which is meaningful because the groups are ordered by score. Empty groups also had to survive table(), which drops unused levels and left the rank-by-quantile cross-tabulation too small for its own dimnames.

• M2() no longer fails on a singular margin covariance. Two causes, both routine on real data. A category nobody chose gives an exact zero in the profile, and the covariance correction then computes 0/0; the value that division stands for is zero. A margin with a vanishingly small probability leaves a direction with no usable variance, which a Cholesky factorisation rejects and a check on the diagonal alone cannot catch, the dependence being off-diagonal. M2() now falls back to an eigendecomposition and works in the subspace with non-negligible eigenvalues, reporting how many directions were dropped; the degrees of freedom count the subspace actually used.

• EM convergence was declared far too early, and on short tests after a single cycle. This affects every EM-based model and is the largest behavioural change in this release: estimates move, and they no longer reproduce the numbers printed in Shojima (2022). Three separate defects, all inherited faithfully from the reference Mathematica implementation:

  1. The starting value. test_log_lik was initialised to -1 / exp(-J), i.e. -exp(J), meant to sit below any attainable log-likelihood. For a short test with many respondents it does not: J = 6 gives -403 against a real log-likelihood near -3900. The first cycle then looked like a decrease, the “likelihood went down” guard fired, and the loop exited after one iteration – while reporting converge = TRUE. Measured: binary LCA() on 6 items x 1000 respondents stopped at 1 cycle; Biclustering() on the bundled J5S1000 stopped at 1 cycle. Tests never caught it because every Mathematica-referenced dataset has J >= 15, where exp(J) is safely below the log-likelihood. Now -Inf, with the comparison skipped on the first pass.

  2. The monitored quantity. The criterion watched the expected log-posterior Q(theta_t | theta_{t-1}) (Shojima 2022, eqs. 5.11-5.12), not the observed-data log-likelihood. EM guarantees the latter increases; the former conditions on a moving point and need not. On 6-item data it does decrease at the second cycle (-3869.26 -> -3922.42), firing the guard on a healthy iteration. LCA() (binary/nominal/rated), LRA() (isotonic and GTM) and LDLRA() now monitor the observed-data log-likelihood, computed by log-sum-exp. LCA.nominal()’s reported log_lik is therefore now a proper marginal likelihood, which also makes its AIC/BIC the textbook quantities. Biclustering keeps its original monitored quantity deliberately – a two-sided mixture has no single obvious observed-data likelihood – so only its starting value and tolerance changed.

  3. The tolerance. A relative 1e-4 on a value of order 1e3 is a threshold of ~0.4 nats, so EM stopped well short of convergence. J15S500 with 5 classes ran 73 cycles to an observed log-likelihood of -4121.53, where a properly converged run reaches -4118.16 in 440. The tolerance is now 1e-8 for the EM engines, matching what the nominal engines and GRM() already used, and maxiter defaults rise from 100 to 1000 (largest observed requirement across the bundled data: 685 cycles, 0.25s). IRT() uses 1e-6: each of its cycles runs one optim() per item, so extra cycles cost real time, and the attainable accuracy is bounded by optim()’s own reltol anyway.

  Effect on the published example (LCA(J15S500, ncls = 5)): 73 cycles -> 337, and the class reference matrix of the book’s Table 5.1 changes in the second decimal (Item 1: .519 .700 .764 .856 .860 -> .590 .662 .772 .853 .884). The Mathematica implementation in develop/mtmk15forVer13/ was corrected in step and agrees with R to full double precision (-3651.903821773122 against -3651.9038217731227); the reference fixtures under tests/testthat/fixtures/mathematica_reference/ were regenerated from it.

• IRT() is substantially faster. The M-step objective is the hot spot of the whole fit (80% of self time). It evaluated the response function twice per call where once suffices and used ifelse() on scalars; optim() was also called without a gradient, so L-BFGS-B approximated one by finite differences at a cost of one extra objective evaluation per parameter per step. An analytic gradient is now supplied. IRT(J35S515, model = 2): 1.55s -> 0.34s at the new tolerance, faster than the 0.63s the old, looser tolerance took. Estimates are unchanged to 5e-6.

• Fixed Biclustering() on ordinal data (Biclustering.ordinal) under Ranklustering (method = "R"): the GTM neighbour-smoothing filter was computed (smoothed_memb <- clsmemb %*% Fil) but never used in estimation — the field E-step and the M-step both consumed the raw, unsmoothed class membership, so ordinal Ranklustering silently reduced to plain Biclustering plus a cosmetic class relabelling by mean score. Both steps now use the smoothed membership, matching Biclustering.binary and LRA.ordinal (for plain Biclustering the filter is the identity, so results there are unchanged). Fit improves slightly (e.g. RMSEA 0.0533 -> 0.0527, AIC 7288 -> 6720 on J35S500, ncls = 5, nfld = 5). No Mathematica reference exists for ordinal Biclustering, so the affected regression-snapshot fit indices in test-polytomous-biclustering.R were updated (R/16_Biclustering_ordinal.R).

• Fixed the GRM item information function grm_iif(). The previous implementation deviated from Samejima’s (1969) information in four ways: the denominator used the cumulative (boundary) probability instead of the category probability, the accumulator started at 1 instead of 0, the first category’s term was missing, and a 1.702 scaling constant was applied even though GRM() estimates its parameters on the pure logistic metric (no scaling constant). Together these inflated the reported information severalfold (e.g. 1.93 vs the correct 0.70 at theta = 0 for a = 1.5, b = c(-1, -0.5, 0.5, 1)). The function now computes I(theta) = sum_k [P'_k(theta)]^2 / P_k(theta) on the same logistic metric as the estimation, verified against numerical differentiation and consistent with the posterior standard deviations (1/PSD^2 ~ TIF + 1). Affects plot(x, type = "IIF") and plot(x, type = "TIF") for GRM objects, and downstream ggExametrika.

• Fixed the ability estimates of GRM() (EAP, MAP, PSD). The posterior over the quadrature grid was built as the sum of the item category probabilities (W %*% L_weighted) instead of their product, which is not a valid likelihood. Rank order was nearly preserved (r > 0.99 with the correct estimates on J5S1000), but the scale was strongly shrunken (EAP sd 0.29 vs the correct 0.79) and PSD did not correspond to the test information. The posterior is now accumulated in log space with a log-sum-exp normalization, and missing responses are skipped explicitly (previously they were skipped only by an R indexing accident: v[NA] <- 1 silently does nothing). ItemFitIndices/TestFitIndices change accordingly, since the analysis-model log-likelihood is evaluated at each examinee’s EAP.

• GRM plots (type = "IRF") no longer produce NA colors for items with more than 8 response categories; the default palette is now recycled.

Performance

• The BNM/LDLRA structure-search functions (BNM_GA(), BNM_PBIL(), LDLRA_PBIL()) no longer rebuild the full model output per candidate. Fitness evaluation now goes through BIC-only internal kernels (BNM_fit_BIC() for BNM, LD_param_est(fit_only = TRUE) for LDLRA) that skip the output-table construction, the igraph round-trips and DAG checks (GA/PBIL candidates live on the upper triangle, so they are always simple DAGs), and the per-candidate benchmark-model recomputation inside TestFit() — the benchmark statistics depend only on the data and are now computed once per run (BNM_bench_stats()). Results are unchanged and agree with the previous implementation exactly (identical(), same seeds: BNM_GA all three crossover types, BNM_PBIL estimate 1/4, LDLRA_PBIL). Measured: BNM_PBIL(J35S515, population = 20, maxGeneration = 15) 14.8s -> 0.7s (~22x); LDLRA_PBIL(J15S500, ncls = 3, population = 20, maxGeneration = 20) 3.8s -> 1.1s (a further ~3.5x on top of the earlier PIRP vectorisation, ~14x cumulative from the original 15.3s).

• BNM()’s parent-response pattern (PIRP) counting is vectorised: the per-(subject, item) binary encoding and the subject x item x pattern one-hot array are replaced by one matrix product and one rowsum() per item (shared helper BNM_pirp_counts(), also used by the fitness kernel). fill_adj()’s element-wise double loop is replaced by a single indexed assignment. Same numbers, no S x J loop, and much less memory on large samples. Profiling after the change shows no remaining hot spot in the GA/PBIL path (the largest self-time item is rowsum()’s internal bookkeeping at ~16%), so C++ is not warranted here; the package-level next bottleneck remains the emclus() E-step.

• BNM_GA(crossover = 2) no longer rebuilds the two-point crossover candidate cut-point matrix (combn(gene_length, 2) filtered) per child per generation; it is built once per run. RNG draw order is unchanged.

• LRA() on ordinal and rated data no longer fails on large tables. The monitored log-likelihood was accumulated as sum(rankProf * log(exp(ll))) – a round trip that is algebraically the identity but underflows on the way: once the test is large enough for the entries of ll to fall below about -700 (2000 respondents x 60 items x 5 categories is enough), exp() returns zero, log(0) is -Inf, and 0 * -Inf is NaN. The convergence check then received NA and the fit died with “missing value where TRUE/FALSE needed”. The sum is now taken on the log scale directly, which is the same quantity without the excursion through the exponent. Found while sizing a simulation study; it affects LRA.ordinal() and LRA.rated() under both isotonic and GTM.

  The corresponding line in each saturated-model loop adds a small constant inside the logarithm and is deliberately left alone: removing it moves the saturated log-likelihood substantially (where exp(ll) < const the old expression was pinned near log(const)), and the Mathematica reference values were produced with that behaviour in place. Changing it is a separate, breaking decision.

• The order-restricted M-step for ordinal data is now implemented in C++ (src/isotonic_core.cpp). LRA.ordinal(method = "isotonic") and Biclustering.ordinal(estimation = "isotonic") call it through the same internal iso_dual_map() entry point. It exploits the fact that raising one dual multiplier theta[c, q] can only change ranks c and c+1, so a trial value rebuilds two rows rather than the whole table.

  Both root finds use the residual’s value rather than only its sign: Newton’s method for the multiplier that normalises a rank, and the Illinois method for the dual variable. The pure-R iso_dual_map_ref() does the same and the two are checked against each other to a tolerance – not to the bit, which a value-driven search cannot promise: a difference in the last bits moves the next trial point and the two paths then differ on their way to the same root.

  For the multiplier, the parameterisation matters more than the root finder. Categories with a zero count are dropped first: their probability is zero whatever the multiplier is, but if one of them attains the smallest offset it drags the lower end of the domain far away from the root. On the shifted variable u = lambda + min(d) the bracket then follows in closed form, sum_{d'=0} m <= u <= sum m, and the search runs on log u, because those two ends can sit thirteen orders of magnitude apart on a rank holding almost no weight – far enough that bisection does not converge within any sane iteration cap and a Newton step from the upper end lands past zero. The probabilities are formed from u + d' rather than lambda + d, which would cancel the shift back out and lose digits when min(d) is large.

  The Illinois search judges its bracket width relatively. On the same low-weight ranks an endpoint can reach 1e8, where the spacing between representable doubles (~3e-8) is coarser than an absolute 1e-12 threshold: the interval stops shrinking, every interpolated point rounds onto an endpoint, and the loop has no way to exit.

  Each sweep also starts its bracket from the value the previous sweep found, which is close to the answer from the second sweep on; the check of whether the constraint binds at zero is kept, being complementary slackness itself.

  The sweeps stop on both halves of the KKT picture, not on the log-likelihood alone. Near the optimum the likelihood moves quadratically while the order violation is still shrinking geometrically, so the likelihood goes quiet several sweeps before the restriction is actually met: on real tables it was stopping with the returned probabilities breaching the stochastic order by around 1e-3. Convergence now also requires the largest violation to fall below viol_tol (1e-6), and the sweep cap rises to 1000 because the number of sweeps grows with the table – 6 ranks need about 100, 20 ranks about 500. Across 60 tables from real EM runs the worst violation drops from 3.2e-3 to 9.9e-7 for a 1.2x cost, and Biclustering(J35S500, ncls = 6, nfld = 5, method = "R", estimation = "isotonic") is unchanged at 2.7s.

  Measured on the dual solver alone: 111x (3 ranks x 3 categories), 289x (12 x 7), 509x (20 x 6; 274s -> 0.54s), and a further 6.8x from the two root finds and the warm start, on tables taken from a real EM run. At the model level, where the remaining EM machinery is still R, Biclustering(J35S500, ncls = 6, nfld = 5, method = "R", estimation = "isotonic") drops from 265s to 11s.

  The multiplier exists to make each rank’s probabilities sum to one, so the row sums measure how well it is found. Across 60 expected-count tables captured from real EM runs the largest row-sum error is 9.6e-15, and every table converges. For binary data the solution must coincide with weighted PAVA, and it does.

  This matters because the ordinal isotonic path was the slowest thing in the package and effectively ruled out large simulation studies. The pure-R implementation is kept as iso_dual_map_ref() (internal, unexported) purely so the test suite can check the two against each other and so the algorithm stays readable.

Internal (no user-visible behavior change)

• Restructured the test suite around a two-tier policy: CRAN runs tiny Mathematica-verified fixtures plus a smoke test per user-facing function, while full-size reference comparisons, reproducibility runs and heavy regressions carry skip_on_cran() and run on every push in CI (GitHub Actions, three platforms, NOT_CRAN=true pinned) and locally. The CRAN-side suite now takes ~17 s sequentially on an M-series laptop (was 38 s), with no test file above 1.5 s, keeping the Windows check comfortably inside CRAN’s 10-minute limit. Enabled Config/testthat/parallel: true. No user-facing behaviour changes.

