Modeling Causal Error Structures in Longitudinal Panel Data: A Monte Carlo Study

Abstract

This research was designed to investigate how much more suitable moving average (MA) and autoregressive-moving average (ARMA) models are for longitudinal panel data in which measurement errors correlate than AR, quasi-simplex, and 1-factor models. The conclusions include (a) when testing for a stochastic process hypothesized to occur in a longitudinal data set, testing for other processes is necessary, because incorrect models often fit other processes well enough to be deceiving; (b) when measurement error correlations are flagged to be relatively high in panel data, the fit and propriety of an MA or ARMA model should be considered and compared to the fit and propriety of other models; (c) when an MA model is fit to AR data, measurement error correlations may nonetheless be deceptively high, though fortunately MA model fit indexes are almost always lower than those for an AR model; and (d) the assumption that longitudinal panel data always contain measurement error correlations is patently false. In summary, whenever evaluating longitudinal panel data, the fit, propriety, and parsimony of all 5 models should be considered jointly and compared before a particular model is endorsed as most suitable.