Dimensionality assesment with factor analysis methods

Researchers in the social and behavioral sciences often collect scores on a set of items, to measure unobservable (i.e. latent) variables. The latter may express, for example, beliefs, traits, attitudes or skills. The dimensionality of a set of items is the number of latent variables. This number is important information in scale construction and scale evaluation. In this dissertation approaches to assess the dimensionality of a set of items with factor analysis methods are investigated. Within the factor analysis framework the relation between a large amount of observed items is described by a smaller amount of latent variables (i.e. factors). The classical factor analysis involves linear relations between variables with multivariate normally distributed continuous item scores. I examined to what extent more elaborated factor analysis methods are suited, and which procedures have to be applied, to determine the dimensionality in situations that are often encountered in practice. Those cases go beyond the classical case. Examples are discrete item scores (e.g., Likert scales ranging from “definitely does not apply” to “definitely does apply"), nonlinear relations between the items, and data with a hierarchical structure (e.g., data pertaining to different pupils from different schools). Under the conditions studied here, the factor analysis models and associated procedures seemed to be able to handle discrete responses, nonlinear relations, and multilevel structures.