Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models
研究了当预测变量存在测量误差时，广义线性混合模型（GLMM）的偏差特征，并采用SIMEX方法进行参数估计，对处理聚类数据中的测量误差问题有参考价值。
Abstract We consider generalized linear mixed models (GLMMs) for clustered data when one of the predictors is measured with error. When the measurement error is additive and normally distributed and the error-prone predictor is itself normally distributed, we show that the observed data also follow a GLMM but with a different fixed effects structure from the original model, a different and more complex random effects structure, and restrictions on the parameters. This characterization enables us to compute the biases that result in common GLMMs when one ignores measurement error. For instance, in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases, both for regression coefficients and for variance components. Parameter estimation is described using the SIMEX method, a relatively new functional method that makes no assumptions about the structure of the unobservable predictors. Simulations and an example illustrate the results.