• Renamed the internal helper iso_surv() in R/00_isotonic_CORE.R to iso_upper_cum(). It computes the upper-cumulative (boundary) probabilities S_cb = P(>= category b+1); the old name suggested a survival function, which is not the concept being used here.

Improvements

• New: M2(), the limited-information goodness-of-fit statistic of Maydeu-Olivares & Joe (2005, 2006), for LCA.nominal and LCA.rated. It tests whether the model reproduces the item-pair cross tables. The reference point is the saturated model of the first- and second-order margins rather than of the full response-pattern table, so no benchmark log-likelihood is needed — which is exactly what nominal data lacks. The analogy that usually lands: an SEM chi-square does not test the whole multivariate distribution, only whether the model reproduces the covariance matrix; M2() is the categorical counterpart, with cross tables in place of the covariance matrix.

  Two things worth knowing. The degrees of freedom are m - rank(Delta), not m - n_param: with the class proportions fixed at 1/C, the second-order margins see the class deviations only through their Gram matrix, which is invariant to rotations of the class space, so the Jacobian loses (ncls - 1)(ncls - 2) / 2 of its rank and the parameters are not identified from bivariate margins once ncls >= 3 (the margins themselves still are, so the statistic is well defined). And the statistic is only interpretable for a maximum likelihood fit — not for filter-based (GTM) estimation, which is a regularisation rather than an MLE, nor for order-restricted estimation, whose limiting distribution is a mixture of chi-squares.

  Cost is dominated by the Cholesky factorisation of a dense m x m matrix: 20 items with 5 categories is m = 3120 and well under a second; 50 items is m = 19800, 2.9 GB and around 20 seconds.

  LCA.nominal() and LCA.rated() now keep Q and Z in the returned object, as Biclustering() already did, so M2() can be computed after the fact.

• New: add_M2() and a second set of fit indices. fit <- add_M2(fit) computes M2 for the model and for the independence baseline and attaches TestFitIndicesM2: NFI, RFI, IFI, TLI, CFI and RMSEA built entirely from margin-based chi-squares. print() then shows the response-pattern indices and the margin-based ones as two labelled blocks, and takes fit_indices = "both" | "pattern" | "margin" to show one alone.

  They are kept apart on purpose. The response-pattern chi-square is a likelihood ratio against the saturated model; M2 is a quadratic form in margin residuals. Combining one with the other inside a single index — a ratio of a pattern chi-square to a margin chi-square, say — has no defensible reading (Shojima, personal communication, 2026-07-26). Within the margin block both the model and the baseline statistic are M2, so the indices are internally consistent.

  For the same reason the margin block carries no AIC/BIC/CAIC. Those need a log-likelihood: chi_sq - 2 df works on the pattern side only because that chi-square is a likelihood ratio, and M2 is not. The likelihood-based information criteria these models already report are the ones to use.

  This is a separate call rather than part of the fit because the cost grows with the square of the item count; for nominal data it is also the only route to an absolute fit statistic at all, since no saturated model can be formed.

• M2() also accepts fits from LRA() on ordinal data and from Biclustering() on ordinal or nominal data, so the three ways of treating the same polytomous data — order-restricted, filter-smoothed, unordered — can be put on one scale. Biclustering shares one category profile across the items of a field, so its Jacobian columns are shared too, and its parameter count is fields x classes x (categories - 1) rather than items x classes x (categories

  • 1). The field partition is taken as given; its uncertainty is not propagated. Items must all have the same number of categories, since a shared profile would otherwise hand an item margins it can never produce (the check is explicit: without it the covariance matrix loses positive definiteness and the failure is unreadable).

  Only a maximum likelihood fit makes the reference distribution hold, so for filter-based (GTM) and order-restricted estimation the statistic is descriptive: recorded, not tested.

• add_M2() covers LRA() on ordinal data and Biclustering() on ordinal or nominal data as well, so any of them can carry both sets of fit indices. For ordinal data the response-pattern indices are complete — a saturated model exists — so two full sets stand side by side, which is precisely where keeping them apart matters.

  Where the reference distribution does not hold, the margin block says so, and names the reason that applies rather than issuing a generic warning: the field partition is taken as given (any biclustering), the order restriction can bind so the limit is a mixture of chi-squares (isotonic), filter smoothing is a regularisation rather than a maximum likelihood estimator (GTM). A nominal LCA gets no such line, being an honest maximum likelihood fit. The numbers are still worth reading as description; the p value is not a test.

• M2() and add_M2() take gc = TRUE, which releases the workspace before returning. The margin covariance and its factor are the largest objects the package allocates and R otherwise keeps the block. Interactive use wants this; a loop over many fits should pass FALSE, where the collection costs time and buys nothing. With verbose = TRUE and a large problem, add_M2() now says which of its two statistics it is working on.

• New: LCA() supports nominal data (LCA.nominal). The model is a finite mixture of product-multinomial distributions — one free category distribution per item within each latent class, with no ordering imposed on the classes or on the categories. Category counts may differ across items. Estimation runs through the shared EM engine emclus_nominal(); the new alpha argument sets a Dirichlet prior on the category profiles (default 1, i.e. the plain multinomial MLE). The returned object carries ICRP (Item Category Reference Profile: one row per item-category, one column per class), LCD, CMD and Students, and prints and plots (type = "ICRP", "LCD", "CMP"). The "ICRP" plot uses grouped bars rather than lines across classes, because neither axis is ordered.

  As in Biclustering.nominal, no benchmark (saturated) model is fitted — with many items and categories nearly every response pattern is unique — so only AIC, BIC and CAIC are reported and the chi-square based indices are NA. Note that these follow the -2 log L + k convention, unlike the chi-square based AIC/BIC/CAIC on the binary path; they are not comparable across response types. Class sizes are not free parameters in this formulation (every class carries the same implicit prior, as in emclus() for binary data), so the parameter count is ncls * sum(ncat - 1).

• New: LCA() supports rated data (LCA.rated), i.e. multiple-choice items with an answer key. Estimation is the nominal one — LCA.nominal() is called internally — and the key is then used to recover the quantities that need a correct answer: IRP[j, c] is the model-implied probability of the keyed category rho[j, CA[j] | c], and TRP is its weighted item sum. Fit is reported in two layers: TestFitIndices from correct/incorrect responses (chi-square based, comparable with binary LCA) and TestFitIndicesNominal from the internal nominal fit (AIC/BIC/CAIC). Full category probabilities remain in ICRP for distractor analysis. Unlike Biclustering.rated, the classes are not sorted by correct response rate: latent classes carry no order, and sorting them would imply one.

• Ordered rating data passed to LCA() is now analysed with the nominal model after a message, instead of stopping: latent classes carry no order, so the category ordering has nothing to attach to. Use LRA() when the ordering should be respected. Symmetrically, nominal data passed to LRA() is handed to LCA.nominal() with a message (a rank ordering is not defined without ordered categories); an nrank argument is carried over as ncls.

• LCA() is now an S3 generic dispatching on response type, matching LRA() and Biclustering(). The former function body is unchanged and now lives in LCA.binary(); LCA.default() formats raw input with dataFormat() and routes it. Binary results are bit-identical to 1.15.0 and non-binary input still raises the same error. This is the wiring for the forthcoming LCA.nominal().

• Biclustering() on binary data (Biclustering.binary) gains an order-restricted estimation of the Field Reference Profiles under Ranklustering (method = "R"), selected by the new estimation argument: "isotonic" (now the default) or "GTM" (the original filter-based smoothing of Shojima 2012). Under "isotonic" the rank ordering — each field’s reference profile monotone non-decreasing across ranks — is imposed directly in the M-step by a weighted PAVA along the class axis (weights are the per-cell expected counts), reusing pava_up() from R/00_isotonic_CORE.R; for the default flat prior this is the exact order-restricted MLE (Ayer et al. 1955), and the crude mic sort is skipped as unnecessary. On typical data it attains a higher likelihood than GTM (e.g. -6941 vs -7273 on J35S515, ncls = 6, nfld = 5). The shape-restricted degrees of freedom (total PAVA block count across fields) feed the fit indices. estimation is ignored for plain Biclustering (method = "B"), whose classes are unordered (R/07_Biclustering.R).

• Biclustering() on ordinal data (Biclustering.ordinal) gains the same estimation argument for Ranklustering (method = "R"): "isotonic" (now the default) or "GTM". Under "isotonic" the rank ordering is imposed as a genuine stochastic-order restriction — each field’s upper-cumulative (boundary) probabilities are monotone non-decreasing across ranks at every category threshold — solved per field in the M-step by the Fenchel-dual algorithm (El Barmi & Dykstra 1994) via iso_dual_map() in R/00_isotonic_CORE.R, replacing the independent per-cell boundary MLE and the crude mic class relabelling. Unlike the binary case, isotonic does not maximise the likelihood relative to GTM: the (now filter-smoothed) GTM path leaves the field profiles unconstrained and so fits better by violating the order (e.g. only 1 of 5 fields is monotone on J35S500), whereas isotonic enforces the order in every field at a modest likelihood cost — this is the intended trade and the point of the method. Shape-restricted df = distinct free boundary levels per field. estimation is ignored for plain Biclustering (method = "B") (R/16_Biclustering_ordinal.R).

• LRA() on binary data (LRA.binary) gains an order-restricted estimation method, method = "isotonic", which is now the default (previously "GTM"). Rather than the GTM filter, the rank ordering — item reference profiles monotone non-decreasing across ranks — is imposed directly in the M-step by a weighted PAVA down each item column; for the default flat prior (beta1 = beta2 = 1) this is the exact order-restricted MLE (Ayer et al. 1955). On typical data it attains a higher likelihood than GTM/SOM. The shape-restricted degrees of freedom (per-item PAVA block count) feed the item/test fit indices. method = "GTM" and method = "SOM" are unchanged and still selectable. New shared internal core R/00_isotonic_CORE.R (pava_up(), emclus_isotonic()); ItemFit() now accepts a per-item nparam vector in addition to a scalar.

• LRA() on ordinal data (LRA.ordinal) gains an order-restricted estimation method, method = "isotonic", now the default (previously the GTM filter). The stochastic-order restriction (item category boundaries monotone across ranks) is solved exactly in the M-step by the Fenchel-dual algorithm (El Barmi & Dykstra 1994) in R/00_isotonic_CORE.R, rather than by filter smoothing; a alpha argument sets the Dirichlet concentration (the polytomous analogue of binary beta1/beta2, default 1 = ML). It attains a higher likelihood than GTM on typical data, handles mixed category counts per item, and reports a shape-restricted degrees of freedom (distinct boundary levels per item). method = "GTM" is unchanged and still selectable.

• LRA() on ordinal data (LRA.ordinal) now supports items with differing numbers of response categories. Previously the ordinal method assumed every item had the same number of categories and raised an error otherwise (directing users to Biclustering.ordinal), because its saturation/restricted reference matrices were laid out on a fixed nitems * max(ncat) stride. The reference matrices, the one-hot design (uuMat), and the null-model term now use a ragged sum(ncat) layout addressed through the design1 index map, so mixed category counts are handled directly. On uniform-category data the results are numerically identical to before. ICBR/ICRP now carry one row per (item, category) pair, so their row counts vary by item under mixed categories (R/12_LRA_ordinal.R).

exametrika 1.15.0

Improvements

• dataFormat()’s id argument, and longdataFormat()’s Sid/Qid/Resp/w arguments, now accept a column name (character string) in addition to a column number. Previously only numeric column indices were accepted; dataFormat() even raised an explicit error when a character value was passed. Column names can now be supplied directly, e.g. dataFormat(data, id = "StudentID") or longdataFormat(data, Sid = "Sid", Qid = "Qid", Resp = "Resp"). Specifying an unknown or ambiguous (duplicated) column name now raises a clear error listing the available columns (R/01_dataFormat.R).

API consistency changes

An API audit across all exported model functions surfaced a number of gratuitous inconsistencies in argument names, argument order, and defaults. They are unified in this release; the changes below alter default behavior or (rarely) positional-argument calls, so please review if you relied on the old defaults.

• The verbose argument now defaults to FALSE in every function that has one. Previously IRT(), GRM(), LCA(), GridSearch(), all Biclustering() methods, all Biclustering_IRM() methods, BNM_GA(), and BNM_PBIL() defaulted to TRUE while LRA(), LDLRA(), LDB(), BINET(), LDLRA_PBIL(), Glasso(), and chatterjee_matrix() defaulted to FALSE. Estimation results are unaffected; pass verbose = TRUE to restore progress messages. Several roxygen pages that claimed “default is TRUE” for functions whose default was already FALSE were corrected as well.

• Biclustering_IRM()’s iteration-limit argument is renamed from max_iter to maxiter, matching Biclustering(), LCA(), LRA(), and the rest of the package. Because the IRM methods accept ..., a maxiter = argument passed under the old assumption was silently swallowed with no effect — an easy trap when switching between Biclustering() and Biclustering_IRM(). The old name is still honored (with a deprecation warning) and will be removed in v2.0.0.

• Biclustering_IRM() for ordinal data now defaults to mic = FALSE and EM_limit = 20, matching LRA()/Biclustering() (ordinal) and the other Biclustering_IRM() methods respectively. It previously defaulted to mic = TRUE and EM_limit = 100 with no documented rationale. Pass mic = TRUE explicitly if you want monotonically increasing Field Reference Profiles.

• BNM(), LDLRA(), LDB(), BINET(), BNM_GA(), BNM_PBIL(), LDLRA_PBIL(), and Biclustering_IRM() (binary) now declare their missing-data arguments in the order na, Z, w — the order used by CTT(), IRT(), GRM(), LCA(), LRA(), and Biclustering() — where they previously used Z, w, na. Only calls that passed these three arguments positionally are affected; named usage (Z = ...) is unchanged.

