Assessing measurement invariance of ordinal indicators in cross-national research

Abstract

Meaningful cross-national comparisons of scales require that the indicators used to operationalize the underlying constructs (e.g., attitudes, values) are measurement invariant across countries. Linear multi-group confirmatory factor (MGCF) analysis is arguably the most common method to assess measurement invariance. Although, strictly speaking, this method assumes continuous variables, in empirical studies typically a covariance matrix for ordinal items (e.g., Likert-type scales) is analyzed. Simulation studies have indeed shown that single-group confirmatory factor analysis is relatively robust against violating the assumption of continuous variables if categorization is based on at least five answer categories and the data does not show excessive skewness and/or kurtosis. New simulation evidence, however, has revealed that these results do not necessarily carry over to multiple groups. These insights and the availability of robust WLS estimators which are considerably less demanding with respect to the required sample size than the full WLS approach strongly advocate the use of appropriate estimation methods for ordinally scaled variables. This paper contributes to comparative cross-cultural research by proposing a procedure for testing measurement equivalence based on the MGCF model for ordinal indicators. The procedure is applied to a cross-national study on attitudes towards a specific advertisement.