Why Ordinal Variables Can (Almost) Always be Treated as Continuous Variables: Clarifying Assumptions of Robust Continuous and Ordinal Factor Analysis Estimation Methods

Abstract

The analysis of factor structures is one of the most critical psychometric applications. Frequently, variables (i.e., items or indicators) resulting from questionnaires using ordinal items with 2 to 7 categories are used. There are plenty of articles that recommend treating ordinal variables in a factor analysis by default as ordinal and not as continuous imposing a multivariate normal distribution assumption. In this article, we critically reflect that the reasoning behind such suggestions is flawed. In our view, findings from simulation studies cannot tell about the right modeling strategy of ordinal variables in factor analysis. Moreover, it is argued that ordinal factor models impose a normality assumption for underlying continuous variables, which might also often be false in empirical applications. However, researchers seldom opt for these much-needed, more flexible modeling strategies if the ordinal nature variables would seriously be modeled in factor analysis. Finally, the consequences of modeling choices for validity, reliability, measurement invariance, and the assessment of global model fit are discussed.

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“…within the model specification [ 59 ]. We treated all variables as continuous in the models, as sum scores were used for each measure [ 65 , 66 ]. All models were estimated using maximum likelihood (ML) estimation to account for nonnormality and nonindependence of data [ 58 , 67 ].…”

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“…In all analyzes, maximum likelihood estimation with robust standard errors (MLR) and the Yaun-Bentler version of the scaled chi-square statistic was used (Yuan & Bentler, 2000). The choice of this estimation method was guided, on the one hand, by previous validation studies (Bear et al, 2011, 2016; Bear, Yang, Mantz, et al, 2014), and on the other hand by methodological analyzes showing that Likert-type items with four response categories can be treated as continuous (Robitzsch, 2020).…”