Testing Process Factor Analysis Models Using the Parametric Bootstrap

ABSTRACT

Process factor analysis (PFA) is a latent variable model for intensive longitudinal data. It combines P-technique factor analysis and time series analysis. The goodness-of-fit test in PFA is currently unavailable. In the paper, we propose a parametric bootstrap method for assessing model fit in PFA. We illustrate the test with an empirical data set in which 22 participants rated their effects everyday over a period of 90 days. We also explore Type I error and power of the parametric bootstrap test with simulated data.

Keywords:

• Dynamic factor analysis
• time series analysis
• parametric bootstrap
• intensive longitudinal data
• model testing

Notes

1 A more complete notation is PFA(n_v, n_f, p, q). The last term is the moving average order that indicates the current shock variables affect the latent factors at the following q time points. The AR process is more commonly used than the moving average process in practice.

2 We thank Peter Borkenau for making available the data set.

3 A distribution package including the executable file, a user guide, and more input files and output files will be made available on the internet.

4 Because the p values presented in Table 2 contain only two decimal places, the value 0.05 are sometimes rounded up from a slightly smaller value and sometimes rounded down from a slightly larger value. If a p value is exactly 0.05, we fail to reject the null hypothesis.