Multidimensional Factor-Analysis-Based Procedures for Assessing Scalability in Personality Measurement

Most personality tests are made up of Likert-type items and analyzed by means of factor analysis (FA). In this type of application, the fit of the model at the level of individual respondents is almost never assessed. This article proposes procedures for assessing individual fit (scalability). The procedures are intended for the analysis of multitrait personality questionnaires, and based on the multiple FA model. A general assessment procedure is described, and 2 multidimensional scalability indexes that use the chi-square and normal distribution are proposed. These indexes are derived both as residual measures and as likelihood-based person-fit measures, and their relations with some item-response, theory-based measures is discussed. The indexes are proposed mainly as first-step exploratory devices, and procedures for obtaining further information about the possible causes of misfit are also discussed. The behavior of the indexes is assessed in simulation studies, and the general procedure is illustrated by means of an empirical example.