DIF Detection With Zero-Inflation Under the Factor Mixture Modeling Framework

Response data containing an excessive number of zeros are referred to as zero-inflated data. When differential item functioning (DIF) detection is of interest, zero-inflation can attenuate DIF effects in the total sample and lead to underdetection of DIF items. The current study presents a DIF detection procedure for response data with excess zeros due to the existence of unobserved heterogeneous subgroups. The suggested procedure utilizes the factor mixture modeling (FMM) with MIMIC (multiple-indicator multiple-cause) to address the compromised DIF detection power via the estimation of latent classes. A Monte Carlo simulation was conducted to evaluate the suggested procedure in comparison to the well-known likelihood ratio (LR) DIF test. Our simulation study results indicated the superiority of FMM over the LR DIF test in terms of detection power and illustrated the importance of accounting for latent heterogeneity in zero-inflated data. The empirical data analysis results further supported the use of FMM by flagging additional DIF items over and above the LR test.

Bifactor Model Is Not the Best-Fitting Model for Self-Esteem: Investigation With a Novel Technique

In the measurement of self-esteem, previous research assumes that all respondents are qualitatively similar. The assumption has not been adequately tested. The current study examines its validity using factor mixture modeling. Results reveal two qualitatively distinct classes: the first provides more consistent responses to positive self-esteem items than the second. The correlations between positive and negative self-esteem suggest that self-esteem is essentially unidimensional in the first class but bidimensional in the second. Furthermore, those with high self-esteem are more likely to belong to the first class; those with low self-esteem are more likely to belong to the second class. The observed dimensionality of self-esteem depends on a person’s level on the trait. Finally, we found that the two-class solution fits the data much better than a simple one-class, two-factor solution or a bifactor solution. Psychometric researchers should no longer ignore the possible existence of qualitatively distinct groups in an underlying population. We include M plus syntax together with a detailed explanation for researchers to conduct similar investigations on constructs of interest.

Testing Measurement Invariance Across Unobserved Groups: The Role of Covariates in Factor Mixture Modeling

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed.