基于正态误差的纵向数据模型的Bayes诊断

BAYESIAN DIAGNOSTICS FOR LONGITUDINAL DATA MEDOLS BASED ON NORMAL ERRORS

本文对线性和非线性纵向数据模型进行Bayes统计诊断,其中包括对数据删除模型(CDM)和均值漂移模型(MOSM)诊断.当MSOM中的漂移参数服从无信息先验(不管其余参数服从何种先验分布),且回归参数的最大后验估计(MBE)在各个模型中存在唯一时,CDM与MSOM中回归参数的MBE等价,但是方差参数的MBE不等价;当MSOM中的漂移参数服从共轭先验时,CDM与MSOM所有参数的MBE一般均不等价.然后通过一组实际数据说明了对纵向数据模型的Bayes诊断的应用.

In this paper,the Bayesian diagnostics for longitudinal data models with the normal errors, including the linear models and the nonlinear models,are discussed through the case deletion models （CDM） and mean shift outlier models（MSOM）.When the shift parameters have noninformative priors in MSOM,no mattter what kind of priors the other parameters have,and maximal Bayesian estimates （MBE） of the regression parameters uniquely exists in every model,the MBEs of the regression parameters in CDM are equivalent to those in MSOM,but the MBE of the variance parameter in CDM is not equivalent to that in MSOM.When the shift parameters have conjugate priors in MSOM,the MBEs of regression parameters and variance parameter are usually not equivalent.An example is used to illustrate the application of Bayesian diagnostics in longitudinal data models.