Bootstrap Methods for Testing P-Technique Factor Analysis

New data collection methods like smartphone applications afford researchers the opportunity to study intra-individual differences with finer details. Data from these types of studies are intensive longitudinal data or time series data. Analyzing such data is more challenging than analyzing the usual data collected from different individuals because data are dependent at adjacent time points. In addition, some routinely collected intensive longitudinal data are non-normal. P-technique factor analysis is a factor analysis model with time series data. The current methods for testing P-technique factor analysis are inappropriate because they ignore the dependence at adjacent time points. We propose using a bootstrapping procedure to account for the dependency of adjacent time points. In addition, the method is robust against non-normal distributions. The method is an adaptation of the asymptotic distribution-free test proposed in [Browne 1984]. We illustrate the test with an empirical study and explore its statistical properties with simulated data.