This is the accompanying R package for the article
Jamil, H., Moustaki, I., & Skinner, C. (2024). Pairwise likelihood estimation and limited-information goodness-of-fit test statistics for binary factor analysis models under complex survey sampling. British Journal of Mathematical and Statistical Psychology. (to appear)
This package contains the functions to compute the test statistics and conduct simulation studies described in the above manuscript. Currently, the package implements the following tests based on univariate and bivariate residuals of a binary factor analysis model:
| Name | R function | Remarks | |
|---|---|---|---|
| 1 | Wald test | Wald_test() |
Described in Reiser (1996) |
| 2 | Wald test (diagonal) | Wald_diag_test() |
A more efficient Wald test |
| 3 | Wald test (VCOV free) | Wald_vcovf_test() |
Described in Maydeu-Olivares and Joe (2005,2006) |
| 4 | Pearson test | Pearson_test() |
Moment matching approximation |
| 5 | Residual sum of squares | RSS_test() |
Moment matching approximation |
| 6 | Multinomial test | Multn_test() |
Moment matching approximation |
Installation
Install this package from this GitHub repository:
# install.packages("pak")
pak::pkg_install("haziqj/lavaan.bingof")
library(lavaan.bingof) # load packageUsage
There are three main functionalities of this package:
Generate simulated data either from an infinite population or from a finite population using a complex sampling procedure.
Obtain the test statistic values, the degrees of freedom of these chi-square variates, and corresponding -values to determine goodness-of-fit.
Wrap functions 1 and 2 in a convenient way to perform simulation studies for Type I errors and power.
Create a simulated data set of ordinal binary responses
The true parameter values are according to the models specified in the research article.
(dat <- gen_data_bin(n = 1000, seed = 123))
#> # A tibble: 1,000 × 5
#> y1 y2 y3 y4 y5
#> <ord> <ord> <ord> <ord> <ord>
#> 1 1 0 0 1 1
#> 2 1 1 1 1 1
#> 3 1 1 1 0 1
#> 4 1 1 0 1 1
#> 5 1 1 0 1 1
#> 6 1 1 1 1 1
#> 7 1 1 1 1 0
#> 8 1 1 1 1 1
#> 9 1 1 1 1 1
#> 10 1 0 0 1 1
#> # ℹ 990 more rowsObtain the various test statistics and -values
# Fit lavaan model using PML estimation
(mod <- txt_mod(model_no = 1))
#> [1] "eta1 =~ NA*y1 + y2 + y3 + y4 + y5"
fit <- lavaan::sem(mod, dat, std.lv = TRUE, estimator = "PML")
# Test statistics
all_tests(fit)
#> # A tibble: 6 × 6
#> X2 df name pval Xi_rank S
#> <dbl> <dbl> <chr> <dbl> <int> <int>
#> 1 2.81 5 Wald 0.730 14 15
#> 2 2.80 5 WaldVCF 0.730 5 15
#> 3 0.862 3.31 WaldDiag,MM3 0.872 15 15
#> 4 1.86 3.63 Pearson,MM3 0.709 15 15
#> 5 2.30 4.18 RSS,MM3 0.707 15 15
#> 6 1.86 3.62 Multn,MM3 0.708 15 15Test statistics under a complex sampling scheme
# Simulate a two-stage stratified cluster sampling with 50 PSUs sampled per
# stratum, and 1 cluster sampled within each PSU.
(dat <- gen_data_bin_strcl(population = make_population(1), npsu = 50,
seed = 9423))
#> # A tibble: 3,040 × 9
#> type school class wt y1 y2 y3 y4 y5
#> <chr> <chr> <chr> <dbl> <ord> <ord> <ord> <ord> <ord>
#> 1 A A105 A105o 0.651 1 1 1 1 1
#> 2 A A105 A105o 0.651 1 1 1 1 1
#> 3 A A105 A105o 0.651 1 1 1 1 1
#> 4 A A105 A105o 0.651 1 1 1 1 1
#> 5 A A105 A105o 0.651 1 1 0 1 1
#> 6 A A105 A105o 0.651 1 1 1 1 1
#> 7 A A105 A105o 0.651 1 1 0 1 1
#> 8 A A105 A105o 0.651 1 1 1 1 1
#> 9 A A105 A105o 0.651 1 1 1 1 1
#> 10 A A105 A105o 0.651 1 1 1 1 1
#> # ℹ 3,030 more rows
# Fit lavaan model and create survey object
fit0 <- lavaan::sem(mod, dat, std.lv = TRUE, estimator = "PML") # ignore wt
fit1 <- lavaan::sem(mod, dat, std.lv = TRUE, estimator = "PML",
sampling.weights = "wt")
# Compare with and without sampling weights
Wald_test(fit0)
#> X2 df name pval Xi_rank S
#> 1 4.561825 5 Wald 0.4716543 13 15
Wald_test(fit1) # with sampling weights
#> X2 df name pval Xi_rank S
#> 1 3.863999 5 Wald 0.5691583 13 15Simulation wrapper
# Conduct a simulation study based on a 5 factor model (32 repetitions only for
# illustration). Data generated according to a stratified complex sample.
(pc <- parallel::detectCores()) # how many cores do we have?
#> [1] 8
res <- run_ligof_sims(model_no = 1, nsim = pc, ncores = pc - 2, samp = "strat",
simtype = "type1")
#> | | | 0% | |========= | 12% | |================== | 25% | |========================== | 38% | |=================================== | 50% | |============================================ | 62% | |==================================================== | 75% | |============================================================= | 88% | |======================================================================| 100%
res
#>
#> ── LIGOF simulations summary ───────────────────────────────────────────────────
#>
#> Model 1 (1F 5V) using stratified sampling design (n = 1000)
#> • Converged: 8 / 8
#> • Rank deficient: 0 / 8
#> • Significance level: 0.05
#>
#>
#> ============ ============== ============= =========
#> Test name Rejection rate Mean X2 value Mean d.f.
#> ============ ============== ============= =========
#> Wald 0 5.21 5.00
#> WaldVCF 0 5.19 5.00
#> WaldDiag,MM3 0 3.60 3.41
#> Pearson,MM3 0 3.73 3.33
#> RSS,MM3 0 4.33 4.00
#> Multn,MM3 0 3.73 3.33
#> ============ ============== ============= =========