The effects of serial correlation on the curve-of-factors growth model.

摘要

This simulation study examined the performance of the curve-of-factors growth model when serial correlation and growth processes were present in the first-level factor structure. As previous research has shown (Ferron, Dailey, & Yi, 2002; Kwok, West, & Green, 2007; Murphy & Pituch, 2009) estimates of the fixed effects and their standard errors were unbiased when serial correlation was present in the data but unmodeled. However, variance components were estimated poorly across the examined serial correlation conditions. Two new models were also examined: one curve-of-factors model was fitted with a first-order autoregressive serial correlation parameter, and a second curve-of-factors model was fitted with first-order autoregressive and moving average serial correlation parameters. The models were developed in an effort to measure growth and serial correlation processes within the same data set. Both models fitted with serial correlation parameters were able to accurately reproduce the serial correlation parameter and approximate the true growth trajectory. However, estimates of the variance components and the standard errors of the fixed effects were problematic. The two models also produced inadmissible solutions across all conditions. Of the three models, the curve-of-factors model had the best overall performance.