• Biclustering() for rated data now exposes conf_class in its signature and documentation. It was already forwarded to the internal nominal engine via ..., but never appeared on the help page. Also documented that the rated method defaults to method = "R" (Ranklustering, classes sorted by correct response rate) while binary/ordinal default to method = "B".

• LDLRA()’s beta1/beta2 defaults remain 2 (the other network models use 1); the help page now notes this follows the original Mathematica implementation of LDLRA rather than being an accident.

Bug fixes

• longdataFormat() falsely reported “Duplicated IDs found” whenever a student answered more than one item. The duplicate check ran on the raw student-ID column, which is expected to repeat once per item in long format; it now checks for duplicated (student, item) pairs instead, so ordinary long-format data (one row per student-item response) no longer triggers a spurious error. A genuine duplicate — the same student answering the same item twice — is still caught (R/01_dataFormat.R).

• IRT(), Biclustering(), BNM(), LDLRA(), LDB(), and BINET() silently treated missing responses as incorrect when computing item-total correlation or correct response rate (crr()). In each case, a response matrix that had already been stripped of its exametrika class (with missing values recoded to 0 via tmp$U * tmp$Z) was passed to ItemTotalCorr(), ItemThreshold(), or crr(). Those functions re-run dataFormat() internally when given an unclassed matrix, but without the original missing -value mask, so missing responses were counted as incorrect answers. This affected IRT()’s initial parameter values (rho/tau, which only seed the EM algorithm — final estimates were unaffected), Biclustering()’s FieldAnalysis$CRR column, and the $crr field returned by BNM(), LDLRA(), LDB(), and BINET() (including their BNM_GA()/BNM_PBIL()/ LDLRA_PBIL() wrappers). Fixed by passing the already-formatted object through instead of the stripped matrix (R/04C_ParameterEstimation.R, R/07_Biclustering.R, R/08A_BNM.R, R/09_LDLRA.R, R/10_LDB.R, R/11_BINET.R).

• CTT(), BNM(), LDLRA(), LDB(), and BINET() crashed when passed raw (unformatted) matrix/data.frame input instead of a pre-built exametrika object, even though this is documented as supported. The response-type check in each function read U$response.type from the raw input argument instead of from the dataFormat()-formatted object, which is NULL for raw input and made the check error out before model fitting ever started. CTT() had a more severe variant of the same bug: its inherits(U, "exametrika") branch was inverted, so raw input skipped dataFormat() entirely and crashed immediately. Fixed to consistently check the formatted object (R/03_CTT.R, R/08A_BNM.R, R/09_LDLRA.R, R/10_LDB.R, R/11_BINET.R).

• BINET() could crash with a cryptic 'dimnames' length error (via NaN values silently produced by log()) on data with missing responses. Two compounding issues were found. First, Ccj (the per-class correct-response count used throughout the RISP estimation) was computed as t(clsmemb) %*% tmp$U, which does not mask out missing cells (encoded as -1 in tmp$U) the way the corresponding incorrect-response count Fcj already did (t(clsmemb) %*% (tmp$Z * (1 - tmp$U))); missing responses therefore contributed -1 to the correct-response count instead of 0, corrupting the conditional correct-response-rate estimates. Second, the smoothing constant that keeps those conditional rates away from 0/0 when a class-by-field cell has no non-missing observations was hardcoded to gamp <- 1 (a flat Beta(1,1) prior, under which 0/0 is undefined) with no way for the caller to change it, unlike the equivalent beta1/beta2 arguments already exposed by BNM(), LDLRA(), and LDB(). Fixed the Ccj computation to mask missing cells via tmp$Z, added beta1 = 1 / beta2 = 1 arguments to BINET() so the prior can be strengthened when needed, and replaced the eventual downstream crash with an immediate, actionable error when a class-by-field cell is still undefined under the requested smoothing (R/11_BINET.R).

• 0-indexed or non-contiguous polytomous category codes were silently dropped in Biclustering()/Biclustering_IRM() for nominal and ordinal data, with no error or warning. Biclustering.nominal(), Biclustering.ordinal(), Biclustering_IRM.nominal(), and Biclustering_IRM.ordinal() (and, via delegation, the rated/rated_IRM variants) built a one-hot response array by indexing directly with each item’s raw category code; a raw code of 0 is a no-op under R’s array-indexing rules, so every response in category 0 vanished from the likelihood and classification with no diagnostic. On the package’s own J15S3810 sample data (categories coded 0..3), this silently discarded 3,854 observed responses. GRM() already remapped each item’s categories to contiguous 1-based indices to avoid exactly this; that remap is now shared (remap_category_codes(), R/00_BiclucterUtils.R) and applied in all four functions.

• Biclustering_IRM.nominal()/Biclustering_IRM.ordinal() corrupted results whenever the data had missing responses. The one-hot response array was built by writing directly at Uq[s, j, tmp$Q[s, j]] <- 1 without checking for missing cells; a missing cell’s -1 sentinel, used as a raw array index, sets every category except the first to 1 under R’s negative-indexing rules instead of leaving the cell at 0. This fed through into the Gibbs sampler’s small-class-adjustment step and the final class/field assignments. With 8% missing data injected into J20S600, 7% of final class assignments differed from the correct (missing-masked) result. Fixed by building the one-hot array with the same missing-value-masked construction already used in the binary/nominal/ ordinal Biclustering() path.

• LDB() crashed with “object ‘conf_mat’ not found” when conf was passed as a matrix or data.frame (only the vector form of conf worked). This is the same class of bug already fixed in Biclustering.ordinal()/ Biclustering.nominal() on 2026-04-27, which LDB() was missed by at the time (R/10_LDB.R).

• LDB()’s beta1/beta2 smoothing arguments had their roles swapped relative to BNM()/LDLRA()/BINET(). All four functions compute a posterior-mode correct-response rate of the form (count + α - 1) / (N + α + β - 2) under a Beta(α, β) prior; BNM(), LD_param_est() (used by LDLRA()), and BINET() consistently use beta1 as α (the “success” pseudo-count, matching the count in the numerator), but LDB() used beta2. At the package default beta1 = beta2 = 1 this made no numerical difference, but a caller following BINET()’s own advice to set an asymmetric prior (e.g. beta1 = 2, beta2 = 2 to avoid a degenerate 0/0 cell) would see the opposite effect in LDB() versus its sibling functions. Traced to the original Mathematica Chapter 10 module (develop/mtmk15forVer13/mod/Module_LDB.nb), which uses beta2 here — this is not an R porting bug but an inconsistency inherited from the reference implementation. Changed LDB() to use beta1, matching the mathematically conventional Beta(α, β) parameterization and the rest of the package (R/10_LDB.R).

• LDLRA(..., method = "C") (local dependence latent Class model) mislabeled its output as the Rank model. A hardcoded model <- 2 right before building the output tables silently overrode the model value that had correctly been set from method earlier in the function, so result$model, result$msg, and the “Rank”/“Class” column headers in Estimation_table/CCRR_table always read “Rank” regardless of the requested method. Numerical estimates were unaffected — only the labeling (R/09_LDLRA.R).

• BNM()’s and BINET()’s graph-validity checks (acyclicFLG, connectedFLG) never actually detected cycles or disconnection. Both used adj^i in a loop intending to count length-i walks, but ^ on a matrix in R is elementwise, not matrix power, so the loop only ever re-tested self-loops and “any edge present.” BINET()’s stop("Your graph is not a DAG") guard was consequently a no-op for any real cycle of length ≥ 2, and BNM() silently fit cyclic “Bayesian networks” with no warning. (BINET()’s connectedFLG was further computing off the student response matrix, not a graph object, so it could not have tested connectivity at all.) Replaced both with igraph::is_dag() / igraph::is_connected(mode = "weak") on the actual adjacency matrix being validated (R/08A_BNM.R, R/11_BINET.R).

• Biclustering_IRM.binary()’s small-class-reduction loop tracked bestclass/class, which resolve to base R’s class() function rather than any local variable, so the intended “roll back to the best-BIC class assignment” step silently did nothing. In practice this had no effect on the final returned model (the class/field assignments are recomputed from scratch after the loop regardless), but the code read as doing something it did not; fixed to track the actual cls vector (R/07_IRM.R).

• CCRR() returned JCRR()’s result when called on non-exametrika input — a copy-paste bug in CCRR.default()’s fallback branch called JCRR(U) instead of recursing into CCRR(U) (R/02_TestItemFunctions.R).

• MutualInformation()’s base argument was ignored for binary data; MutualInformation.binary() always computed log base 2 regardless of the requested base, unlike the ordinal/nominal/rated path which already respected it (R/02_TestItemFunctions.R).

• JSR() and CSR() crashed instead of falling back cleanly when given binary data. Both message “using X instead” and call the binary equivalent, but never return()ed its result, so execution fell through into polytomous-only code (NCOL(U$Q), U$Z == 0 on nonexistent U$Q) and crashed (R/02_TestItemFunctions.R).

• ItemTotalCorr.ordinal() did not mask missing responses before summing total scores. total <- rowSums(U$Q) included the -1 missing sentinel directly in the sum, so any student with even one missing item got a wrong total score, corrupting their item-total correlation with every item, not just the missing one. Fixed to mask by Z before summing, matching ItemThreshold.ordinal()’s existing pattern (R/02_TestItemFunctions.R).

• ITBiserial(), ScoreReport(), and ItemReport() crashed when passed raw (unformatted) data — each called dataFormat() but stored the result in a variable that was never used, leaving the original unformatted argument in place for the subsequent $response.type check and computation (R/02_TestItemFunctions.R, R/02_QitemFunctions.R).

• dataFormat() silently skipped value validation for ordinal/rated/ nominal data. The branch was guarded by response.type == "polytgomous" (a typo — no response.type value is ever literally "polytomous", since the actual values are "ordinal"/ "rated"/"nominal"), so the “must be non-negative integers” check never ran for any polytomous type. Fixed to check response.type %in% c("ordinal", "rated") (deliberately excluding "nominal", whose category codes are arbitrary labels rather than ordered counts and may legitimately be negative) (R/01_dataFormat.R).

• longdataFormat() misaligned ID/response-matrix rows whenever numeric student or item IDs were not an exact 1..N sequence (e.g. student IDs 10, 20, 30). Numeric IDs were used directly as row/column indices instead of being remapped to a dense index, so nrow(result$U) could be far larger than the actual number of students, with most rows entirely empty. Both Sid/Qid are now always remapped through as.factor() to a dense, correctly-ordered 1-based index, regardless of whether the raw IDs are numeric or character (R/01_dataFormat.R).

• longdataFormat()’s w (item weight) argument was misused as a row index. w_vec[unique(Qid_num)] indexed the long-format weight column by item-ID values rather than by the row where each item first appears, so weights were essentially always wrong unless item IDs happened to be an exact 1..N sequence starting from the first item column. Fixed to look up each item’s weight via its first occurrence in the long-format data (R/01_dataFormat.R).

• print(GridSearch(...)) always crashed. print.exametrika()’s internal switch() had no case for the "GridSearch" class, and a trailing comma after the last real case created an empty unnamed fallback branch that errors when evaluated. GridSearch() is a top-level function whose result is auto-printed at the console in normal interactive use, so this reliably crashed on first use. Added a proper GridSearch print case summarizing the fit-index grid and optimal setting (R/00_exametrikaPrint.R).

• plot(x) without an explicit type argument crashed with a confusing "the condition has length > 1" error instead of the intended "The 'type' argument must be specified." message. The missing(type) check ran after type had already been evaluated (forcing its multi-element default) for an unrelated uses_layout computation, so by the time missing() was checked, type was no longer missing in the technical sense needed for the check to matter — and the multi-element default itself broke the preceding if first. Reordered so the missing(type) check runs first (R/00_exametrikaPlot.R).

• plot(grm_result, type = "ICC") failed even though the identical call works for IRT models. GRM’s plot-type alias handling for "ICC" was implemented but never reachable, because valid_types$GRM in the upstream validation list omitted "ICC" (only "IIC"/"TIC" were listed). Added "ICC" to valid_types$GRM (R/00_exametrikaPlot.R).

• print(bnm_result, digits = ...)/print(ldlra_result, digits = ...) ignored the requested digits for the “Conditional Correct Response Rate” table. A typo (x$CCRR_tabje instead of x$CCRR_table, in two places) wrote the formatted string into a nonexistent list field instead of the one actually printed immediately afterward. Also propagated the existing digits argument to two related tables (IRPIndex/FRPIndex in the LDLRA/LDB print sections) that were missing it while equivalent tables elsewhere already had it (R/00_exametrikaPrint.R).

• print(InterItemAnalysis(ordinal_data)) never displayed the Conditional Selection Ratio — it printed x$JSR (Joint Selection Ratio, already shown just above) a second time instead of x$CSR (R/00_exametrikaPrint.R).

• GridSearch() could report the wrong optimal (ncls, nfld) when multiple grid cells tied for the best fit index. which(ret == ..., arr.ind = TRUE) returns one row per tied match; optimal_idx[1]/ optimal_idx[2] read the matrix’s column-major-flattened first two values instead of the first tie’s row/col pair, so with ≥ 2 ties the reported optimum could combine the row of one tie with the column of another — a combination that was not actually the best (or even necessarily tied). Fixed to read optimal_idx[1, "row"]/ optimal_idx[1, "col"] (R/00_GridSearch.R).

• GridSearch(..., max_ncls = 1) silently tested ncls = 2 anyway. 2:max_ncls is R’s descending-sequence trap: with max_ncls = 1 it evaluates to c(2, 1) rather than an empty range, so a value the caller explicitly excluded was tested regardless. Added an explicit max_ncls/max_nfld < 2 guard that stops with a clear message instead (R/00_GridSearch.R).

