Bondell Howard D, Krishna Arun, Ghosh Sujit K
Department of Statistics, North Carolina State University, Raleigh, North Carolina 27695-8203, USA.
Biometrics. 2010 Dec;66(4):1069-77. doi: 10.1111/j.1541-0420.2010.01391.x.
It is of great practical interest to simultaneously identify the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects (LME) model. Typical approaches perform selection separately on each of the fixed and random effect components. However, changing the structure of one set of effects can lead to different choices of variables for the other set of effects. We propose simultaneous selection of the fixed and random factors in an LME model using a modified Cholesky decomposition. Our method is based on a penalized joint log likelihood with an adaptive penalty for the selection and estimation of both the fixed and random effects. It performs model selection by allowing fixed effects or standard deviations of random effects to be exactly zero. A constrained expectation-maximization algorithm is then used to obtain the final estimates. It is further shown that the proposed penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.
在线性混合效应（LME）模型中同时识别与固定效应和随机效应成分相对应的重要预测因子具有重大的实际意义。典型方法是对固定效应和随机效应成分分别进行选择。然而，改变一组效应的结构可能会导致另一组效应的变量选择不同。我们提出使用修正的Cholesky分解在LME模型中同时选择固定因子和随机因子。我们的方法基于惩罚联合对数似然，对固定效应和随机效应的选择与估计采用自适应惩罚。它通过允许固定效应或随机效应的标准差恰好为零来进行模型选择。然后使用约束期望最大化算法来获得最终估计值。进一步表明，所提出的惩罚估计器具有神谕性质，即渐近地它的表现与事先知道真实模型时一样好。我们基于模拟研究和实际数据示例展示了我们方法的性能。
