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Semiparametric generalized linear models

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  • Paul Rathouz

    () (Department of Health Studies, University of Chicago)

Abstract

I propose a new class of generalized linear models. As with the existing models, these new models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. However, here, the “baseline” distribution of Y when the linear predictor is zero is left unspecified and is estimated from the data. The response distribution when the linear predictor differs from zero is then generated via exponential tilting of the baseline distribution, yielding a response model that is a member of the natural exponential family, with corresponding canonical link and variance functions. The resulting model has a similar level of flexibility as the proportional odds model. Maximum likelihood estimators are developed for response distribution with finite support, and the new model is studied and illustrated through simulations and example analyses from aging and psychiatry research.

Suggested Citation

  • Paul Rathouz, 2008. "Semiparametric generalized linear models," Summer North American Stata Users' Group Meetings 2008 15, Stata Users Group, revised 28 Aug 2008.
  • Handle: RePEc:boc:nsug08:15
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