• Glasso()’s edge_tol argument was documented as controlling edge detection but did not affect model selection. The EBIC computation used internally to choose lambda_opt had its own hardcoded 1e-6 edge-count threshold, so changing edge_tol only affected the reported n_edge, not which lambda was actually selected. Threaded edge_tol through to compute_EBIC_glasso() so it consistently governs both (R/22_GlassoUnit.R).

• dataFormat() could silently miss items with no real variance whenever the item also had missing responses, letting them through into IRT(), which then crashed with the uninformative “object ‘result’ not found” (the EM optimizer’s initial parameter, seeded from an item-total correlation of NaN, made every retry of optim() fail). The existing zero-variance check computed sd() on the raw response column, which still contains the -1 missing-value sentinel; an item that only a handful of students answered, all identically, therefore looked non-constant (-1 mixed with the real value) even though it truly had zero variance among actual respondents. sd.check is now computed on each item’s valid (Z == 1) responses only. Additionally, items with no variance among valid responses are now excluded from the data (with a message identifying them) instead of merely warned about and left in, matching the original Mathematica dataformat[], which drops such items before any analysis; an item with CA specified (rated data) has its CA entry dropped along with it so the two stay aligned. All-missing items (no valid responses at all) are unaffected and continue to be kept with a separate warning (R/01_dataFormat.R).

• DistractorAnalysis() counted raw category codes against columns 1..maxQ of its frequency tables. For rated data coded from 0 (or with gaps in the codes), every category-0 response silently vanished from the frequency/proportion tables and the remaining categories were shifted by one column — inconsistent with the fitted model itself, whose category probabilities are computed on codes remapped to 1..K per item since the category-code fix earlier in this release. The stored Q and correct answers are now remapped the same way before tabulation (R/21_DistractorAnalysis.R).

• A conf given as a data.frame was wrongly rejected (“The conf matrix should only contain 0s and 1s”) by Biclustering() and LDB(), because the 0/1 validation ran before coercion and %in% compares whole columns on a data.frame. The input is now coerced with as.matrix() first (R/07_Biclustering.R).

• GridSearch()’s help-page example called a nonexistent function grid_serch(data_matrix, ...); it now calls GridSearch(J35S515, ...) (R/00_GridSearch.R).

• LDLRA() now stops with an informative error when a rank-by-parent-pattern cell has no (smoothed) observations under beta1 = beta2 = 1 (0/0), instead of silently propagating NaN through the log-likelihood, matching the diagnostic added to BINET() earlier in this release (R/09_LDLRA.R).

• LRA() for rated data has a minFreqRatio argument that is documented to pool response categories rarer than nobs * minFreqRatio into a single bucket, but the feature was doubly broken: the collapse test compared each category’s frequency against the correct-answer code (catfreq != CA, almost always true), so no category was ever pooled; and had it fired, the report assembly indexed the full category-label set and would have stopped on a length mismatch. The condition now reads “keep a category if it is frequent enough or it is the correct answer” (the correct answer must never be pooled), and the Item-Category Reference Profile labels the pooled bucket “CatX”, using only the labels of the categories actually estimated. The default minFreqRatio = 0 keeps every category and is unaffected (R/13_LRA_rated.R).

• Fixed user-visible typos in printed output: “Dimensionality Analyeis” → “Dimensionality Analysis”, “Cummurative Percentage” → “Cumulative Percentage”, and “Conditonal” → “Conditional” (in “Conditional Correct Response Ratio” and “Conditional Selection Ratio” headings) (R/00_print_ctt_irt.R).

Removed

• Removed LLtheta_mat()/EAP_PSD() (R/04B_AbilityEstimation.R) and the corresponding dead print.exametrika() "IRT_EAP_PSD" case. Neither function was exported or called anywhere in the package; IRT() computes ability EAP/PSD inline instead. Also removed a handful of other now-dead assignments left over from the same tmp$U * tmp$Z class-stripping pattern fixed above, and one duplicated-then-discarded array/loop in LDLRA()’s internal LD_param_est(), none of which were ever read after being written (R/06_LRA.R, R/08C_BNM_GA.R, R/09B_LDLRA_GA.R, R/09_LDLRA.R, R/11_BINET.R).

Internal (no user-visible behavior change)

Follow-up cleanup after the audit above, consolidating logic that had drifted out of sync across near-identical call sites (the same root cause behind several of the bugs fixed above):

• Progress messages in R/00_EMclus.R, R/04C_ParameterEstimation.R, R/07_Biclustering.R, R/08C_BNM_GA.R, R/09B_LDLRA_GA.R, R/15_Biclustering_nominal.R, and R/16_Biclustering_ordinal.R used a carriage-return (\r) “overwrite in place” style, which reads as one long run-on line when logged to a file or captured non-interactively rather than the intended per-iteration progress. Switched to \n.
• Extracted beta_posterior_mode() (R/08A_BNM.R) for the (count + beta1 - 1) / (total + beta1 + beta2 - 2) formula duplicated across BNM(), LD_param_est() (used by LDLRA()), and BINET() — the same formula whose numerator/denominator role LDB() had swapped, above.
• Extracted build_conf_mat() (R/07_Biclustering.R) for the conf (vector/matrix/data.frame) parsing and validation duplicated across Biclustering(), Biclustering.nominal(), Biclustering.ordinal(), and LDB() — the same parsing whose missing as.matrix(conf) step caused the LDB() crash fixed above.
• Extracted stop_if_all_grid_failed(), report_failed_grid_settings(), and select_optimal_grid_index() (R/00_GridSearch.R) for the all-cells-failed check, failed-settings warning, and optimal-index selection duplicated between GridSearch()’s Biclustering (2-D) and LCA/LRA (1-D) branches — the same duplication in which both the tie-break bug and the max_ncls < 2 bug above were independently present.
• Added regression tests pinning the bug fixes of this release (tests/testthat/test-regression-1150.R) and smoke tests for AlphaCoefficient(), OmegaCoefficient(), and BiserialCorrelation(), which previously had no direct tests (tests/testthat/test-smoke-reliability.R).
• Renamed R/00_BiclucterUtils.R to R/00_BiclusterUtils.R (filename typo) and fixed a “Bicluter” comment typo; removed a stray .png file accidentally committed to the repository root in 2024, and broadened the .Rbuildignore rule for Rplots.pdf so a leftover tests/testthat/Rplots.pdf can no longer slip into the CRAN tarball.

exametrika 1.14.0

Improvements

• plot.exametrika() now forwards graphical parameters supplied via ... to every plot type (R Journal review request). Previously the ... argument documented on the plot.exametrika() help page was captured but never passed on: the internal dispatch functions (plot_irt_model(), plot_grm_model(), plot_common_profiles(), the polytomous Biclustering plotters, the array plot, and the network plotters) did not accept or propagate it, so standard graphical parameters were silently ignored. For example, plot(result.LRA, type = "IRP", items = 1:4, nc = 2, nr = 2, las = 2, pch = 16) changed neither the axis-label orientation (las) nor the plotting symbol (pch).

  User-supplied parameters are now forwarded consistently to the underlying base R plotting calls (plot, barplot, image, lines, curve) for all plot types, including manually drawn axes so that las, cex.axis, and similar parameters take effect on every axis. Standard parameters such as pch, las, cex, col, lty, and lwd work as expected, and user values take precedence over the package defaults, so xlab, ylab, main, etc. can be overridden. This is achieved without adding any dependency: the package remains lightweight and base-graphics only.

  Internally this is implemented via small helpers (merge_plot_dots(), call_plot(), draw_curve()) that merge the package defaults with the user’s ... (user wins) and dispatch through do.call(); the IRT/GRM curves are drawn by grid evaluation through draw_curve() instead of curve() so that the non-standard evaluation of curve()’s first argument does not block parameter forwarding.

Bug fixes

• IRT Test Information Function plot title typo. The type = "TIF" plot for IRT models had main = "Test Informaiton Function"; it now reads "Test Information Function" (R/00_plot_irt.R).

• User-facing message typos and missing-word fixes. Four cosmetic but user-visible string fixes following a family-wide audit (exametrika, ggExametrika, shinyExametrika) prompted by the Clusterd -> Clustered rename. No behaviour change; messages now read correctly.

  • R/04C_ParameterEstimation.R: IRT slope warning had a missing space after the period ("... exceeds 10.Please exercise caution ..." -> "... exceeds 10. Please exercise caution ...").
  • R/02_TestItemFunctions.R: CCRR.nominal() info message was missing the verb “Using” ("... binary data only. Conditional Selection Rate for your polytomous data instead." -> "... binary data only. Using Conditional Selection Rate for your polytomous data instead."), now matching the parallel messages in CCRR.ordinal/CCRR.rated/CCRR.binary.
  • R/09_LDLRA.R and R/10_LDB.R: max-parents warning had a comma where a period belongs ("... is N, Please check." -> "... is N. Please check.").

• plot.exametrika() Biclustering panel: typo “Clusterd” -> “Clustered”. Fixed a long-standing misspelling in the base-R Biclustering array plot (R/00_plot_biclustering.R): the panel title "Clusterd Data" is now "Clustered Data", the inline comment ## Clusterd Plot is corrected to ## Clustered Plot, and the internal variable clusterd_data is renamed to clustered_data. No user-facing API change. The downstream ggExametrika::plotArray_gg() had inherited and propagated the typo into its argument names (Clusterd, Clusterd_lines, Clusterd_lines_color); that is being corrected in ggExametrika 1.1.1 as a coordinated release.

• Binary IRM: crash on real data with missing values. Biclustering_IRM on a binary exametrika data object containing missing cells (tmp$Z[s, j] == 0) crashed with “確率ベクトル中にNAがあります” (NA in probability vector) inside rmultinom(), after log() produced NaN in the Gibbs sampler. The cause was that tmp$U retains the -1 missingness marker from dataFormat() and the IRM aggregated it directly (tmp$U %*% fld01), producing negative counts in CcfPlus whose log was NaN. The pre-existing line U <- tmp$U * tmp$Z was a dead variable. R/07_IRM.R now assigns the masked matrix back as tmp$U <- tmp$U * tmp$Z, so all downstream tmp$U references see zero in missing cells. Reproduced on HCI (651×20, 1.5% missing) and SAT12 (600×32 binarised, 0.4% missing).

• Graphical Lasso: graceful handling of numerical divergence. When the inner block coordinate descent (BCD) of Glasso() produced non-finite values — typically with high-dimensional, near-singular polychoric correlation matrices (N <= p regime) and very small lambdas — the previous implementation crashed in R’s if (diff < eps) test with “missing value where TRUE/FALSE needed”, discarding all of the intermediate work along the lambda grid.

  • glasso_one() now detects non-finite values in the BCD update of beta, in the inner convergence statistic diff, and in the working covariance W, and returns converged = FALSE instead of crashing.
  • Glasso() now reacts to converged = FALSE (or a non-finite EBIC) by emitting a warning() that names the offending lambda and the best lambda found so far, and breaks the lambda search, returning the best solution encountered up to that point. If divergence happens on the very first lambda the call still errors out, since no solution exists to return.
  • The path element of the result preserves NA for any lambda values skipped by the early break, making the breakpoint visible to the user.

  Observed concretely on a 98-item / 143-respondent ordinal dataset (polychoric condition number ~1.4e5): the old Glasso() crashed at lambda = 0.0096 after ~25 minutes of work; the new implementation returns the same lambda_opt = 0.1003 solution with a clear warning and a path whose two trailing entries are NA.

exametrika 1.13.1

Resubmission of the 1.13.0 release. The 1.13.0 submission was rejected by the CRAN auto-check service for a single Overall checktime NOTE on r-devel-windows-x86_64 (11 min vs. the 10 min limit). The package itself passed cleanly on both Windows and Debian (Status: OK / OK).

Test suite (no user-visible changes)

• The two heaviest test files now skip their slowest blocks on CRAN to keep R CMD check comfortably under the 10-minute Windows limit. The same tests continue to run locally and on R-hub / win-devel via the NOT_CRAN environment variable that testthat sets.
  • test-grm.R: the J15S3810 regression (a 15-item / 3,810-respondent fit, ~60s) and the nitems >= 8 underflow regression (~8s) are skipped on CRAN. Default-coverage GRM tests on small data continue to run on CRAN.
  • test-irm.R: the J35S515 shared-fixture Gibbs run (~23s) and the two reproducibility tests that re-run Gibbs (~22s combined) are skipped on CRAN. The Default seed is 123 structural check still runs on CRAN.

exametrika 1.13.0

This release also incorporates the development changes from 1.12.0–1.12.2 (never published to CRAN). Their entries are retained below for traceability.

New features

• Graphical Lasso (Glasso): New function for sparse precision matrix estimation from ordinal item response data. The polychoric correlation matrix is computed internally and the optimal regularization parameter is selected by Extended Bayesian Information Criterion (EBIC; Foygel and Drton 2010). Implements block coordinate descent (Friedman, Hastie, Tibshirani 2008; Algorithm 17.2 of Hastie, Tibshirani, Friedman 2009) with cyclical coordinate descent for the inner lasso step. Warm-starting across the lambda grid accelerates the search.

  Internal helpers glasso_one() (single-lambda solver) and compute_EBIC_glasso() (EBIC computation) are available but not exported.

  Returns a list with theta (selected precision matrix), lambda_opt (selected lambda), ebic_opt, n_edge, and path (data frame of lambda, ebic, n_edge over the search grid).

• print.exametrika Glasso method: Added a Glasso branch to the shared print.exametrika() dispatcher to summarize the estimated model (optimal lambda, EBIC value, edge count, precision matrix).

