Limited information GOF tests
The lavaan.bingof package provides a set of LIGOF tests for CFA models with binary data. Models estimated using the lavaan.pl package are directly compatible.
library(lavaan.pl)
#> ℹ Loading required package: lavaan
#> This is lavaan 0.6-19
#> lavaan is FREE software! Please report any bugs.
#>
#> ── Conflicts ─────────────────────────────────────────── lavaan.pl 0.1.0.9002 ──
#> ✖ lavaan.pl::cfa() masks lavaan::cfa()
library(lavaan.bingof)
(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 rows
mod <- "eta =~ y1 + y2 + y3 + y4 + y5"
fit <- cfa(mod, dat, std.lv = TRUE)
expect_true(inherits(fit, "plFAlavaan"))
#> ----- PASSED : <-->
#> call| expect_true(inherits(fit, "plFAlavaan"))
# Test statistics
all_tests(fit)
#> # A tibble: 6 × 6
#> X2 df name pval Xi_rank S
#> <dbl> <dbl> <chr> <dbl> <int> <int>
#> 1 2.82 5 Wald 0.728 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 15As a comparison, we can look at the output from using the
cfa() function in the lavaan package.
fit1 <- lavaan.pl::cfa(mod, dat, std.lv = TRUE)
fit2 <- lavaan::cfa(mod, dat, std.lv = TRUE, estimator = "PML")
# Test equality of coefficients and standard errors
expect_equal(coef(fit1), coef(fit2), tolerance = 1e-5)
#> ----- PASSED : <-->
#> call| expect_equal(coef(fit1), coef(fit2), tolerance = 1e-05)
expect_equal(fit1@Fit@se, fit2@Fit@se, tolerance = 1e-5)
#> ----- FAILED[data]: <-->
#> call| expect_equal(fit1@Fit@se, fit2@Fit@se, tolerance = 1e-05)
#> diff| Mean relative difference: 0.03419516
# Test equality of test statistics and p-values
c(
"Wald_test",
"Wald_vcovf_test",
"Wald_diag_test",
"Pearson_test",
"RSS_test",
"Multn_test"
) |>
set_names() |>
map(.f = function(x) {
out1 <- do.call(x, list(fit1))
out2 <- do.call(x, list(fit2))
expect_equal(out1, out2, tolerance = 5e-3)
})
#> $Wald_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)
#>
#> $Wald_vcovf_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)
#>
#> $Wald_diag_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)
#>
#> $Pearson_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)
#>
#> $RSS_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)
#>
#> $Multn_test
#> ----- PASSED : <-->
#> call| .f(.x[[i]], ...)Testing differences
information_matrix <- function(fit, type) {
lavargs <- list(
lavmodel = fit@Model,
lavsamplestats = fit@SampleStats,
lavdata = fit@Data,
lavoptions = fit@Options,
lavcache = fit@Cache,
inverted = FALSE
)
if (type == "observed")
out <- do.call("lav_model_information_observed", lavargs,
envir = asNamespace("lavaan"))
else if (type == "expected")
out <- do.call("lav_model_information_expected", lavargs,
envir = asNamespace("lavaan"))
else if (type == "first.order")
out <- do.call("lav_model_information_firstorder", lavargs,
envir = asNamespace("lavaan"))
else stop("Invalid type")
return(out)
}Sensitivity (inverted) matrix
# From lavaan.pl
Hinv1 <- with(fit1@external, computeVar(lavaan.pl, D)$invH[idx_plFA2lav, idx_plFA2lav])
fit1 <- cfa(mod, dat, std.lv = TRUE, estimator.args = list(computevar_numderiv = TRUE), verbose = TRUE)
#> - Computing frequencies...
#> - Initialised at user-supplied values.
#> - Optimising with ucminf...
#> Done! (0.01 secs)
#> - Computing Delta...
#> Done! (0 secs)
#> - Computing H numerically...
#> Done! (0.01 secs)
#> - Estimating J...
#> Done! (0.02 secs)
#> - Inverting H...
#> - Computing the variances...
#> Done! (0.02 secs)
Hinv2 <- with(fit1@external, computeVar(lavaan.pl, D)$invH[idx_plFA2lav, idx_plFA2lav])
Hinv3 <- solve(information_matrix(fit1, "observed"))
expect_equal(Hinv1, Hinv2, tolerance = 1e-5) # ucminf vs numderiv
#> ----- PASSED : <-->
#> call| expect_equal(Hinv1, Hinv2, tolerance = 1e-05)
expect_equal(Hinv1, Hinv3, tolerance = 1e-5) # ucminf vs lavaan
#> ----- FAILED[data]: <-->
#> call| expect_equal(Hinv1, Hinv3, tolerance = 1e-05)
#> diff| Mean relative difference: 0.1720939
expect_equal(Hinv2, Hinv3, tolerance = 1e-5) # numderiv vs lavaan
#> ----- FAILED[data]: <-->
#> call| expect_equal(Hinv2, Hinv3, tolerance = 1e-05)
#> diff| Mean relative difference: 0.1720939Variability matrix
# From lavaan.pl
J1 <- with(fit1@external, computeVar(lavaan.pl, D)$J[idx_plFA2lav, idx_plFA2lav])
J2 <- information_matrix(fit1, "first.order")
expect_equal(J1, J2, tolerance = 1e-5) # ucminf vs numderiv
#> ----- PASSED : <-->
#> call| expect_equal(J1, J2, tolerance = 1e-05)Session information
sessioninfo::session_info()
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