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

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 AIC indicators it gives additional information which can help in choosing the model.