Testing for homogeneity in cross-lagged panel studies

Panel studies are statistical studies in which two or more variables are observed for two or more subjects at two or more points in time. Cross-lagged panel studies are those studies in which the variables are continuous and divide naturally into two effects or impacts of each set of variables on the other. If a regression approach is taken, a regression structure is formulated for the cross-lagged model. This structure may assume that the regression parameters are homogeneous across waves and across subpopulations. Under such assumptions the methods of multivariate regression analysis can be adapted to make inferences about the parameters. These inferences are limited to the degree that homogeneity of the parameters is supported by the data. We consider the problem of testing the hypotheses of homogeneity and consider the problem of making statistical inferences about the cross-effects should there be evidence against one of the homogeneity assumptions. We demonstrate the methods developed by applying them to two panel data sets.