Information criteria are a common approach for joint fixed and random effects selection in mixed models. While straightforward to implement, a major difficultly when applying information criteria is that they are typically based on maximum likelihood estimates, yet calculating such estimates for one, let alone multiple, candidate mixed models presents a major computational hurdle. To overcome this, we study penalized quasilikelihood estimation and use it as the basis for performing fast joint selection. Under a general framework, we show that penalized quasilikelihood estimation produces consistent estimates of the true parameters. Then, we propose a new penalized quasilikelihood information criterion whose distinguishing feature is the way it accounts for model complexity in the random effects, since penalized quasilikelihood estimation effectively treats the random effects as fixed. We demonstrate that the criterion asymptotically identifies the true set of important fixed and random effects. Simulations show the quasi-likelihood information criterion performs competitively with and sometimes better than common maximum likelihood information criteria for joint selection, while offering substantial reductions in computation time.

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关于惩罚拟似然信息准则在广义线性混合模型中的应用

信息标准是混合模型中联合固定效应和随机效应选择的常用方法。尽管易于实现，但应用信息标准时的一个主要困难是它们通常基于最大似然估计，但为一个（更不用说多个）候选混合模型计算此类估计带来了主要的计算障碍。为了克服这个问题，我们研究了惩罚拟似然估计，并将其用作执行快速关节选择的基础。在一般框架下，我们证明了惩罚拟似然估计会产生真实参数的一致估计。然后，我们提出了一种新的惩罚拟似然信息准则，该准则的区别特征是它在随机效应中考虑模型复杂性的方式，因为惩罚的拟似然估计有效地将随机效应视为固定的。我们证明了该准则渐近地标识出重要的固定和随机效应的真实集合。仿真显示，对于联合选择而言，准似然信息标准的性能与通用最大似然信息标准相比具有竞争优势，有时甚至更好，同时大大减少了计算时间。