• Chatterjee’s xi correlation (chatterjee_xi, xi_stable, chatterjee_matrix): New family of functions implementing Chatterjee’s (2021) rank-based correlation coefficient. chatterjee_xi() computes the single-shot value with random tie-breaking. xi_stable() averages B replications (default B = 1000) to stabilize against tie-induced variability and returns a list with the mean, standard deviation, standard error, and B. chatterjee_matrix() produces the p x p asymmetric pairwise xi matrix from ordinal data with pairwise-complete handling of missing values; the asymmetry between xi(j, k) and xi(k, j) enables direction detection in graphical-model construction.

Documentation and CRAN check cleanup

• Roxygen Markdown bracket escapes: Wrapped bracketed expressions inside roxygen blocks of Glasso() and chatterjee_matrix() in backticks (e.g., `[0, 1]`, `[j, k]`, `Q[i, j]`) so that roxygen2 no longer rewrites them as \link{} cross-references. Resolves R CMD check WARNINGs about missing link targets.
• Glasso() ... documented: Added @param ... to Glasso() so that R CMD check’s “Undocumented arguments” WARNING is cleared.
• compute_EBIC_glasso() partial-match fix: Replaced determinant(Theta, log = TRUE) with the full argument name logarithm = TRUE, removing the partial-argument-match NOTE.

exametrika 1.12.2

Bug fixes

• dataFormat(response.type = "rated") no longer errors when a CA category is unobserved: previously, if no respondent chose item j’s correct-answer category (e.g., everyone got it wrong on a hard item, or the sample was small enough that the CA category did not appear by chance), dataFormat() aborted with "CA for item j is not a valid response category". This rejected legitimate test data where an item is uniformly difficult or where the sample size is small. The check has been relaxed to a warning(); the affected items are encoded as all-incorrect (U[, j] == 0), which is the correct downstream behavior. This applies to both the matrix-input path (dataFormat) and the long-format path (longdataFormat). Mistyped CAs (e.g., CA[j] = 8 when categories are 1–7) still surface as warnings, so the diagnostic value is preserved.

exametrika 1.12.1

Bug fixes

• Biclustering EM stability for empty fields/classes: Both Biclustering.nominal() and Biclustering.ordinal() no longer abort with "missing value where TRUE/FALSE needed" when extreme grid configurations (e.g., very small ncls combined with very large nfld) leave fields or classes empty during EM. The two log-likelihood checks inside the EM loop — the relative convergence test and the monotonicity guard — now treat a non-finite test_log_lik as a non-converged exit instead of throwing. Affected cells are returned with converge = FALSE so that GridSearch() skips them automatically when comparing criteria. This also resolves the same crash in Biclustering.rated(), which calls Biclustering.nominal() internally.

exametrika 1.12.0

New features

• Class-side Confirmatory Biclustering: Biclustering() now accepts a conf_class argument that fixes class memberships during EM. Like conf (which fixes field memberships), conf_class accepts either a vector of class labels (one per respondent) or a 0/1 membership matrix (respondents x classes). When supplied, the class-side E-step is overridden every iteration. For Ranklustering (method = "R"), the neighbour-smoothing step is skipped (smoothed_memb <- clsmemb) since smoothing pre-fixed labels would defeat the purpose of fixing them. Available for binary, ordinal, nominal, and rated data; can be combined with conf to fix both fields and classes simultaneously. Note: rated re-orders classes by correct rate after estimation, so the output class labels may not match the input labels (the individual-to-class mapping is preserved up to relabeling).

  Number of model parameters (nparam) is intentionally not adjusted when conf or conf_class is in effect: only PiFR / BCRM cell probabilities count as parameters in this implementation, and membership matrices are latent posteriors, not parameters.

Bug fixes

• Confirmatory ordinal Biclustering: field membership now stays fixed during EM: Biclustering.ordinal() was overwriting fldmemb with the E-step estimate every iteration, so the conf/conf_mat argument only affected the initial value. Aligned the implementation with Biclustering.binary() by re-applying fldmemb <- conf_mat immediately after the field-side E-step. With this fix result$FieldEstimated matches the user-supplied assignment exactly.

• Confirmatory nominal Biclustering: conf argument is now actually honored: Biclustering.nominal() validated length(conf) against NCOL(U), but U is an exametrika list object so NCOL(U) always returned 1. The check rejected every well-formed conf vector with “conf vector size does NOT match with data.”, making confirmatory nominal Biclustering unreachable since v1.10.0. Replaced with NCOL(U$Q) (and the matrix-form NROW(conf) check, plus the conf_mat allocation, in the same way).

• Confirmatory ordinal Biclustering: conf length check actually validates input: same NCOL(U) issue as nominal, but in Biclustering.ordinal(). Fixed by switching to NCOL(U$Q).

• Confirmatory binary Biclustering: conf size checks now reference the formatted response matrix explicitly: Biclustering.binary() happened to work because U is rebound to tmp$U * tmp$Z before the conf block, so NCOL(U) returned the item count. Switched to NCOL(tmp$U) for consistency with the ordinal/nominal fixes and to make the intent obvious to readers.

• Confirmatory Biclustering: matrix-form conf is no longer silently dropped: when conf was supplied as a membership matrix (items x fields) instead of a vector, all three implementations (binary, ordinal, nominal) validated the matrix but never copied it into conf_mat, so the subsequent nfld <- NCOL(conf_mat) failed with object 'conf_mat' not found. Added conf_mat <- as.matrix(conf) in the matrix branch.

• Biclustering.ordinal() now honors the maxiter argument: The inner EM iteration cap was hardcoded to 100 (maxemt <- 100) and ignored the user-supplied maxiter. This mirrors the bug that was fixed for Biclustering.nominal() in 1.11.0. Callers that pass a larger maxiter (e.g. 2000 in Monte Carlo studies) now actually use that ceiling.

• GRM() fit indices no longer return NaN for moderate or larger item counts: The benchmark model used const <- exp(-nitems * 100) as a log-domain epsilon inside sum(cat_counts * log(cat_probs + const)). For about 8 or more items this expression underflows to exactly 0 in IEEE-754 double precision, so log(0) = -Inf propagates through 0 * -Inf = NaN and poisons every downstream index (model_Chi_sq, NFI, CFI, RMSEA, AIC, CAIC, BIC). The benchmark and null loops now skip zero-count categories explicitly, removing the need for an additive epsilon.

• GRM() degrees of freedom were computed incorrectly: The model df was set to n_pattern * (ncat - 1) + 1 and the null df to n_pattern * (ncat - 1), which is neither (# bench params) - (# model params) nor (# bench params) - (# null params). The inflated df then clamped CFI, TLI, IFI, and RMSEA to zero whenever chi^2 < df (and the previous df_A > df_B inequality was the wrong direction to begin with). The convention now matches Biclustering.ordinal():

  • bench_nparam_j = n_pattern * (ncat_j - 1)
  • null_nparam_j = ncat_j - 1
  • model_nparam_j = ncat_j (one slope plus ncat_j - 1 thresholds)
  • df_A_j = bench_nparam_j - model_nparam_j
  • df_B_j = bench_nparam_j - null_nparam_j

• GRM() now accepts any integer-coded ordinal responses, not just 1..K: Category counts were derived from apply(dat, 2, max), which assumes responses are already 1-indexed. Data coded from 0 (e.g. 0..3) or with gaps (e.g. 1, 2, 4) undercounted ncat[j] by one or more and then indexed grm_prob()[resp] / v[resp] out of range, producing either an outright invalid subscript type 'list' error (on J15S3810-style data) or silently truncated threshold columns. Each item’s responses are now remapped to contiguous 1..K codes via match() against the sorted unique values on entry, with ncat[j] derived from the mapped levels; both the R model-fit blocks and the C++ log-likelihood receive 1-based input regardless of the user’s coding.

• GridSearch() now tolerates per-cell fit errors: Previously, a single Biclustering() (or LCA() / LRA()) call that raised an error at a grid corner (for example, empty-cluster edge cases at large ncls/nfld with small nobs/nitems) would propagate out of GridSearch() and abort the entire grid. The call to the underlying analysis function is now wrapped in tryCatch, and errors are handled the same way as non-convergence: the cell is marked NA in the index matrix and the (ncls, nfld) pair is recorded in failed_settings. GridSearch() still raises only when all grid cells fail, preserving the existing “all-failed” error.

Performance

• C++ implementation of the IRM Gibbs sampler core: The collapsed Gibbs sampler shared by Biclustering_IRM.nominal(), Biclustering_IRM.ordinal(), and Biclustering_IRM.rated() is now implemented in C++ via Rcpp (src/irm_gibbs_core.cpp). The R reference implementation in R/00_IRM_Gibbs_CORE.R is preserved behind irm_gibbs_core(..., use_cpp = FALSE) for cross-checking.

  • Numerical reproducibility (revised 2026-05-07): RNG calls are routed through R-level sample.int() and rmultinom() (via Rcpp::Function) so the unif_rand() consumption order matches base R exactly. The C-level entry points (Rcpp::sample, R::rmultinom) consume RNG differently from base R and were explicitly avoided.

    The C++ and R reference paths are bit-identical for the first Gibbs iterations on the bundled test datasets and on real polytomous data (verified through iteration 2 on J143S32 ordinal), but diverge from iteration 3 onward on real data due to sub-LSB floating-point ordering differences accumulating through the lmvbeta() calls in the CRP likelihood. Once the divergence flips a single rmultinom() outcome, the two chains follow different sample paths.

    Empirically the two paths still target the same posterior: on a 50-seed comparison (M = 66 ordinal items, N = 143), the marginal distributions of n_field and n_class are statistically indistinguishable between paths (Wilcoxon p = 0.56 / 0.81). Use either path for inference; do not rely on a single seed reproducing the same (n_field, n_class) across the two paths.

    The parity tests in tests/testthat/test-irm-gibbs-cpp.R cover only short runs (<= 10 iterations) and therefore did not catch this. A longer-iteration test on real-data-like configurations is on the roadmap.

  • Wall-clock: roughly 4x speedup on the inner Gibbs loop on the bundled test datasets (J20S600 nominal: 82 to 20 ms/iter; J35S500 ordinal: 76 to 19 ms/iter). The end-to-end Biclustering_IRM() call also benefits proportionally on larger iteration counts (e.g. simulation runs).

  • No new dependencies: Rcpp is already in LinkingTo:; the implementation uses only Rcpp::Function and <vector>/<cmath>.

• Vectorized EM hot path in Biclustering.ordinal(): The per-iteration cost of the ordinal EM loop has been reduced by rewriting five hot spots in base R without introducing new package dependencies.

  • Replaced apply(Ufcq_prior, c(1, 2), function(x) rev(cumsum(rev(x)))) with an in-place reverse cumulative sum loop over the category axis. The previous form dispatched nfld * ncls R-level calls per EM iteration; the new form performs maxQ - 1 vectorized array additions.
  • Replaced apply(X, 1, min) and apply(X, 1, max) with do.call(pmin.int, as.data.frame(X)) / do.call(pmax.int, as.data.frame(X)). These compute the row-wise reduction in a small number of C-level calls rather than one R-level call per row. apply(X, 1, which.max) was similarly replaced by max.col(X, ties.method = "first").
  • Precomputed log(BBRM[,,q] - BBRM[,,q+1] + const) once per EM iteration instead of independently in the class-side and field-side E-steps for every q.
  • Precomputed Z * Uq[,,q] once per fit (call it ZU) via column-major recycling (Uq * as.vector(Z)), replacing about eight separate elementwise products per EM iteration and reusing the same array in the post-EM fit-index blocks. The replicate(maxQ, Z) allocation that produced Zrep has been removed as a byproduct.
  • Replaced apply(X, c(1, 2), sum) and apply(X, c(2, 3), sum) on 3-D arrays with rowSums(X, dims = 2) / colSums(X, dims = 1), and apply(M, 2, sum) on matrices with colSums(M).

  Output is bit-identical to 1.11.0 on every tested configuration (max(abs(old - new)) == 0 for BCRM, BBRM, ClassMembership, FieldMembership, TestFitIndices, and the full EM trajectory). Single-fit wall-clock on typical sizes (ncls, nfld up to 20 by 15 on J35S500) improves by roughly 1.2 to 1.3 times; the per-EM-iteration speedup compounds across GridSearch() grids.

• Vectorized 3-D apply reductions in Biclustering.nominal(): The same rowSums/colSums(X, dims = ...) substitutions were applied to the nominal M-step and null-model blocks, and Zrep was eliminated in favor of the ZU precomputation. Output is bit-identical to 1.11.0.

• Vectorized Uq one-hot encoding in Biclustering.ordinal() and Biclustering.nominal(): The construction of the one-hot response array Uq[i, j, tmp$Q[i,j]] = 1 previously used a nobs * nitems nested R loop. It now writes all ones in one C-level matrix-index assignment, restricted to non-missing cells (tmp$Z == 1). Single-fit wall-clock on the validation matrix improves by 1.2-5.3x over 1.11.0 (up to 5x on small cases where the loop overhead dominated). Output is bit-identical to 1.11.0 at every downstream location (the missing entries of the old Uq were never read because every consumer applies the tmp$Z mask).

Output structure

• Biclustering.ordinal() now returns SmoothedMembership: The smoothed (Ranklustering-filtered) class membership matrix is now part of the return value, mirroring Biclustering.binary(). This fills a long-standing gap (only the binary form previously exposed it) and makes Ranklustering with conf_class introspectable: callers can verify that the smoothing step is correctly skipped when class labels are pre-fixed (SmoothedMembership equals ClassMembership in that case).

