Dimensionality assessment of ordinal variable An evaluation of classic and modern methods

Résumé

ABSTRACT The aims of this study are to first evaluate the performance of factor retention criteria in the dimensionality assessment of ordinal variables, and, second, to offer clear and easy-to- follow guidelines for researchers who work with ordinal-level data in practice. The determination of the number of factors is considered to be a crucial decision within the context of exploratory factor analysis (EFA) and structural equation modeling (SEM), but unfortunately, has been largely overlooked as it pertains to ordinal observed variables, which are typically encountered in the social and behavioral sciences. The current study seeks to address this issue by taking an in-depth look at the performance of three ¿classic¿ factor retention criteria (the Minimum Average Partial method [MAP], Parallel Analysis [PA], and the eigenvalue-greater-than-1 rule [K1]), as well as four fit indices (CFI, TLI, RMSEA, and SRMR), in the dimensionality assessment of ordinal variables. In order to broadly evaluate the accuracy of the factor retention criteria, a comprehensive set of factors was systematically manipulated using Monte Carlo methods, including the factor loading, number of variables per factor, number of factors, factor correlation, sample size, number of response categories, level of skewness, extraction method, and type of correlation matrix. The results showed that PA with principal component analysis, polychoric correlations, and the mean eigenvalue criteria, along with the CFI and TLI indices at a cutoff value of 0.95, perform adequately in determining the number of factors with ordinal variables. The other four methods, however, could not be recommended due to the strong levels of bias they exhibited. The performances of the factor retention criteria are put into theoretical context and guidelines are offered on how to assess the dimensionality of ordinal-level data in practice.