A Parametric test to discriminate between a Linear Regression Model and a Linear Latent growth Model: Advanced Study

In longitudinal studies with subjects measured repeatedly across time, an important problem is how to select a model generating data by choosing between a linear regression model and a linear latent growth model. Approaches based both on information criteria and asymptotic hypothesis tests of the variances of “random” components are widely used but not completely satisfactory. We propose a test statistic based on the trace of the product of an estimate of a variance covariance matrix defined when data come from a linear regression model and a sample variance covariance matrix. We studied the sampling distribution of the test statistic giving a representation in terms of an infinite series of generalized F-distributions. Knowledge about this distribution allows us to make inference within a classical hypothesis testing framework. The test statistic can be used by itself to discriminate between the two models and/or, if duly modified, it can be used to test randomness on single components. Moreover, in conjunction with some model selection criteria, it gives additional information which can help in choosing the model. The test statistic proposed in this paper has been applied to two data sets. With the tourism data it is used by itself to discriminate between the two models, with the Cadralazine data it is used in conjunction with several indicators based on information criteria that give an estimate of the probability of accepting or rejecting the model chosen.