Sample Size and Tests of Measurement Invariance

Though widely used, confirmatory factor analysis tests of measurement invariance are not well understood. Results of a simulation study indicated that the power of invariance tests varied widely depending on sample size, factor over-determination, and item communality. Accurate estimation of parameters provide a possible explanation for these results. Measurement equivalence/invariance (ME/I) can be thought of as operations yielding measures of the same attribute under different conditions (Horn & McArdle, 1992). These different conditions include stability of measurement over time (Golembiewski, Billingsley, & Yeager, 1975), across different populations (e.g., cultures; Riordan & Vandenberg, 1994), different mediums of measurement administration (e.g., web-based survey administration verses paper and pencil measures; Taris, Bok, & Meijer, 1998), or different rater groups in multi