Measures of Dependence for Cross-Lagged Panel Models

Abstract

Panel studies are statistical studies in which two or more responses are measured for two or more individuals, or other sampling units, at two or more waves, or points in time. Typically the number of responses and the number of waves are small but the number of subjects is large. Cross-lagged panel studies are those in which the responses are continuous and divide naturally into two sets. One focus in such studies is to estimate and test the temporal effects with emphasis given to the effects of each set on the other. One approach to making such inferences involves casting the model as a set of regression equations and then estimating and testing the parameters by some variant of classical regression methods. Within this regression approach several authors have considered the problem of summarizing the degree of dependence by adapting the principle of “reduction in error.” We consider the same problem and develop measures from the multivariate likelihood ratio test statistics. We interpret these measures by relating them, for a stationary process, to the “feedback” measures developed for vector autoregressive processes. Finally we display the use of these measures on two sets of panel data.