The Effect of Small Sample Size on Measurement Equivalence of Psychometric Questionnaires in MIMIC Model: A Simulation Study

Evaluating measurement equivalence (also known as differential item functioning (DIF)) is an important part of the process of validating psychometric questionnaires. This study aimed at evaluating the multiple indicators multiple causes (MIMIC) model for DIF detection when latent construct distribution is nonnormal and the focal group sample size is small. In this simulation-based study, Type I error rates and power of MIMIC model for detecting uniform-DIF were investigated under different combinations of reference to focal group sample size ratio, magnitude of the uniform-DIF effect, scale length, the number of response categories, and latent trait distribution. Moderate and high skewness in the latent trait distribution led to a decrease of 0.33% and 0.47% power of MIMIC model for detecting uniform-DIF, respectively. The findings indicated that, by increasing the scale length, the number of response categories and magnitude DIF improved the power of MIMIC model, by 3.47%, 4.83%, and 20.35%, respectively; it also decreased Type I error of MIMIC approach by 2.81%, 5.66%, and 0.04%, respectively. This study revealed that power of MIMIC model was at an acceptable level when latent trait distributions were skewed. However, empirical Type I error rate was slightly greater than nominal significance level. Consequently, the MIMIC was recommended for detection of uniform-DIF when latent construct distribution is nonnormal and the focal group sample size is small.