Random Permutation Testing Applied to Measurement Invariance Testing with Ordered-Categorical Indicators. Issue 4 (4th July 2018)

• Record Type: Journal Article
• Authors: Kite, Benjamin A.; Jorgensen, Terrence D.; Chen, Po-Yi
• Is Part Of: Structural equation modeling. Volume 25:Issue 4(2018)
• Page Start: 573
• Page End: 587
• Publication Date: 2018-07-04
• Subjects: measurment invariance -- permutation testing -- categorical indicators; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2017.1421467
• Languages: English
• ISSNs: 1070-5511

Abstract

Abstract : We describe and evaluate a random permutation test of measurement invariance with ordered-categorical data. To calculate a p -value for the observed (∆) χ 2, an empirical reference distribution is built by repeatedly shuffling the grouping variable, then saving the χ 2 from a configural model, or the ∆ χ 2 between configural and scalar-invariance models, fitted to each permuted dataset. The current gold standard in this context is a robust mean- and variance-adjusted ∆ χ 2 test proposed by Satorra (2000), which yields inflated Type I errors, particularly when thresholds are asymmetric, unless samples sizes are quite large (Bandalos, 2014; Sass et al., 2014). In a Monte Carlo simulation, we compare permutation to three implementations of Satorra's robust χ 2 across a variety of conditions evaluating configural and scalar invariance. Results suggest permutation can better control Type I error rates while providing comparable power under conditions that the standard robust test yields inflated errors.