The latent curve ARMA (p, q) panel model: longitudinal data analysis in educational research and evaluation

Abstract

Autocorrelated residuals in longitudinal data are widely reported as common to longitudinal data. Yet few, if any, researchers modeling growth processes evaluate a priori whether their data have this feature. Sivo, Fan, and Witta (2005) found that not modeling autocorrelated residuals present in longitudinal data severely biases latent curve parameter estimates. The purpose of this article is to explain how educational researchers and evaluators analyzing longitudinal data might approach longitudinal data in which change is hypothesized to occur over time. Specification of the latent curve ARMA model (i.e., the growth curve ARMA model) is introduced as an approach to filtering out the effects of autocorrelation on latent curve parameter estimates by modeling this nuisance condition so that the estimates of primary interest are more accurate.

Keywords:

• latent curve ARMA
• autoregressive-moving average
• longitudinal data
• time series
• structural equation modeling