Fusion of data sets in multivariate linear regression with errors-in-variables

Abstract

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regression models with errors--in--variables, in the case where various data sets are merged into a single analysis and the observable variables deviate possibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possible non--normality of the data, normal--theory methods yield correct inferences for the parameters of interest and for the goodness--of--fit test. The theory described encompasses both the functional and structural model cases, and can be implemented using standard software for structural equations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.