Tests

• Added a print() smoke test for Biclustering_IRM.rated() results (test-irm-rated.R).
• Added an nrank = 4 LRA.rated regression test for DistractorAnalysis() to cover varying rank counts (test-distractor.R).

Notes

• No changes to package Imports or Depends. The new C++ Gibbs sampler uses Rcpp, which was already declared in LinkingTo:.
• No new exported functions. The new conf_class argument on Biclustering() is additive and defaults to NULL, preserving the previous behavior for all existing callers.

exametrika 1.11.0

New Features

• Biclustering_IRM.rated(): Rated IRM (Infinite Relational Model for multiple-choice data): Performs IRM-based biclustering for rated data (items with correct answers and multiple response categories). Internally calls Biclustering_IRM.nominal() for estimation via Dirichlet-Multinomial collapsed Gibbs sampler, then post-processes the results: classes are sorted by correct response rate (ranklustering), and two layers of fit indices are reported — binary (item correct/incorrect, with full benchmark model including CFI/RMSEA) and nominal (category-level, AIC/BIC/CAIC only). Returns TestFitIndices (binary, default) and TestFitIndices_nominal (nominal) in the output.

• DistractorAnalysis(): Distractor analysis for rated models: S3 generic function for analyzing response category distributions by rank/class. Computes observed frequency tables, proportion tables, chi-square tests against chance level, and Cramer’s V effect sizes for each item-by-rank cell. Works with LRA.rated and Biclustering.rated / Biclustering_IRM.rated results. For Biclustering models, output is grouped by field. Supports items and ranks filtering in both print() and plot() methods.

New Data

• J21S300: New rated sample dataset (21 items, 300 students, 4 response categories) for testing rated Biclustering and IRM models. Smaller and faster than J35S5000 (35 items, 5000 students).

Bug Fixes

• Fixed maxiter parameter ignored in Biclustering.nominal(): The maxiter parameter was accepted but internally overridden by a hardcoded maxemt <- 100. Now correctly uses maxiter as the iteration limit.

• Fixed spurious “No ID column detected” message in Biclustering.rated() and Biclustering_IRM.rated(): The crr() function was called with a raw matrix (tmp$Z * tmp$U) instead of an exametrika object, triggering an unnecessary dataFormat() call. Now creates a temporary binary-typed exametrika object to avoid the message.

exametrika 1.10.2

New Features

• Biclustering.rated(): Rated (multiple-choice) Biclustering: Performs biclustering for rated data (items with correct answers and multiple response categories). Internally calls Biclustering.nominal() for estimation, then post-processes the results: classes are sorted by correct response rate (ranklustering), and two layers of fit indices are reported — binary (item correct/incorrect, with full benchmark model) and nominal (category-level, AIC/BIC/CAIC only). The binary layer uses item-level correct response rates per class without field constraints (nparam = nitems * ncls). Supports both Biclustering (method = "B") and Ranklustering (method = "R") modes. Returns TestFitIndices (binary) and TestFitIndices_nominal (nominal) in the output. Added 16 tests for rated Biclustering using J35S5000.

Improvements

• Renamed ItemFRP to quasiFRP in Biclustering.rated() output: The item-level correct response rate matrix (J x C) is computed without field constraints because the field assignments come from nominal analysis and have different meaning in the binary context. The name quasiFRP (quasi Field Reference Profile) clarifies this distinction from the standard field-constrained FRP.

Bug Fixes

• Fixed subscript out of bounds in nominal/ordinal Biclustering with large nfld: The initial field assignment ceiling(1:nitems / (nitems / nfld)) could exceed nfld due to floating-point rounding. Added pmin(..., nfld) clamping, consistent with the binary Biclustering fix already in place.
• Fixed redundant dataFormat() call in Biclustering.rated(): The function was unnecessarily re-calling dataFormat() on already-formatted data, causing repeated “No ID column detected” messages during GridSearch(). Now reuses the existing exametrika object directly.
• Fixed Array plot for polytomous Biclustering (rated/nominal/ordinal): Array plots for polytomous Biclustering models were rendered in black and white because x$U (binary correctness matrix) was used instead of x$Q (polytomous responses). Now correctly uses x$Q for polytomous models.
• Fixed FCRP plot invalid graphics state error: par(mfrow=...) and layout() conflicted when plotting FCRP/FCBR. Now skips par(mfrow=...) for plot types that use layout() internally.
• Improved id parameter validation in dataFormat(): When a vector (e.g., id = tmp$ID) was passed instead of a column number, the error message was cryptic (the condition has length > 1). Now validates that id is a single integer and provides a clear error message.
• Fixed nominal Biclustering/IRM fit indices: Removed benchmark (saturated) model for nominal data. With many items and categories, every examinee has a unique response pattern, making the benchmark model trivially saturated (ell_B = 0) and chi-square based indices (NFI, RFI, IFI, TLI, CFI, RMSEA) meaningless. These indices are now reported as NA for nominal data. Information criteria (AIC, BIC, CAIC) are computed directly from the model log-likelihood and remain available. Also fixed a length(benchGroup) → length(unique(benchGroup)) bug in Biclustering.nominal() (the unique() call was missing).

Improvements

• Added empty field warning for all Biclustering models: When some fields have no items assigned (e.g., due to specifying too many fields), a warning message is now emitted suggesting to reduce nfld. Affects Biclustering() (binary/ordinal/nominal), Biclustering_IRM() (binary/ordinal/nominal).
• Renamed field to fld in Biclustering_IRM.binary(): Internal variable name changed from field to fld for consistency with other Biclustering models. No change to the public API (FieldEstimated output name is unchanged).

Documentation Fix

• Fixed J35S5000 UseCase in data format tables: Corrected from “Nominal LRA” to “Rated LRA” in getting-started vignette, and from “名義LRA” to “評定LRA” in Japanese guide. J35S5000 is a rated (multiple-choice with correct answers) dataset, not nominal.
• Fixed J15S3810 roxygen documentation: The @format field incorrectly stated “nominal responses” but the dataset is ordinal (response.type=ordinal). Also fixed “A ordinal” to “An ordinal” in @description.

exametrika 1.10.1

Vignette Build Time Reduction

• Reduced vignette build time from ~46 minutes to ~5 minutes: Added eval=FALSE to computationally intensive code chunks in vignettes (GridSearch, IRM, LDLRA, LDLRA_PBIL, LDB, BINET, ordinal/nominal Biclustering, ordinal/rated LRA). The Japanese guide (guide-ja) now uses eval=FALSE for all model estimation chunks to avoid duplicating computation from English vignettes. Full rendered output is available on the pkgdown site.

exametrika 1.10.0

Bug Fixes

CAIC (Consistent AIC) Formula Correction

• Fixed CAIC formula to match Bozdogan (1987) original definition: The CAIC penalty term was log(n + 1) but should be log(n) + 1 per Bozdogan (1987, Psychometrika, 52(3), p.358, Proposition 2, Eq.44). The original Mathematica implementation had this error (Log[nobs + 1]), and the R port inherited it. Both the R version (R/00_ModelFitModule.R) and the Mathematica version (develop/mtmk15forVer13/mod/Module_ModelFit.nb) have been corrected. The numerical difference is approximately 1 (constant), but the corrected formula now matches the published definition: CAIC(k) = -2 log L + k * (log(n) + 1). This affects all models that compute fit indices: IRT, LCA, LRA (binary/ordinal/rated), Biclustering (binary/ordinal/nominal), IRM, BNM, LDLRA, LDB, BINET, and GRM. All 873 tests pass with the corrected formula.

GRM Example Fix

• Changed GRM examples from \donttest to \dontrun: GRM’s multi-panel plot examples caused “invalid graphics state” errors in non-interactive environments (pkgdown, CI). Changed to \dontrun to prevent build failures.

dataFormat Robustness Improvements

• Fixed auto-detection ignoring CA parameter: When CA (correct answer vector) was provided but response.type was not explicitly specified, dataFormat() incorrectly classified the data as "ordinal" instead of "rated". This caused $U (binary scoring matrix) to be NULL. The auto-detection now checks for CA before ordinal/nominal detection: binary → rated (if CA provided) → ordinal → nominal.
• Fixed id parameter not working for column 1: Changed id default from 1 to NULL. Previously, id = 1 (both default and explicit) triggered auto-detection heuristics, making it impossible to explicitly specify the first column as the ID column. Now id = NULL triggers auto-detection, and any numeric value (including 1) forces that column to be used as ID.
• Improved ID auto-detection for consecutive integers: Simplified the first-column heuristic to treat unique consecutive integers (e.g., 1:N) as ID regardless of whether they also look like valid response values. Previously, 1:10 was misclassified as response data because looks_like_response_data() returned TRUE.
• Fixed missing values in rated U matrix: When the response matrix contained missing values (-1), the binary scoring matrix U incorrectly scored them as 0 (incorrect) instead of -1 (missing). Now U[i,j] = -1 when Q[i,j] = -1.
• Fixed drop=FALSE missing in item exclusion: When items were excluded due to invalid variance (e.g., containing Inf), the column subsetting response.matrix[, mask] dropped matrix dimensions if only one item remained, causing a crash. Added drop = FALSE.
• Added diagnostic messages: dataFormat() now reports via message() when it detects problematic data:
  • Items with all missing values
  • Items with zero variance (constant response values)
  • Students with all missing responses

BINET g_list / adj_list Input Path Fix

• Fixed g_csv variable undefined error when using g_list or adj_list input: BINET() crashed with an undefined variable error at the graph construction step when the DAG was specified via g_list or adj_list parameters. The internal variable g_csv (used to build the integrated graph object all_g) was only defined in the adj_file code path. Added logic to reconstruct g_csv from adj_list for the g_list and adj_list input paths, ensuring all_g is correctly built with Field edge attributes regardless of input method.
• Fixed g_list / adj_list length validation: The length check for g_list and adj_list incorrectly compared against ncls (number of classes) instead of nfld (number of fields). In BINET, each element of adj_list represents the DAG structure at a specific field, so the list length should equal nfld. Also fixed g_list type check from g_list[[1]] (always checking the first element) to g_list[[j]] (checking each element).

Biclustering_IRM.binary S3 Method Consistency Fix

• Added ... to Biclustering_IRM.binary() signature: The S3 generic Biclustering_IRM(U, ...) requires all methods to include ... in their formal arguments. The .binary method was missing it, causing an R CMD check WARNING. Added ... to match the generic and the .nominal/.ordinal methods.

Biclustering_IRM msg Field Fix

• Fixed IRM msg field to correctly distinguish Rank vs Class models: Binary IRM and Ordinal IRM are Ranklustering models (ordered latent classes), so msg = "Rank" is correct. Nominal IRM has no Ranklustering concept (unordered latent classes), so msg = "Class" is correct. Previously all three methods had inconsistent values; now Biclustering_IRM.binary and Biclustering_IRM.ordinal return msg = "Rank", while Biclustering_IRM.nominal returns msg = "Class". Also updated internal column names of cls01 and FRP from "Class" to "Rank" for binary/ordinal IRM. The shared Gibbs core (irm_gibbs_core()) output column names were also updated.

Biclustering_IRM.binary Missing LRD Alias

• Added LRD (Latent Rank Distribution) alias to Biclustering_IRM.binary() return value: The binary IRM was the only Biclustering model that did not include LRD in its return value (it only had LCD). Other Biclustering models (binary Biclustering, nominal IRM, ordinal IRM) all return both LRD and LCD. Added LRD = clsdist as an alias for LCD to ensure consistency across all Biclustering-family models. This improves interoperability with downstream packages (ggExametrika) that look up LRD when msg == "Rank".

Biclustering_IRM Seed Default

• Reverted Biclustering_IRM() seed default back to 123: Ensures reproducibility by default.

Biclustering_IRM t(apply()) Dimension Drop Fix

• Fixed t(apply(log_S, 1, irm_log_to_prob)) dimension drop in Nominal/Ordinal IRM: When the Gibbs sampler converged to ncls=1 or nfld=1, apply() on a single-column matrix returned a vector instead of a matrix, causing t() to produce a 1-row matrix instead of an N-row matrix. This led to incorrect class/field membership assignment. Replaced all 6 instances of t(apply(mat, 1, fun)) with explicit for-loops in both Biclustering_IRM.nominal() (3 locations: EM E-step, final class membership, final field membership) and Biclustering_IRM.ordinal() (3 locations: same). Consistent with the project’s apply() caution policy.

Biclustering_IRM Log-Probability Normalization Fix

• Fixed log-to-probability conversion in Biclustering_IRM() Gibbs sampler: Changed exp(ptab - min(ptab)) to exp(ptab - max(ptab)) for numerical stability. The previous implementation subtracted the minimum log-probability, which could cause overflow (exp(large positive) = Inf) when the range of log-probabilities was large, resulting in NaN after normalization. Subtracting the maximum ensures the largest value becomes exp(0) = 1 and all others underflow harmlessly to near-zero values.

Biclustering.nominal Model Fit Fix

• Fixed Biclustering.nominal() using stale log-likelihood in model fit indices: When the EM algorithm exited due to log-likelihood decrease, BCRM was correctly reverted to the previous iteration’s value, but test_log_lik was not. The model fit section recalculated the correct log-likelihood as testell, but chi_A, model_log_like, log_lik, and LogLik all referenced the stale test_log_lik instead of testell. Also removed a duplicated model fit code block (copy-paste error).

J20S400 Dataset Fix

• Fixed J20S400 response type from nominal to binary: The J20S400.rda dataset was incorrectly stored with response.type = "nominal" despite being a binary (0/1) dataset with -99 as missing values. Missing values were not properly handled (Z was all 1s, Q contained raw -99 values). Regenerated from the original CSV source (develop/sampleData/J20S400.csv) with dataFormat(..., na = -99), now correctly typed as binary with 86 missing values properly masked in Z.

