Package {lillardhaz}

lillardhaz: Simultaneous-Equations Hazard/Probit Models

Description

Fits two-equation simultaneous models in the style of Lillard (1993): a pair of processes – each a binary probit outcome or a continuous-time hazard duration – linked through a single correlation parameter between their underlying error terms, estimated jointly by maximum likelihood via a Gaussian copula. See fit_lillardhaz.

Author(s)

Maintainer: Nobutaka Fukuda nobutaka.fukuda@tohoku.ac.jp

Authors:

• Nobutaka Fukuda nobutaka.fukuda@tohoku.ac.jp

See Also

Useful links:

• https://github.com/nobifukuda/lillardhaz

• Report bugs at https://github.com/nobifukuda/lillardhaz/issues

Fit a Lillard-style simultaneous-equations hazard/probit model

Description

Fits a two-equation simultaneous model in the style of Lillard (1993): a pair of processes, each either a binary probit outcome or a continuous- time hazard duration, linked through a single correlation parameter between their underlying error terms and estimated jointly by maximum likelihood via a Gaussian copula.

Usage

fit_lillardhaz(
  eq1,
  eq2,
  data,
  y1,
  d1 = NULL,
  y2,
  d2,
  x1 = character(0),
  x2 = character(0),
  nodes1 = NULL,
  nodes2 = NULL,
  corr = TRUE,
  start = NULL,
  method = "BFGS"
)

Arguments

Value

An object of class "lillardhaz": a list with components

coefficients

named numeric vector of maximum-likelihood estimates (equation 1 and 2 location coefficients, ancillary parameters such as ln_sigma or piecewise-Gompertz slopes, and atanh_rho if corr = TRUE).

se

standard errors from the inverse negative Hessian (NA if the Hessian is singular).

loglik

maximized log-likelihood.

rho, rho_se

estimated copula correlation between the two equations' error terms and its delta-method standard error (0 and NA when corr = FALSE).

fit

the underlying maxLik object.

eq1type, eq2type, nodes1, nodes2, corr, x1, x2, y1name, y2name

the model specification.

n

number of observations.

call

the matched call.

Methods for print, summary and predict are available.

Examples

set.seed(1)
n <- 2000
x1 <- rnorm(n); x2 <- rbinom(n, 1, 0.5)
t1 <- exp(1 - 0.3 * x1 + 0.5 * rnorm(n))
c1 <- -log(runif(n)) / 0.05
t2 <- exp(0.6 + 0.4 * x2 + 0.6 * rnorm(n))
c2 <- -log(runif(n)) / 0.05
d <- data.frame(
  time1 = pmin(t1, c1), event1 = as.integer(t1 <= c1),
  time2 = pmin(t2, c2), event2 = as.integer(t2 <= c2),
  x1 = x1, x2 = x2
)
fit <- fit_lillardhaz("lognormal", "lognormal", d,
                       y1 = "time1", d1 = "event1", y2 = "time2", d2 = "event2",
                       x1 = "x1", x2 = "x2")
summary(fit)
head(predict(fit, type = "surv2"))

Predicted survival/density/index from a fitted lillardhaz model

Description

Predicted survival/density/index from a fitted lillardhaz model

Usage

## S3 method for class 'lillardhaz'
predict(object, newdata, type = "surv2", ...)

Arguments

Value

A numeric vector with one element per row of newdata, evaluated at the estimated coefficients. Its meaning depends on type:

"xb1", "xb2"

the linear location index x'\beta of equation 1 or 2 (for a log-normal equation, the mean of log duration; for a piecewise-Gompertz equation, the log of the proportional hazard shift).

"pr1"

the predicted probability that the binary outcome of equation 1 equals 1, \Phi(x'\beta); only available when eq1 = "probit".

"surv1", "surv2"

the marginal survival probability S(t), a value in [0, 1], of equation 1 or 2 evaluated at the observed duration in newdata (variable y1 or y2 used in the fit).

"dens1", "dens2"

the marginal density f(t) of equation 1 or 2 evaluated at that duration.

The survival and density predictions are marginal (per equation) and do not condition on the other equation's outcome.