Model Selection for the Trend Vector Model

Abstract

Model selection is an important component of data analysis. This study focuses on issues of model selection for the trend vector model, a model for the analysis of longitudinal multinomial outcomes. The trend vector model is a so-called marginal model, focusing on population averaged evolutions over time. A quasi-likelihood method is employed to obtain parameter estimates. Such an optimization function in theory invalidates likelihood-based statistics, such as the likelihood ratio statistic. Moreover, standard errors obtained from the Hessian are biased. In this paper, the performances of different model selection methods for the trend vector model are studied in detail. We specifically focused on two aspects of model selection: variable selection and dimensionality determination. Based on the quasi-likelihood function, selection criteria analogous to the likelihood ratio statistics, AIC and BIC, were employed. Additionally, Wald and resampling statistics were included as variable selection criteria. A series of simulations were carried out to evaluate the relative performance of these criteria. The results suggest that model selection can be best performed using either the quasi likelihood ratio statistic or the quasi-BIC. A special study on dimensionality selection found that the quasi-AIC also performs well for cases with degrees of freedom greater than 8. Another important finding is that the sandwich estimator for standard errors used in Wald statistics does not perform well. Even for larger sample sizes, the bias-correction procedure for the sandwich estimator is needed to give satisfactory results.