Sampling bias and logistic models

• 成果类型: Article
• 署名作者: McCullagh, Peter
• 署名单位: University of Chicago
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/j.1467-9868.2007.00660.x
• 发表日期: 2008
• 页码: 643-664
• 关键词: GENERALIZED LINEAR-MODELS; longitudinal data-analysis; mixed models; binary data; statistical-analysis

摘要

In a regression model, the joint distribution for each finite sample of units is determined by a function p(x)(y) depending only on the list of covariate values x=(x(u(1)),...,x(u(n))) on the sampled units. No random sampling of units is involved. In biological work, random sampling is frequently unavoidable, in which case the joint distribution p(y,x) depends on the sampling scheme. Regression models can be used for the study of dependence provided that the conditional distribution p(y vertical bar x) for random samples agrees with p(x)(y) as determined by the regression model for a fixed sample having a non-random configuration x. The paper develops a model that avoids the concept of a fixed population of units, thereby forcing the sampling plan to be incorporated into the sampling distribution. For a quota sample having a predetermined covariate configuration x, the sampling distribution agrees with the standard logistic regression model with correlated components. For most natural sampling plans such as sequential or simple random sampling, the conditional distribution p(y vertical bar x) is not the same as the regression distribution unless p(x)(y) has independent components. In this sense, most natural sampling schemes involving binary random-effects models are biased. The implications of this formulation for subject-specific and population-averaged procedures are explored.