A parametric test to discriminate between a linear regression model and a linear latent growth model

In longitudinal studies with subjects measured repeatedly across time, an important problem is how to select a model generating data choosing between a linear regression model and a linear latent growth model. Approaches based both on information criteria and on asymptotic hypothesis test on the variances of "random" components are largely used but not completely satisfactory. In the paper we propose a finite sample parametric test based on the trace of the product of estimates of two variance covariance matrices, one defined when data come from a linear regression model, the other defined when data come from a linear latent growth model. The sampling distribution of the test statistic so defined depends on the model generating data. It can be a "standard" F -distribution or a linear combination of F -distributions. In the paper a unified sampling distribution based on a generalized F -distribution is proposed. The knowledge of this distribution allows us to make inference in a classical hypothesis testing framework. The test statistic can be used by itself to discriminate between the two models and/or, duly modified, it can be used to test randomness on single components of the linear latent growth model avoinding the boundary problem of the likelihood ratio test statistic. Moreover, it can be used in conjunction with some indicators based on information criteria giving estimates of probability of accepting or rejecting the model chosen.