Estimation Methods for Mixed Logistic Models with Few Clusters
Estimation Methods for Mixed Logistic Models with Few Clusters
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DOI：
10.1080/00273171.2016.1236237
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发表时间：
2016-11
影响因子：
3.8
通讯作者：
Daniel M. McNeish
中科院分区：
文献类型：
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作者：
Daniel M. McNeish
摘要对于混合模型，众所周知，用很少的聚类建模数据会导致有偏估计，特别是方差分量和固定效应标准误。在线性混合模型中，小样本偏倚通常通过限制最大似然估计（REML）和Kenward-Roger校正来解决。然而，对于二元结果，没有任何一种程序的直接模拟。对于较大数量的聚类，用于二进制结果的估计方法（其近似可能性以规避封闭形式解决方案的缺乏，诸如自适应高斯求积和拉普拉斯近似）已被示出为比线性地近似模型的线性化估计方法产生较少偏差的估计。然而，自适应高斯求积和拉普拉斯近似的全似然，而不是限制的可能性;全似然是已知的，以产生有偏估计与少数集群。另一方面，线性化方法线性地近似模型，这允许应用受限的最大似然和Kenward-Roger校正。因此，出现了以下问题：哪一个更可取，有偏函数的更好近似或无偏函数的更差近似？我们解决这个问题的模拟和说明性的实证分析。
ABSTRACT For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.