Using Contrasts

This vignette demonstrates the use of contrasts in the pinSearch() function based on a real data set.

Load Data

data(lui_sim)

Descriptive Statistics

summary(lui_sim)
#>      class1          class2          class3          class4     
#>  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
#>  1st Qu.:2.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:1.000  
#>  Median :2.000   Median :2.000   Median :2.000   Median :1.000  
#>  Mean   :1.779   Mean   :1.577   Mean   :1.703   Mean   :1.432  
#>  3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000  
#>  Max.   :2.000   Max.   :2.000   Max.   :2.000   Max.   :2.000  
#>      class5          class6          class7          class8         class9     
#>  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00   Min.   :1.000  
#>  1st Qu.:1.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:1.00   1st Qu.:1.000  
#>  Median :1.000   Median :1.000   Median :2.000   Median :2.00   Median :2.000  
#>  Mean   :1.379   Mean   :1.223   Mean   :1.655   Mean   :1.58   Mean   :1.638  
#>  3rd Qu.:2.000   3rd Qu.:1.000   3rd Qu.:2.000   3rd Qu.:2.00   3rd Qu.:2.000  
#>  Max.   :2.000   Max.   :2.000   Max.   :2.000   Max.   :2.00   Max.   :2.000  
#>     class10         class11         class12         class13     
#>  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.000  
#>  1st Qu.:1.000   1st Qu.:1.000   1st Qu.:1.000   1st Qu.:1.000  
#>  Median :2.000   Median :2.000   Median :2.000   Median :1.000  
#>  Mean   :1.513   Mean   :1.722   Mean   :1.653   Mean   :1.356  
#>  3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:2.000  
#>  Max.   :2.000   Max.   :2.000   Max.   :2.000   Max.   :2.000  
#>     class14         class15          group      
#>  Min.   :1.000   Min.   :1.000   Min.   :1.000  
#>  1st Qu.:1.000   1st Qu.:1.000   1st Qu.:2.000  
#>  Median :2.000   Median :1.000   Median :4.000  
#>  Mean   :1.742   Mean   :1.436   Mean   :3.615  
#>  3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:5.000  
#>  Max.   :2.000   Max.   :2.000   Max.   :6.000

Specification search

Configural invariance

config_mod <- "
f1 =~ class1 + class2 + class3 + class4 + class5 + class6 + 
      class7 + class8 + class9 + class10 + class11 + class12 + 
      class13 + class14 + class15
"
config_fit <- cfa(config_mod, data = lui_sim, group = "group", ordered = TRUE)
# Release covariance between class1 and class2
config_fit2 <- update(config_fit, c(config_mod, "class1 ~~ class2"))
anova(config_fit, config_fit2)
#> 
#> Scaled and Shifted Chi-Squared Difference Test (method = "satorra.2000")
#> 
#> lavaan->lavTestLRT():  
#>    lavaan NOTE: The "Chisq" column contains standard test statistics, not the 
#>    robust test that should be reported per model. A robust difference test is 
#>    a function of two standard (not robust) statistics.
#> 
#>              Df AIC BIC  Chisq Chisq diff  RMSEA Df diff Pr(>Chisq)    
#> config_fit2 534         354.80                                         
#> config_fit  540         411.35     36.784 0.2357       6   1.94e-06 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Forward search

knitr::kable(ps[[2]])

group	lhs	rhs	type
6	f1	class3	loadings
6	f1	class6	loadings
2	f1	class15	loadings
6	f1	class8	loadings
1	f1	class13	loadings
2	f1	class11	loadings
4	f1	class7	loadings
4	f1	class4	loadings
5	f1	class5	loadings
2	f1	class14	loadings
1	f1	class3	loadings
3	f1	class9	loadings
2	f1	class5	loadings
5	f1	class6	loadings
5	f1	class15	loadings
4	f1	class8	loadings
1	f1	class12	loadings
2	f1	class8	loadings
4	class14	t1	thresholds
3	class3	t1	thresholds
2	class9	t1	thresholds
5	class8	t1	thresholds
2	class10	t1	thresholds
2	class12	t1	thresholds
1	class10	t1	thresholds
4	class1	t1	thresholds
1	class15	t1	thresholds
4	class2	t1	thresholds
3	class8	t1	thresholds

