Cluster effects and simultaneity in multilevel models
研究了当随机聚类效应与解释变量相关时，多水平模型中GLS估计量的偏误和不一致性，并比较了固定效应估计量，同时考虑了部分解释变量与因变量联立决定的情况。
For small group sizes, the GLS estimator in multilevel models is biased and inconsistent when the random cluster effects are correlated with the regressors. A fixed effects approach, conditioning on the cluster effects, provides consistent estimates for the slope parameters. The two estimators are equivalent when group sizes are large. The same results obtain for two-stage estimation procedures that allow for some of the regressors to be simultaneously determined with the dependent variable. The GLS and fixed effects estimators are applied to data on acute care hospital utilization in the UK, allowing for health authority district effects.