论文标题
使用LME4计算和应用广义线性混合模型衍生物
Computation and application of generalized linear mixed model derivatives using lme4
论文作者
论文摘要
由于随机效应的边缘化，很难对广义线性混合模型（GLMM）的最大似然估计。拟合GLMM的可能性（相对于模型参数）的计算衍生物也很困难，尤其是因为衍生物不是流行估计算法的副产物。在本文中，我们描述了GLMM衍生物以及一种正交方法来有效计算它们，重点是具有单个聚类变量的LME4模型。我们描述了与IRT相关的心理测量结果如何有助于获得这些衍生物以及验证衍生物的准确性。在描述了衍生计算方法之后，我们说明了这些导数的许多可能用途，包括可靠的标准误差，固定效应参数的得分测试以及非巢模型的似然比测试。本文中描述的衍生计算方法和应用都在易于体现的R软件包中获得。
Maximum likelihood estimation of generalized linear mixed models(GLMMs) is difficult due to marginalization of the random effects. Computing derivatives of a fitted GLMM's likelihood (with respect to model parameters) is also difficult, especially because the derivatives are not by-products of popular estimation algorithms. In this paper, we describe GLMM derivatives along with a quadrature method to efficiently compute them, focusing on lme4 models with a single clustering variable. We describe how psychometric results related to IRT are helpful for obtaining these derivatives, as well as for verifying the derivatives' accuracies. After describing the derivative computation methods, we illustrate the many possible uses of these derivatives, including robust standard errors, score tests of fixed effect parameters, and likelihood ratio tests of non-nested models. The derivative computation methods and applications described in the paper are all available in easily-obtained R packages.