Effect Size

# Obtain fmacs effect size
(f_omni <- pin_effsize(ps[[1]]))
#>       class1-f1 class2-f1 class3-f1  class4-f1  class5-f1 class6-f1  class7-f1
#> fmacs 0.1199234 0.1105238 0.2381024 0.09092262 0.04957459 0.1858849 0.09464019
#>       class8-f1 class9-f1 class10-f1 class11-f1 class12-f1 class13-f1
#> fmacs 0.1744948 0.1149935   0.126812  0.0353763  0.1087859  0.0708557
#>       class14-f1 class15-f1
#> fmacs  0.1860244   0.142588
# fmacs by gender
(f_gender <- pin_effsize(ps[[1]], group_factor = c(1, 1, 1, 2, 2, 2)))
#>        class1-f1  class2-f1 class3-f1  class4-f1  class5-f1  class6-f1
#> fmacs 0.03579041 0.03298516 0.1443592 0.02713531 0.03031336 0.04858438
#>       class7-f1  class8-f1 class9-f1 class10-f1 class11-f1 class12-f1
#> fmacs 0.0282448 0.03521963  0.083309 0.04836829 0.01813981 0.01888187
#>       class13-f1 class14-f1 class15-f1
#> fmacs 0.02702558 0.03136801 0.04376062
# fmacs by ethnicity
(f_eth <- pin_effsize(ps[[1]], group_factor = c(1, 2, 3, 1, 2, 3)))
#>       class1-f1  class2-f1 class3-f1  class4-f1  class5-f1 class6-f1  class7-f1
#> fmacs 0.0580995 0.05354566 0.1249914 0.04404945 0.01246479 0.1131955 0.04585051
#>        class8-f1  class9-f1 class10-f1 class11-f1 class12-f1 class13-f1
#> fmacs 0.08975193 0.07570749 0.07851749 0.02558737 0.08675476 0.04387133
#>       class14-f1 class15-f1
#> fmacs 0.07596325  0.1148166
# interaction (using contrast matrix)
contr <- local({
    gen <- factor(c("F", "M"))
    contrasts(gen) <- contr.sum(length(gen))
    eth <- factor(1:3)
    contrasts(eth) <- contr.sum(length(eth))
    model.matrix(~ gen * eth, data = expand.grid(eth = eth, gen = gen))
})
(f_int <- pin_effsize(ps[[1]], contrast = contr[, 5:6, drop = FALSE]))
#>       class1-f1  class2-f1 class3-f1  class4-f1  class5-f1 class6-f1  class7-f1
#> fmacs 0.0580995 0.05354566 0.1641827 0.04404945 0.04276027 0.1131955 0.04585051
#>       class8-f1  class9-f1 class10-f1 class11-f1 class12-f1 class13-f1
#> fmacs 0.1310042 0.07570749 0.07851749 0.02558737 0.08675476 0.04387133
#>       class14-f1 class15-f1
#> fmacs  0.1208021 0.07983613

# Render as table
item_names <- gsub("class", replacement = "Item ", colnames(f_omni)) |>
    gsub(pattern = "-f1", replacement = "")
t(rbind(f_omni, f_gender, f_eth, f_int)) |>
    as.data.frame() |>
    `dimnames<-`(list(
        item_names,
        c("Overall", "Gender", "Ethnicity", "Gender x Ethnicity")
    )) |>
    knitr::kable(digits = 2, caption = "$f_\\text{MACS}$ effect sizes")

\(f_\text{MACS}\) effect sizes
	Overall	Gender	Ethnicity	Gender x Ethnicity
Item 1	0.12	0.04	0.06	0.06
Item 2	0.11	0.03	0.05	0.05
Item 3	0.24	0.14	0.12	0.16
Item 4	0.09	0.03	0.04	0.04
Item 5	0.05	0.03	0.01	0.04
Item 6	0.19	0.05	0.11	0.11
Item 7	0.09	0.03	0.05	0.05
Item 8	0.17	0.04	0.09	0.13
Item 9	0.11	0.08	0.08	0.08
Item 10	0.13	0.05	0.08	0.08
Item 11	0.04	0.02	0.03	0.03
Item 12	0.11	0.02	0.09	0.09
Item 13	0.07	0.03	0.04	0.04
Item 14	0.19	0.03	0.08	0.12
Item 15	0.14	0.04	0.11	0.08

Using Contrasts

Mark Lai

2026-08-26

Load Data

Descriptive Statistics

Specification search

Configural invariance

Effect Size