Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests

摘要

The problems of determining selection criteria and misspecification tests for the inter-cluster correlation structure (ICS) in longitudinal data analysis are considered. The asymptotic distributions of the correlation information criterion (CIC) test statistic when the dispersion parameter is either known or unknown are derived under null hypothesis. A corresponding new working ICS selection method is established by standardizing the selection criterion as the p- value from the CIC test. It is observed that the CIC and other related criteria are introduced for working ICS selection, while both CIC and other related tests are introduced for working ICS misspecification test, though their corresponding working ICS selection methods are established based on the p-values from these tests. It is observed that the CIC test is found to be powerful in detecting misspecification of the working ICS structures, while with respect to the working ICS selection, the standard CIC test is also shown to have satisfactory performance. Both simulation studies and real time longitudinal data sets are considered to illustrate the usefulness of the proposed selection criteria and misspecification tests. (21 refs.)