Factor-analyzing Likert-scale data under the assumption of multivariate normality complicates a meaningful comparison of observed groups or latent classes

Treating Likert scale data as continuous outcomes in confirmatory factor analysis violates the assumption of multivariate normality. Given certain requirements pertaining to the number of categories, skewness, size of the factor loadings, etc., it seems nevertheless possible to recover true parameter values if the data stem from a single homogenous population. It is shown in a multi-group and a latent class context that analyzing Likert data under the assumption of multi-variate normality may distort the factor structure differently across groups or classes. Hence, investigating measurement invariance, which is a necessary requirement for a meaningful comparison of observed groups or latent classes, is problematic. Analyzing subscale scores computed from Likert items does not necessarily solve the problem. Based on a power study, some conditions are established to obtain acceptable results. Questionnaires designed to measure latent variables such as personality factors or attitudes typically use Likert scales as a response format. In response to statements such as ‘does the student yell at others’, participants are asked to choose one of a given number of ordered response categories which run for instance from ‘almost never’ to ‘almost always’. In case the interest of a study focuses on the latent variables underlying the items, data analysis will include fitting latent variable models such as confirmatory factor models. A special type of factor models, growth curve models, are used for the analysis of longitudinal data. Data arising from Likert-type items are often analyzed as multivariate normal outcomes in these models although the data are in fact ordered categorical. The present article focuses on analysis of ordered categorical outcomes from observed groups or latent classes while incorrectly assuming multivariate normality. The main difference between multivariate normal and ordered categorical outcomes lies in parameters that govern the distribution of the items. The distribution of multivariate normal outcomes is completely specified by the item means and covariances. For ordered categorical items, information concerning the means and covariances is not sufficient.