Factor-analytic procedures for assessing response pattern scalability

This paper proposes procedures for assessing the fit of a psychometric model at the level of the individual respondent. The procedures are intended for personality measures made up of Likert-type items, which, in applied research, are usually analyzed by means of factor analysis. Two scalability indices are proposed, which can be considered as factor-analytic counterparts of the lo and lz IRT-based person fit indices. The present indices can be derived both as likelihood-based measures and as residual measures, and this makes it possible to relate them with previous methodologies such as Bollen's residual analysis and Lanning's scalability index. The indices are intended to be used mainly as exploratory devices, and a factor-analytic version of the person response curve is also proposed as a tool for obtaining further information about the possible causes of misfit. The behavior of the procedures is assessed by means of simulation studies. Finally, an empirical example in personality measurement shows how the procedures can be used in applied research.