Logistic linear mixed models are widely used in experimental designs and genetic analyses of binary traits. Motivated by modern applications, we consider the case of many groups of random effects, where each group corresponds to a variance component. When the number of variance components is large, fitting a logistic linear mixed model is challenging. Thus, we develop two efficient and stable minorization-maximization (MM) algorithms for estimating variance components based on a Laplace approximation of the logistic model. One of these leads to a simple iterative soft-thresholding algorithm for variance component selection using the maximum penalized approximated likelihood. We demonstrate the variance component estimation and selection performance of our algorithms by means of simulation studies and an analysis of real data.

中文翻译：

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逻辑线性混合模型中方差分量估计与选择的MM算法

Logistic 线性混合模型广泛应用于二元性状的实验设计和遗传分析。受现代应用的推动，我们考虑多组随机效应的情况，其中每组对应一个方差分量。当方差分量的数量很大时，拟合逻辑线性混合模型具有挑战性。因此，我们开发了两种有效且稳定的最小化最大化（MM）算法，用于基于逻辑模型的拉普拉斯近似估计方差分量。其中之一导致了一种简单的迭代软阈值算法，用于使用最大惩罚近似似然来选择方差分量。我们通过模拟研究和实际数据分析来展示我们算法的方差分量估计和选择性能。