New Features

Polytomous IRM (Biclustering_IRM.nominal / Biclustering_IRM.ordinal)

• New Biclustering_IRM.nominal() for nominal/polytomous data: Extends the Infinite Relational Model (IRM) from binary to nominal scale data using a Dirichlet-Multinomial collapsed Gibbs sampler. The Chinese Restaurant Process (CRP) automatically determines the optimal number of classes and fields. After the Gibbs sampling phase, small classes are consolidated and refined with an EM algorithm. The Dirichlet prior concentration parameter alpha controls smoothing of category probabilities.
• New Biclustering_IRM.ordinal() for ordinal/polytomous data: Extends IRM to ordinal scale data. Shares the same Dirichlet-Multinomial collapsed Gibbs sampler as nominal IRM (Phase 1), then applies ordinal-specific EM refinement (Phase 2) with cumulative normalization to enforce monotonic category boundaries. The mic parameter (default TRUE) enforces monotone increasing class ordering by expected score sum. Reports BFRP (Bicluster Field Reference Profile), FRPIndex, TRP, and Strongly/Weakly Ordinal Alignment Conditions (SOACflg/WOACflg).
• Biclustering_IRM() is now an S3 generic: Dispatches to Biclustering_IRM.binary (existing binary IRM), Biclustering_IRM.nominal (new), and Biclustering_IRM.ordinal (new). Raw data is automatically formatted and dispatched based on response.type.
• Shared Gibbs sampler core: The collapsed Gibbs sampler has been extracted into a shared internal function irm_gibbs_core() (in R/00_IRM_Gibbs_CORE.R), used by both nominal and ordinal IRM. Helper functions (irm_calc_Ufcq, irm_lmvbeta, irm_log_to_prob, irm_bic_calc, etc.) are also shared.
• Performance optimization: The Gibbs sampler uses differential updates for the sufficient statistics array U_fcq, computing only the contribution of the target student/item rather than recalculating the full array at each step.

Confirmatory LCA/LRA (Test Equating)

• LCA() and LRA() now support a conf parameter for confirmatory analysis: The conf argument accepts an IRP matrix (ncls/nrank x testlength) where non-NA values are held fixed throughout EM estimation and NA values are freely estimated. This enables test equating scenarios where anchor items retain their known IRPs while new items are calibrated against them.
• Label-based item matching: When conf has column names, items are matched by label rather than by position. This allows conf to contain a subset of items (anchor items only) or items in a different order than the data. Items in the data but not in conf are automatically set to freely estimated. Unknown labels in conf produce an informative error.
• Works with both GTM and SOM methods for LRA.

Internal Refactoring: SOM Estimation

• Extracted SOM estimation into somclus() internal function: The Self-Organizing Maps estimation code previously inlined in LRA.binary() (~100 lines) has been extracted into a standalone internal function somclus() in 00_EMclus.R. This parallels emclus() (GTM/EM) and returns the same structure. Also fixed a pre-existing typo (h_cout → h_count) and another (oldsBIC → oldBIC).

Test Suite Modernization

• Complete migration from Excel to CSV fixtures: Removed all 14 legacy test files that depended on tidyverse and readxl for reading Excel-based Mathematica reference data. Replaced with 24 modern test files using base R read.csv() and test_path() to load CSV fixtures from tests/testthat/fixtures/mathematica_reference/. The new test suite has zero external package dependencies beyond testthat.
• Removed readxl/tidyverse from test dependencies: DESCRIPTION Suggests no longer requires any packages beyond knitr, rmarkdown, and testthat.
• Fixture file reorganization: Shortened overly long CSV fixture filenames to comply with CRAN’s 100-byte portable path requirement.
• Test coverage: 26 test files, 321 test blocks, covering all models (CTT, IRT 2PL/3PL/4PL, LCA, LRA binary/ordinal/nominal, Biclustering binary/ordinal/nominal, IRM binary/nominal/ordinal, BNM, LDLRA, LDB, BINET, GRM, GridSearch, dataFormat, polychoric correlation, scoring, student/test analysis, confirmatory LCA/LRA). 85 Mathematica reference CSV files for cross-validation.
• Added Nominal IRM tests (test-irm-nominal.R): 18 test blocks for Biclustering_IRM.nominal() using J20S600 data — basic execution, dimensions, FRP validity, membership, fit indices, backward compatibility, seed reproducibility, alpha validation.
• Added Ordinal IRM tests (test-irm-ordinal.R): 25 test blocks for Biclustering_IRM.ordinal() using J35S500 data — basic execution, dimensions, FRP validity, expected scores, TRP, BFRP, FRPIndex, SOAC/WOAC flags, mic parameter, fit indices, backward compatibility, seed reproducibility, alpha validation.

Documentation

• TestStatistics example: Added stem-and-leaf plot example using stem(nrs(dataFormat(J15S500))) to demonstrate score distribution visualization.

Internal Improvements

• pkgdown migration: Migrated documentation site from Jekyll (main/docs) to pkgdown (gh-pages branch via GitHub Actions).
• CI/CD: Added GitHub Actions workflows for automated R CMD check, test coverage reporting, and pkgdown site deployment. Removed Codecov upload step from test-coverage workflow.
• .Rbuildignore cleanup: Removed ^tests$ and ^inst$ entries that were incorrectly excluding tests and vignettes from the built package.

exametrika 1.9.0

Bug Fixes

GridSearch index Parameter Fixes

• Index alias support: GridSearch() now accepts common aliases for fit indices. "loglik", "log_lik", "LogLik", and "LL" are mapped to "model_log_like". "Chi_sq" and "chi_sq" are mapped to "model_Chi_sq". Previously, using these aliases caused silent NULL extraction and eventual errors.
• Early validation: Invalid index names are now caught immediately at the start of GridSearch(), before the computationally expensive grid search loop runs. The error message lists all valid options including available aliases.
• Log-likelihood optimization direction: model_log_like is now correctly treated as a maximization target (larger log-likelihood = better fit). Previously, it was incorrectly placed in the minimization group, which would have selected the worst-fitting model.

Test Tolerance Fix

• Q3 matrix test: Changed the 2PL Q3 matrix test from relative tolerance (tolerance = 1e-2 in expect_equal) to absolute difference comparison (threshold 0.005). Q3 residual correlations include values near zero where relative tolerance comparisons are unreliable.

NAMESPACE Fix

• Missing imports: Added layout and plot.new from graphics to NAMESPACE. These functions are used by the legend strip layout helpers for polytomous Biclustering plots.

LRA.ordinal / LRA.rated Category Computation Fix

• Fixed apply(U$Q, 2, unique) returning matrix instead of list: When all items have the same number of response categories (e.g., all 5-point Likert), apply() returns a matrix rather than a list. The subsequent lapply() then iterates over individual elements instead of per-column vectors, causing ncat to be a vector of 1s and crashing the algorithm. Replaced with lapply(seq_len(nitems), function(j) sort(unique(U$Q[, j]))) which always returns a proper list. Same fix applied to catfreq999 computation. Both LRA.ordinal and LRA.rated were affected.

GRM ItemFitIndices Computation Fix

• Fixed apply(tmp$Q, 2, table) returning matrix instead of list: Same class of bug as the LRA.ordinal/LRA.rated fix above. In GRM(), the null model log-likelihood computation used apply(tmp$Q, 2, table) to compute per-item category frequencies. When all items have the same number of response categories (e.g., all 5-point Likert), apply() returns a matrix instead of a list, causing response_list[[j]] to extract a single number rather than the full frequency table. This produced incorrect null_log_like values and consequently wrong chi-square statistics, RMSEA, TLI, and CFI in ItemFitIndices. Replaced with lapply(seq_len(nitems), function(j) table(tmp$Q[, j])) which always returns a proper list.

LRA.ordinal Mixed Category Count Validation

• Added input validation for mixed category counts: LRA.ordinal() now raises an informative error when items have different numbers of response categories (e.g., some items with 3 categories and others with 5). The internal matrix algebra uses fixed-stride indexing that assumes uniform category counts. The error message suggests alternatives (LRA.rated, Biclustering.ordinal) that support mixed category counts via list-based designs.

LCA/LRA FRP Plot Type Removal

• Removed “FRP” from valid plot types for LCA and LRA: Field Reference Profile (FRP) requires a field structure (item grouping), which LCA and LRA do not have. Previously, plot(lca_result, type = "FRP") passed validation but failed at runtime because the $FRP field does not exist in LCA/LRA return values. Now properly rejected with an informative error message at the validation stage.

New Features

New Sample Datasets for Polytomous Biclustering

• J35S500: Simulated ordinal dataset (500 students, 35 items, 5 categories) with a cumulative staircase pattern (5 latent classes, 5 fields). Contains approximately 0.5% missing values.
• J20S600: Simulated nominal dataset (600 students, 20 items, 4 categories) with a cyclic category preference pattern (5 latent classes, 4 fields). Contains approximately 0.5% missing values.

New Plot Types for Polytomous Biclustering

• FRP (Field Reference Profile): Expected score line plot per field, with stat parameter supporting "mean" (default), "median", and "mode".
• FCRP (Field Category Response Profile): Category probability plot per field, with style parameter supporting "line" (default) and "bar" (stacked bar chart).
• FCBR (Field Cumulative Boundary Reference): Boundary probability plot per field (ordinal Biclustering only).
• ScoreField: Heatmap of expected scores across fields and latent classes/ranks.
• RRV (Rank Reference Vector): Transposed view with fields on x-axis and expected scores on y-axis, with stat parameter.

FRPIndex for Ordinal Biclustering

• Ordinal Biclustering now computes FRPIndex (Field Reference Profile indices) including location parameters (Alpha, Beta), slope parameters (A, B), and monotonicity indices (Gamma, C).

New Parameters for plot.exametrika()

• stat: Controls the summary statistic for FRP and RRV plots ("mean", "median", "mode").
• style: Controls the display style for FCRP plots ("line", "bar").

Array Plot Improvements

• Missing value display: Array plots now display missing values in a distinct color. Binary data uses gray (#808080) to distinguish from white (incorrect) and black (correct). Polytomous data uses black (#000000) to distinguish from the category color palette.

Print Method Improvements

• Ordinal Biclustering: print() now displays FRPIndex (Field Reference Profile Indices) with a note that the values are based on normalized expected scores (E[score]-1)/(maxQ-1).

Documentation Improvements

• FRPIndex: Expanded documentation for the 6 profile shape indices (Alpha, A, Beta, B, Gamma, C) in ?Biclustering, including detailed definitions and polytomous adaptation logic.

Return Value Structure Unification

Systematic unification of return value structures across all analysis functions for consistency and interoperability.

snake_case Field Names Extended to All Functions

• LDLRA: Added n_class (retaining Nclass for backward compatibility)
• LDB: Added n_rank, n_field (retaining Nrank, Nfield)
• BINET: Added n_class, n_field (retaining Nclass, Nfield)
• Biclustering.nominal: Added n_class, n_field, n_cycle (retaining Nclass, Nfield, N_Cycle)
• Biclustering.ordinal: Added n_class, n_field, n_cycle (retaining Nclass, Nfield, N_Cycle)
• Biclustering_IRM: Added n_cycle, N_Cycle (retaining em_cycle, EM_Cycle as IRM-specific aliases)

Top-Level log_lik Added to All Functions

• All analysis functions now consistently provide log_lik at the top level of the return object, matching TestFitIndices$model_log_like.
• Functions updated: IRT, LCA, LRA.binary, BNM, LDLRA, LDB, BINET, Biclustering.binary, Biclustering_IRM

TestFitIndices Structure Unified

• GRM, Biclustering.nominal, Biclustering.ordinal: TestFitIndices now uses the full 16-field structure with ModelFit class, matching the format used by IRT/LCA/LRA and other functions. Previously these used bare calcFitIndices() output (9 fields, no class). Added fields: model_log_like, bench_log_like, null_log_like, model_Chi_sq, null_Chi_sq, model_df, null_df.
• GRM ItemFitIndices: Also unified to the full 16-field structure with ModelFit class.
• BINET: TestFitIndices added as primary name for multigroup fit indices (previously only MG_FitIndices). MG_FitIndices retained as backward-compatible alias. SM_FitIndices (saturated model) remains unchanged.

Students Matrix Enhanced

• Biclustering.nominal: Added Estimate column (most probable class assignment) to the Students matrix.
• Biclustering.ordinal: Added Estimate column (most probable class assignment) to the Students matrix.

Other Structural Improvements

• Biclustering_IRM: Added FRPIndex (Field Reference Profile indices) for consistency with Biclustering.binary and LDB.
• LDB: Fixed TRP from matrix(1×ncls) to numeric vector, consistent with all other functions.
• GridSearch: Added class = c("exametrika", "GridSearch") to return value for method dispatch support.

