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Sampling bias and logistic models

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  • Peter McCullagh
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    Abstract

    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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    Bibliographic Info

    Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

    Volume (Year): 70 (2008)
    Issue (Month): 4 ()
    Pages: 643-677

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    Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:643-677

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