Generalized linear models with unspecified reference distribution
Generalized linear models with unspecified reference distribution
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DOI：
10.1093/biostatistics/kxn030
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发表时间：
2009-04-01
期刊：
影响因子：
2.1
通讯作者：
Gao, Liping
中科院分区：
文献类型：
--
作者：
Rathouz, Paul J.;Gao, Liping
提出了一类新的半参数广义线性模型。与现有模型一样，这些模型是通过一个线性预测器和响应Y的均值作为预测器x的函数的链接函数来指定的。然而，在这里，Y在给定参考均值mu(0)处的“基线”分布没有指定，而是从数据中估计。然后通过基线分布的指数倾斜生成均值偏离mu(0)时的响应分布，得到一个自然指数族的响应模型，具有相应的规范链接和方差函数。由此产生的模型具有一定程度的灵活性，类似于流行的比例赔率模型。提出了有限支持下响应分布的最大似然估计，并通过仿真和老化研究实例分析对新模型进行了研究和说明。
We propose a new class of semiparametric generalized linear models. As with existing models, these models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. Here, however, the "baseline" distribution of Y at a given reference mean mu(0) is left unspecified and is estimated from the data. The response distribution when the mean differs from mu(0) is then generated via exponential tilting of the baseline distribution, yielding a response model that is a natural exponential family, with corresponding canonical link and variance functions. The resulting model has a level of flexibility similar to the popular proportional odds model. Maximum likelihood estimation is developed for response distributions with finite support, and the new model is studied and illustrated through simulations and example analyses from aging research.