A Parametric Test to Discriminate between a Linear Regression Model and a Linear Latent Growth Model: Advanced Study

An significant issue in longitudinal studies of subjects evaluated repeatedly over time is deciding between a linear regression model and a linear latent growth model for data generation. Approaches based on knowledge criteria and asymptotic hypothesis tests of the variances of “random” components are common, but they aren’t perfect. We suggest a test statistic based on the trace of the product of a variance covariance matrix estimate and a sample variance covariance matrix when data comes from a linear regression model. We looked at the test statistic’s sampling distribution, which can be expressed as an infinite sequence of generalised F-distributions. We may make inferences about this distribution using a traditional hypothesis testing method. The test statistic can be used to distinguish between the two models on its own, or it can be used to test randomness on single components if properly modified. Furthermore, when used in combination with other model selection criteria, it provides additional information that can aid in model selection. Two data sets were used to assess the test statistic proposed in this article. With the tourism data, it is used alone to distinguish between the two models; with the Cadralazine data, it is combined with other metrics based on knowledge parameters to provide an estimation of the likelihood of approving or rejecting the chosen model.

Author (s) Details

Marco Barnabani
Department of Statistics, Informatics, Applications V.le Morgagni, 59 50134 Florence, Italy.

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