Model-Based Direct Adjustment
针对传统直接调整法在子类较多时权重不稳定的问题，提出基于模型的直接调整方法，在保留其优点的同时稳定小样本子类的权重，并应用于AP生物学考试的非随机样本数据。
Abstract Direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population. Direct adjustment has several attractive features, but when there are many subclasses it can attach large weights to small quantities of data, often in a fairly erratic manner. In the extreme, direct adjustment can attach infinite weight to nonexistent data, a noticeable inconvenience in practice. This article proposes a method of model-based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses. The sample mean and conventional direct adjustment are both special cases of model-based direct adjustment under two different extreme models for the subclass-specific selection probabilities. The discussion of this method provides some insights into the behavior of true and estimated propensity scores: the estimated scores are better than the true ones for almost the same reason that direct adjustment can outperform the sample mean in a simple random sample. The method is applied to a nonrandom sample in an effort to estimate a discrete distribution of essay scores in the College Board's Advanced Placement Examination in Biology.