具有随机效应的SEMMS：一种混合模型扩展用于簇状和纵向数据中的变量选择
SEMMS with Random Effects: A Mixed-Model Extension for Variable Selection in Clustered and Longitudinal Data
AI总结：
本文扩展了SEMMS模型以处理纵向和簇状数据中的随机效应，通过交替坐标上升算法改进变量选择性能，并在不同数据集上验证了其有效性。
摘要：
SEMMS（可扩展经验贝叶斯标记选择模型）是一种用于广义线性模型的变量选择过程，使用三个成分正态混合先验对回归系数进行建模。在原始形式中，SEMMS假设所有观测都是独立的。然而，许多现实世界的数据集来源于重复测量或分层设计，其中同一主体内的观测是相关的。忽略这种相关性会高估残差方差并严重损害变量选择性能。我们通过交替坐标上升算法扩展SEMMS以处理随机截距、随机斜率或两者。在每次固定效应变量选择轮次后，使用lmer（高斯）或glmer（非高斯）更新主体水平的最佳线性无偏预测（BLUPs）；固定效应步骤则在随机效应调整后的响应上进行操作。我们描述了该算法，评估了其在三个高斯模拟研究中的性能，涵盖了信号强度、随机效应大小和样本/预测空间范围，并展示了半合成真实数据示例。我们进一步扩展框架以适应非高斯家庭（泊松、二项式）通过IRLS工作响应适应：在每次外迭代中，固定效应步骤使用从当前glmer拟合值计算的RE调整工作响应，而不是原始响应。当固定效应信号相对于随机效应方差较强时，原始和扩展程序表现相当。当随机效应方差主导——最可能导致普通SEMMS失效的场景——混合模型扩展在93%（高斯）、61%（泊松）和65%（二项式）的模拟数据集中恢复了精确的真实预测器集，而普通SEMMS分别为1%、45%和39%。
英文摘要：
SEMMS (Scalable Empirical-Bayes Model for Marker Selection) is a variable-selection procedure for generalized linear models that uses a three-component normal mixture prior on regression coefficients. In its original form, SEMMS assumes that all observations are independent. Many real-world datasets, however, arise from repeated-measures or clustered designs in which observations within the same subject are correlated. Ignoring this correlation inflates the apparent residual variance and can severely degrade variable-selection performance. We extend SEMMS to accommodate random intercepts, random slopes, or both, via an alternating coordinate-ascent algorithm. After each round of fixed-effect variable selection, the subject-level best linear unbiased predictors (BLUPs) are updated with \texttt{lmer} (Gaussian) or \texttt{glmer} (non-Gaussian); the fixed-effect step then operates on the random-effect-adjusted response. We describe the algorithm, evaluate its performance in three Gaussian simulation studies spanning a range of signal strengths, random-effect magnitudes, and sample/predictor-space regimes, and present a semi-synthetic real-data example. We further extend the framework to non-Gaussian families (Poisson, binomial) via an IRLS working-response adaptation: at each outer iteration the fixed-effects step uses the RE-adjusted working response computed from the current \texttt{glmer} fitted values rather than the raw response. When the fixed-effect signal is strong relative to the random-effect variance, both the original and extended procedures perform comparably. When the random-effect variance dominates -- the scenario most likely to cause plain SEMMS to fail -- the mixed-model extension recovers the exact true predictor set in 93\% of simulated datasets (Gaussian), 61\% (Poisson), and 65\% (binomial), compared with 1\%, 45\%, and 39\% for plain SEMMS respectively.
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