pinSearch: Search for noninvariant parameters across groups.

In marklhc/pinvsearch: Specification search for partial factorial invariance

Search for noninvariant parameters across groups.

Description

The function implements the sequential selection method similar to that discussed in Yoon and Millsap (2007). The function proceeds in the order of metric, scalar (threshold), and strict invariance. In each stage, invariance constraints in all items, and the constraint associated with the biggest test statistic above a predefined threshold is freed, before recomputing the test statistic for the next constraint to free.

Usage

pinSearch(
  config_mod,
  ...,
  type = c("loadings", "intercepts", "thresholds", "residuals", "residual.covariances"),
  inv_test = c("mod", "score", "lrt"),
  sig_level = 0.05,
  control_fdr = FALSE,
  effect_size = FALSE,
  progress = FALSE
)

Arguments

config_mod	Syntax of a configural invariance model to be passed to lavaan::cfa().
...	Additonal arguments passed to lavaan::cfa().
type	Character variable indicating the stage of invariance to be searched. Currently supported options are (a) for continuous indicators, "loadings", "intercepts", "residuals", and "residual.covariances", and (b) "loadings", "thresholds", "residual.covariances", in an increasingly strict order. A stricter model (e.g., "residual.covariances") will have constraints of all previous stages.
inv_test	Character variable indicating the statistical test to be used for specification search. Currently supported options are "mod" for modification index using lavaan::modindices(), "score" for score test statistic using lavaan::lavTestScore(), and (experimental) "lrt" for likelihood ratio test statistic using lavaan::lavTestLRT().
sig_level	Significance level used to determine whether the parameter associated with the highest modification index should be removed. Default is .05.
control_fdr	Logical; whether to use adjust for false discovery rate for multiple testing. If TRUE, the method by Benjamini & Gavrilov (2009) will be used.
effect_size	Logical; whether to compute dmacs (two groups) or fmacs (> two groups) effect size or not (default). This is an experimental feature.
progress	Logical; an experimental feature of showing a progress bar if TRUE. Because the number of steps is unknown until the stopping criteria are reached, the progress bar may be inaccurate.

Details

Note that when an item has a non-invariant loading, the corresponding intercept constraint will automatically be freed, as intercept difference across groups is sensitive to the location of the zero point for the latent variable and the item.

For a particular stage of invariance constraints, the Benjamini & Gavrilov method uses an adjusted alpha level of

iq / [m + 1 - i(1 - q)]

where i is the step index in the search, m is the maximum number of constraints that can be freed, and q is the desirable significance level.

Value

A list of three elements:

• ⁠Partial Invariance Fit⁠: A lavaan::lavaan object containing the final partial invariance model.

• ⁠Non-Invariant Items⁠: A data frame of non-invariant parameters.

• effect_size: Effect size statistics obtained from pin_effsize().

References

Yoon, M., & Millsap, R. E. (2007). Detecting violations of factorial invariance using data-based specification searches: A Monte Carlo study. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 435-463.

Examples

library(lavaan)
library(MASS)
# Simulate random data
set.seed(14) # for reproducible results
mod_ninv <- "f =~ c(1, 0.8, .6)*y1 + c(0.8, 1.2, 1.0)*y2"
mod_inv <- paste0("1*y", 3:6, collapse = " + ")
sim_mod <- paste(
    paste(mod_ninv, "+", mod_inv),
    "f ~~ c(1, 1.3, 1.5)*f
     f ~ c(0, 0.5, 1.0)*1
     y1 ~ c(0, 0.3, 0)*1
     y3 ~ c(0.3, 0, -0.3)*1
     y1 ~~ c(1, .5, 1)*y1",
    sep = "\n"
)
# The uniqueness of each item is assumed to be 1.0
dat_sim <- simulateData(sim_mod, sample.nobs = c(100, 100, 100))
# Fit configural model:
sam_config <- paste(
    paste0("f =~ ", paste0("y", 1:6, collapse = " + "))
)
pinSearch(sam_config,
    data = dat_sim, group = "group",
    type = "intercepts"
)

marklhc/pinvsearch documentation built on June 11, 2025, 6:43 a.m.