Sampling bias and logistic models
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 | 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 | 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. Copyright (c) 2008 Royal Statistical Society.
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Volume (Year): 70 (2008)
Issue (Month): 4 ()
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