论文标题
由随机效应与相应模型矩阵之间的依赖性引起的线性混合模型估计器中偏差的诊断
A Diagnostic for Bias in Linear Mixed Model Estimators Induced by Dependence Between the Random Effects and the Corresponding Model Matrix
论文作者
论文摘要
我们探讨了违反固定的线性混合模型中随机效应模型矩阵的违规假设是如何固定的（因此与随机效应矢量无关）会导致固定效应的可估计功能的估计值偏见。但是，如果原始混合模型的随机效应也被视为固定效应，或者固定效应和随机效应模型矩阵相对于误差协方差矩阵的逆（具有概率一个），或者如果随机效应和相应的模型矩阵是独立的，则这些估计值是公正的。一般情况下的偏差进行了量化并将其与预测的随机效应的随机排列分布进行了比较，从而为每个感兴趣的估计值提供了信息的摘要图形。通过检查用于估计主场优势的体育成果，可以证明这一点。
We explore how violations of the often-overlooked standard assumption that the random effects model matrix in a linear mixed model is fixed (and thus independent of the random effects vector) can lead to bias in estimators of estimable functions of the fixed effects. However, if the random effects of the original mixed model are instead also treated as fixed effects, or if the fixed and random effects model matrices are orthogonal with respect to the inverse of the error covariance matrix (with probability one), or if the random effects and the corresponding model matrix are independent, then these estimators are unbiased. The bias in the general case is quantified and compared to a randomized permutation distribution of the predicted random effects, producing an informative summary graphic for each estimator of interest. This is demonstrated through the examination of sporting outcomes used to estimate a home field advantage.
