Aspects Of Model Selection Research Articles

Model Selection for the Trend Vector Model

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.

‘Which model?’ is the wrong question

A perspective is presented in which the search for a suitable model on which to base inferential statements related to the analysed dataset is not useful and leads, with the established practice, to invalid statements. Composition is proposed as an alternative, in which the candidate estimators are (linearly) combined. Three generic examples are discussed: the analysis of variance in which model selection is a direct cause of inefficiency, clinical trials (experiments) in which model selection is not practiced and small‐area estimation in which one aspect of model selection has been dismissed decisively a long time ago, and there are more effective criteria for the other aspects of the problem.

Modeling strategies in longitudinal data analysis: Covariate, variance function and correlation structure selection

A modeling paradigm is proposed for covariate, variance and working correlation structure selection for longitudinal data analysis. Appropriate selection of covariates is pertinent to correct variance modeling and selecting the appropriate covariates and variance function is vital to correlation structure selection. This leads to a stepwise model selection procedure that deploys a combination of different model selection criteria. Although these criteria find a common theoretical root based on approximating the Kullback–Leibler distance, they are designed to address different aspects of model selection and have different merits and limitations. For example, the extended quasi-likelihood information criterion (EQIC) with a covariance penalty performs well for covariate selection even when the working variance function is misspecified, but EQIC contains little information on correlation structures. The proposed model selection strategies are outlined and a Monte Carlo assessment of their finite sample properties is reported. Two longitudinal studies are used for illustration.

MODEL SELECTION IN PERIODIC AUTOREGRESSIONS†

textabstractThis paper focuses on the issue of period autoagressive time series models (PAR) selection in practice. One aspect of model selection is the choice for the appropriate PAR order. This can be of interest for the valuation of economic models. Further, the appropriate PAR order is important for an adequate empirical application of tests for unit roots since too many parameters affect the performance of such tests. In fact, another aspect of PAR model selection is the decision on the number of unit roots. Finally, in case of unit roots, model choice involves a decision on the most suitable differencing filter to ensure stationarity of the transformed series.