Predictive cross-validation for the choice of linear mixed-effects models with application to data from the Swiss HIV Cohort Study

Model choice in linear mixed-effects models for longitudinal data is a challenging task. Apart from the selection of covariates, also the choice of the random effects and the residual correlation structure should be possible. Application of classical model choice criteria such as Akaike information criterion (AIC) or Bayesian information criterion is not obvious, and many versions do exist. In this article, a predictive cross-validation approach to model choice is proposed based on the logarithmic and the continuous ranked probability score. In contrast to full cross-validation, the model has to be fitted only once, which enables fast computations, even for large data sets. Relationships to the recently proposed conditional AIC are discussed. The methodology is applied to search for the best model to predict the course of CD4+ counts using data obtained from the Swiss HIV Cohort Study.     

副溶血性弧菌温度-盐度双因素预测模型的建立

本文以副溶血性弧菌VP BJ1.1997为研究对象, 采用均匀设计试验方法, 建立并验证了温度范围为7°C~43°C, 盐度范围为0.5%~9.5%NaCl的生长动力学模型。结果表明, 所选一级模型的拟合效果优劣依次为Logistic方程>Gompertz方程>Linear方程, 以Logistic方程为一级模型计算生长参数; 二级模型采用平方根模型进行拟合, 得到模型相关系数r为0.9863, 最低生长温度T min为9.0506°C, 最高生长盐度为5.93%NaCl(对应最低生长水分活度Aw min     

Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution

Summary We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85 , 1–11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.