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SUMMARY:Sampling bias in logistic models - Peter McCullagh (University of 
 Chicago)
DTSTART:20081114T160000Z
DTEND:20081114T173000Z
UID:TALK14339@talks.cam.ac.uk
CONTACT:8419
DESCRIPTION:This talk is concerned with regression models for the effect o
 f\ncovariates on correlated binary and correlated polytomous responses.\nI
 n a generalized linear mixed model\, correlations are induced by\na random
  effect\, additive on the logistic scale\, so that\nthe joint distribution
  p_x(y) obtained by integration\ndepends on the covariate values x on the 
 sampled units.\nThe thrust of this talk is that the conventional formulati
 on\nis inappropriate for most natural sampling schemes in which\nthe sampl
 ed units inevitably arise from a random process.\nThe conventional analysi
 s incorrectly predicts parameter attenuation\ndue to the random effect\, t
 hereby giving a misleading impression of the\nmagnitude of treatment effec
 ts.\nThe error in the conventional analysis is a subtle consequence\nof sa
 mpling bias that arises from random sampling of units.\nThis talk will des
 cribe a non-standard but mathematically natural formulation\nin which the 
 units are auto-generated by an explicit sampling plan.\nFor a quota sample
  in which the x-configuration is pre-specified\,\nthe model distribution c
 oincides with p_x(y) in the GLMM.\nHowever\, if the sample units are selec
 ted at random\,\nfor example by simple random sampling from the available 
 population\,\nthe conditional distribution p(y | x)$\nis different from p_
 x(y).\nBy contrast with conventional models\,\nconditioning on x is not eq
 uivalent to stratification by x.\nThe implications for likelihood computat
 ions and estimating equations\nwill be discussed.\n
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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