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The Effect of Cross-loading on Measurement Equivalence of Psychometric Multidimensional Questionnaires in MIMIC Model: a Simulation Study

Jamshid Jamali, Seyyed Mohammad Taghi Ayatollahi, Peyman Jafari.

Abstract
Introduction: In recent years, Multiple Indicators Multiple Causes (MIMIC) model has been widely used to assess measurement in variance, called Differential Item Functioning (DIF) analyses, in psychological and medical studies. Aim: This simulation study aimed at assessing the effect of sample size, scale length, and magnitude of the uniform-DIF on detecting uniform-DIF with the MIMIC model when it has cross-loading in multidimensional scales. Material and Methods: In this Monte Carlo simulation study, we calculated power, Type I error rates, the bias of parameters estimation, Coverage Probability (CP), and Convergence Rate (CR) was used to assess the performance of the MIMIC model. The means of RMSEA, SRMR, CFI, and TLI, as indices of the goodness-of-fit for the MIMIC model, were computed across 1000 replications for each simulation condition. Result: Approximately, in all scenarios simulated, the bias of DIF parameters estimation was negligible. The existence of cross-loading caused a decrease of approximately 11.8% in the power and increase of 0.04-unit in bias parameter estimation. By increasing the relationship between dimensions, the power and CP of MIMIC model decreased, however, bias and CR were increased. In all scenarios that were performed in this study, all goodness-of-fit indices were at an acceptable level. Conclusion: Our results indicated that the performance of the MIMIC model improved, when sample size, the number of items, and the magnitude of DIF increased. When the scale is multidimensional and model have cross-loading, the performance of the MIMIC model becomes questionable.

Key words: Reproducibility of Results, Monte Carlo Method, Psychometrics, Surveys and Questionnaires.



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