Measurement invariance is an important assumption in a test. When it is violated for a variable, the variable could be biased against one or more groups in a test. Confirmatory factor analysis (CFA) and item response theory (IRT) are widely used for testing measurement invariance, and measurement invariance is also termed by differential item functioning (DIF) in IRT. But CFA is not adequately comparable to DIF analysis under IRT because CFA assumes that observed variables are continuous and normally distributed. The CFA for ordered-categorical variables (CCFA) with a threshold structure is an extension of CFA and for analyzing ordered-categorical data (i.e., DIF).
This paper was used multiple-group categorical CFA (MCCFA) and IRT with the backward likelihood ratio (LR) test under three strategies for detecting measurement invariance through a series of simulation studies. The results show that, (1) IRT showed superiority to MCCFA when considering both true positive and false positive rates; (2) the Oort adjustment of critical values could resolve the problem of the false positive rates in the backward LR test.
Questions
1. Is the simulation result can be generalized to long test length? Because six-item test length and one non-invariant item only used in the study.
2. Based on Equation 11 (page 225), how to prove that the false positive and true positive rates can be improved by adopted the adjusted chi-square critical value?