Statistical inferences for cross-lagged panel models without the assumption of normal errors

Abstract

Panel studies are statistical studies in which two or more variables are observed for two or more subjects at two or more waves or points in time. Cross-lagged panel studies are those studies in which the variables are continuous and divide naturally into two sets. Such studies usually focus, in part, on estimating and testing the cross-effects which are the impacts of each set of variables on the other over time. If a regression approach is taken, then the cross-lagged model is formulated as one or more regression models and regression methods are used to make inferences about the parameters. Traditionally this approach has assumed that the errors in the model have a joint normal distribution. We contribute to this approach by replacing the assumption of normal errors by the weaker assumption that the errors are independent and identically distributed with finite variances. For this independent-error model we show that the usual least-squares estimators of the regression coefficients are consistent and asymptotically normal. We also display large sample tests for the hypotheses of no effects and no cross-effects. We demonstrate our methods by analyzing a set of psychiatric panel data.