Quantifying Model Error in P-technique Factor Analysis

P-technique factor analysis is an exploratory factor model for multivariate time series data. Assessing model fit of P-technique factor models is non-trivial because time series data are correlated at nearby time points. We present a test statistic that is appropriate for P-technique factor analysis. In addition, the test statistic allows researchers to quantify the amount of model error. We explore the statistical properties of the test statistic with simulated data and we illustrate its use with an empirical study of personality states. Results of the simulation study include (1) the empirical distributions of the test statistic approximately followed their respective theoretical chi-square distributions, (2) the empirical Type I error rates of the test of perfect fit are close to the nominal level and the empirical Type I error rates of the test of close fit are slightly lower than the nominal level, and (3) the empirical power rates of the test of perfect fit are satisfactory but the empirical power rates of the test of close fit are only satisfactory for small models.