The Performance of a Higher Order Invariance Idiographic Filter in Confirmatory Factor Analysis of Cross Sectional and Longitudinal Data

This work evaluates the performance of a methodology for analyzing cross sectional and longitudinal latent factor data featuring measurement non-invariance. An overview of the historical context and current methodologies for establishing factorial invariance is presented, and the higher-order invariance idiographic filter (HOIIF) method is proposed as a candidate for establishing factorial invariance in conditions of measurement non-invariance. HOIIF allows for flexibility in the measurement structure of a latent factor model, while constraining invariance on a higher factor order. However, the method is currently in a nascent stage and the performance of the HOIIF method in conditions of varying sample size, measurement model, and higher-order equivalence has not yet been established. Therefore, the current study implements a Monte Carlo simulation of A) cross-sectional and B) longitudinal data sets in order to evaluate HOIIF based on recovery of the first-order factor loadings and expected error, ratios of rejected to non-rejected first-order constrained models, ratios of rejected to non-rejected second-order constrained models, and model convergence. Following the Monte Carlo simulations, a practical application of HOIIF to empirical data is employed. Results indicate that the HOIIF method is sufficiently sensitive (fails to reject correct models) and specific (rejects incorrect models), and can produce accurate parameter estimates. The study highlights the importance of following the procedure in order, correct model specification, and consideration of sample size and model complexity.