Bug Fixes

• LCA msg field assignment: Fixed msg <- "Class" to msg = "Class" inside structure() call (line 150 of 05_LCA.R). The <- operator was being interpreted as a standalone assignment rather than a named list element, causing the msg field name to be empty.
• RMP/CMP single student plot error: Fixed dimension drop error when plotting RMP or CMP for a single student (e.g., plot(r, type="RMP", students=1)). Added drop = FALSE to prevent matrix-to-vector coercion when extracting a single row from the Students matrix.
• LRA.ordinal / LRA.rated TestFitIndices log-likelihood fields: Fixed null_log_like which incorrectly stored the saturated model log-likelihood (log_lik_satu) instead of the null model log-likelihood (sum(null_itemll)). Added missing bench_log_like field containing the saturated model log-likelihood (sum(satu_itemll2)). Note: the chi-square-based fit indices (NFI, CFI, TLI, RMSEA, AIC, BIC, etc.) were always computed correctly; only the stored log-likelihood labels were affected.
• LRA.ordinal / LRA.rated FitIndices structure: Unified TestFitIndices and ItemFitIndices to the standard 16-field structure with ModelFit class (c("exametrika", "ModelFit")), matching all other analysis functions. Added model_log_like, bench_log_like, null_log_like to ItemFitIndices. Removed ScoreRankCorr / RankQuantCorr from TestFitIndices (already available at the top level of the return object).
• LRA.ordinal / LRA.rated test updates: Updated test-12OLR.R and test-13NLR.R to handle the new ModelFit class (add unclass() before as.data.frame()) and adjusted column/index references to match the unified 16-field structure.

Plot Layout Improvements

• Legend strip layout: Moved per-panel legends to a shared legend strip below the plot area for FCRP (line/bar), FCBR, GRM IRF, and IRT overlay (IRF/IIF) plots. Uses layout() with a thin dedicated row (height ratio 0.2) to reduce visual clutter in data panels. Added setup_legend_layout() and draw_legend_strip() internal helper functions.
• FCBR reference line: Added P(Q>=1)=1.0 reference line at the top of FCBR plots for visual completeness.

exametrika 1.8.1

Bug Fixes

dataFormat Function

• Fixed factor ID column detection: dataFormat() now correctly identifies factor-type ID columns before converting factors to numeric. Previously, the factor-to-numeric conversion occurred before ID detection, causing factor ID columns with many levels (>=20) to trigger a “Too many categories” error instead of being recognized as IDs.
• Removed unused helper function: Removed dead code (is_response_data()) that was defined but never called.

GridSearch Function

• Fixed ordinal data support: GridSearch now correctly handles ordinal data by using obj$Q instead of obj$U for test length calculation
• Resolved nfld=1 parameter issue: Eliminated invalid parameter ranges that caused crashes with ordinal datasets

Biclustering.ordinal Function

• Enhanced numerical stability: Added pmax(Ufcq_prior, 1e-10) to prevent division by zero and NaN errors
• Fixed convergence failures: Resolved “missing value where TRUE/FALSE needed” errors in specific parameter combinations (e.g., ncls=4 with nfld=5)
• Improved robustness: Algorithm now handles edge cases where field membership probabilities approach zero

Impact

• GridSearch now works reliably with ordinal data across all parameter combinations
• Biclustering analysis completes successfully for previously problematic parameter settings
• Enhanced overall stability for large-scale grid searches

exametrika 1.8.0

Naming Convention Improvements

This release improves naming consistency across the package while maintaining full backward compatibility through a deprecation path.

New Field Names (Recommended)

All analysis functions now return results with snake_case field names for better consistency:

• n_class - Number of latent classes (replaces Nclass)
• n_field - Number of latent fields (replaces Nfield)
• n_rank - Number of latent ranks (replaces Nrank)
• n_cycle - Number of EM iterations (replaces N_Cycle)
• log_lik - Log-likelihood value (replaces LogLik)

Deprecated Field Names (Still Supported)

The old field names continue to work for backward compatibility:

• Nclass, Nfield, Nrank, N_Cycle, LogLik - Deprecated but functional
• These fields will be removed in version 2.0.0
• Please update your code to use the new snake_case names

Example Migration

# Old code (deprecated but still works)
result <- LCA(data, ncls = 3)
n_classes <- result$Nclass

# New code (recommended)
result <- LCA(data, ncls = 3)
n_classes <- result$n_class

Output Formatting Improvements

Progress messages now display properly in R Markdown documents:

• GridSearch() - Added verbose parameter (default: TRUE)
  • Output organized by row: ncls = 2: nfld=2 nfld=3 nfld=4 ...
  • Set verbose = FALSE to suppress all progress messages
• Biclustering_IRM() - Improved iteration display
  • Format: iter 1: match=0 nfld=15 ncls=30
  • Class adjustment messages: Adjusting classes: BIC=-99592.5 ncls=21 (min size < 20)
• LRA.ordinal() - Fixed verbose behavior
  • Changed default from verbose = TRUE to verbose = FALSE (consistent with binary/rated versions)
  • Saturation Model: Saturation Model - iter 1: log_lik=-1.234567
  • Restricted Model: Restricted Model - iter 1: log_lik=-0.987654
• LRA.rated() - Fixed verbose behavior
  • Changed default from verbose = TRUE to verbose = FALSE (consistent with binary/ordinal versions)
  • Same improved format as LRA.ordinal

All progress messages now use proper line breaks instead of carriage returns, ensuring clean output in R Markdown/knitr documents and web documentation.

Bug Fixes

• Fixed Array plot color mapping for binary data
  • Used sort(unique(...)) to ensure consistent ordering: 0 (white/incorrect) → 1 (black/correct)
  • Previously, color mapping could be reversed depending on data order
• Fixed Ranklustering Array plot sorting order
  • Students with higher correct response rates now appear at the bottom of the plot
  • Previously, high performers were incorrectly placed at the top

Internal Improvements

• Standardized internal variable naming (e.g., testEll → test_log_lik)
• Improved code readability and maintainability
• All output messages now use consistent log_lik terminology

exametrika 1.7.0

• Renamed IRM() to Biclustering_IRM() for consistency with structure learning naming conventions
  • Follows the same pattern as BNM_GA(), LDLRA_PBIL(), etc. (model_method naming)
  • IRM() function still works but is now deprecated with a warning using .Deprecated()
  • The new name clarifies that this function performs Biclustering structure learning using the Infinite Relational Model
  • All documentation and examples updated to use Biclustering_IRM()
• Added .Deprecated() warnings to renamed functions from version 1.6.5
  • StrLearningGA_BNM() now shows deprecation warning, recommending BNM_GA()
  • StrLearningPBIL_BNM() now shows deprecation warning, recommending BNM_PBIL()
  • StrLearningPBIL_LDLRA() now shows deprecation warning, recommending LDLRA_PBIL()
  • Old function names still work for backward compatibility but display warnings

exametrika 1.6.5

• Critical bugfix for LCA() response type validation
  • Fixed incorrect variable reference in response type checking
• Added beta1 and beta2 parameters to all Beta distribution-based functions
  • LRA.binary(): beta1=1, beta2=1 (GTM method)
  • LCA(): beta1=1, beta2=1
  • Biclustering.binary(): beta1=1, beta2=1
  • BNM(): beta1=1, beta2=1
  • LDB(): beta1=1, beta2=1
  • LDLRA(): beta1=2, beta2=2
  • LD_param_est(): beta1=2, beta2=2 (internal helper function)
  • LDLRA_PBIL(): beta1=2, beta2=2
  • These parameters control the prior density parameters in Bayesian parameter estimation
  • Users can now customize Beta distribution parameters for EM algorithm parameter updating
  • Default values preserve backward compatibility with previous versions
• Added alpha parameter to polytomous models for Dirichlet prior control
  • Biclustering.ordinal(): alpha=1 (flat Dirichlet prior)
  • Biclustering.nominal(): alpha=1 (flat Dirichlet prior)
  • These parameters control the concentration parameter for Dirichlet priors in category probability estimation
  • Users can customize Dirichlet parameters to adjust prior strength (alpha > 0)
  • Default values (alpha=1) preserve backward compatibility with previous versions
• Simplified function names for structure learning functions
  • StrLearningGA_BNM() renamed to BNM_GA()
  • StrLearningPBIL_BNM() renamed to BNM_PBIL()
  • StrLearningPBIL_LDLRA() renamed to LDLRA_PBIL()
  • Shorter, more intuitive function names for improved usability
  • All documentation and examples updated accordingly

exametrika 1.6.4

• Critical bugfix for Biclustering() field initialization
  • Fixed subscript out of bounds error when nfld values cause ceiling() to exceed nfld
  • Added pmin() constraint to ensure fld0 values never exceed nfld parameter
  • Resolves crashes with specific nfld/testlength combinations (e.g., nfld=15, testlength=21)
• Enhanced GridSearch() fit index optimization logic
  • Added support for all fit indices returned by TestFitIndices()
  • Correctly handles minimization indices: model_log_like, model_Chi_sq, RMSEA, AIC, CAIC, BIC
  • Correctly handles maximization indices: NFI, RFI, IFI, TLI, CFI
  • Added validation to prevent unknown index specification

exametrika 1.6.3

• Major performance enhancement for GRM (Graded Response Model)
  • Replaced R implementation with high-performance C++ code using Rcpp
  • Implemented analytical gradient computation for significant speed improvements
  • Achieved 5-6x faster convergence compared to numerical differentiation
  • Maintains identical mathematical accuracy to previous implementation
  • Full compatibility with existing GRM() function interface
• Added converge variable to all EM-based functions to indicate algorithm convergence status
  • Functions affected: Biclustering(), LCA(), LRA(), and related methods
  • Returns TRUE if converged within maxiter iterations, FALSE otherwise
  • Displays convergence warning messages when maxiter is reached
• Enhanced GridSearch() function with convergence handling
  • Automatically excludes non-converged results from optimization
  • Displays warning messages for parameter combinations that failed to converge
  • Returns list of failed settings in output
  • Terminates with error message if all parameter combinations fail to converge
• Improved numerical stability in Biclustering()
  • Implemented conditional pmax() application to avoid unnecessary log-likelihood inflation
  • Applied numerical correction only when NaN/Inf values are detected
• High-performance polychoric correlation computation
  • Implemented C++ acceleration for polychoric correlation calculations
  • Achieved significant speed improvements over R-based implementation
• Improved Array-type plot visualization with enhanced color palette
  • Replaced dull default colors with vibrant, high-contrast color palette
  • Added colorblind-friendly color scheme for better accessibility
  • Binary data (2 categories) now uses black and white for optimal contrast
  • Multi-category data uses enhanced colorblind-accessible palette

exametrika 1.6.2

• Biclustering: Fixed floating-point arithmetic errors causing NaN results

exametrika 1.6.1 on Aug 26, 2025

• Biclustering: Fixed improper handling of missing values

exametrika 1.6.0 on Aug 12, 2025

• Biculustring.norminal is available!
• Biclustering.ordinal is available!
• New function GridSerch() for grid search optimization of model parameters
• Bugfix: Fix output typos(class/rank)
• Added duplicate ID validation to dataFormat()
• Bugfix: Fix ID column detection in dataFormat()
• Bugfix: Fix stanine division error when unable to split data

exameterika 1.5.2 on March 29, 2025

• Bugfix: Fix output typos(TestStatisticsFunction,GRMs)

exameterika 1.5.1 on March 8, 2025

• Field analysis for Biclustering is included in the Biclustering() function
• Class/Rank Reference Vector plot is now available.
• Bug Fix for polychoric correlations

exametrika 1.5.0 on March 5, 2025

• New function GRM is available!

exametrika 1.4.4 on March 3, 2025

• In Exametrika 1.4.1, bug fixes were made.
• In 1.4.2, it became possible to calculate polychoric correlation and polyserial correlation.
• In 1.4.3, item analysis for polytomous items became available.
• In 1.4.4, we renamed “ICC” to “IRF,” although they refer to the same concept (Item Characteristic Curves and Item Response Functions are interchangeable terms). The function will interpret “ICC” input as “IRF” automatically. Additionally, Test Response Function (TRF) output was also made available.

exametrika 1.4.0 on Feb 25, 2025

• New function LRA() now supports rated data
• Hex icon available

exametrika 1.3.0 on Feb 11, 2025

• Added implementation of latent rank model for ordinal scale data

• New function LRA() now supports ordinal response data

  • Added visualization methods for ordinal scale analysis:
    • Score frequency with rank thresholds (ScoreFreq)
    • Score-rank probability heatmap (ScoreRank)
    • Item category boundary reference (ICBR)
    • Item category response profile (ICRP)

• Bug fixes and improvements

• Standardized terminology: unified the usage of “class” and “rank” throughout the package

• Various minor bug fixes

Exametrika 1.2.0 on Jan 30, 2025.

• Improved numerical stability for model estimation
• Bug fixes for log-likelihood calculation

Exametrika 1.1.0 on Oct 30, 2024.

• Added support for polytomous response data

Exametrika 1.0.2 on Aug 17, 2024.

• Bug fix for Issue #12

Exametrika 1.0.1 on July 31, 2024.

• Bug fix for Item Total Correlation
• Bug fix for Fit indices
• New function called ItemStatistics

Exametrika 1.0.0 on June 9, 2024.

• Initial Release

Exametrika 0.11.5 on Mar 30, 2024.

• Bug fix for plot labels for TRP/LRD

Exametrika 0.11.4 on Jan 27, 2024.

• Bug fix for LCD/LRD for IRM

Exametrika 0.11.3 on December 15, 2023.

• Bug fix for item information curve

Exametrika 0.11.2 on October 27, 2023.

• Plot manual update

Exametrika 0.11.1 on October 27, 2023.

• All model tested by testthat environment

Exametrika 0.11.0 on October 26, 2023.

• Added BINET model

Exametrika 0.10.0 on October 18, 2023.

• Added LDB model

Exametrika 0.9.0 on October 17, 2023.

• Added Structure Learning for LDLRA using PBIL
• Added LDLRA model

Exametrika 0.8.1 on October 10, 2023.

• Added Structure Learning for BMN with simple GA and PBIL model

Exametrika 0.8.0 on October 4, 2023.

• Added BNM model

Exametrika 0.7.0 on October 4, 2023.

• Added IRM model

Exametrika 0.6.1

• Added Q3 matrix output to the IRT function