Publication: Equivalence of conditional and marginal regression models for clustered and longitudinal data
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Equivalence of conditional and marginal regression models for clustered and longitudinal data

- Article in a journal -
 

Area
Statistics

Author(s)
John Ritz , Donna Spiegelman

Published in
Statistical Methods in Medical Research

Year
2004

Abstract
Certain statistical models specify a conditional mean function, given a random effect and covariates of interest. On the other hand, one may instead model a marginal mean only in terms of the covariates. We discuss some common situations where conditional and marginal means coincide. In a Gaussian linear mixed effects model we have equivalent interpretations of the conditional and marginal regression parameter estimates. Similar results exist for more general link functions. In this paper we give a short overview of some models, where conditional and marginal results are equivalent and we illustrate this with some examples. When the conditional mean is additive in a random effect on the log scale, it is seen that the marginal mean equals the conditional mean plus a constant, such that slope parameters have the same interpretation in both formulations. No further distributional assumptions are needed in either of these cases. With a logit link and a double exponential random effect, a closed form marginal link function is derived from the conditional model. When a logit or probit link is used with a normal random effect, the marginal mean parameters become attenuated by a factor which depends on parameters of the distribution of the covariates. In a conditional Weibull proportional hazards model with a positive stable frailty, the marginal hazards are again Weibull but with slope parameters attenuated towards zero.

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BibTeX
@ARTICLE{
         Ritz2004Eoc,
       author = "John Ritz and Donna Spiegelman",
       title = "Equivalence of conditional and marginal regression models for clustered and
         longitudinal data",
       journal = "Statistical Methods in Medical Research",
       volume = "13",
       number = "4",
       pages = "309--323",
       year = "2004",
       doi = "10.1191/0962280204sm368ra",
       url = "http://dx.doi.org/10.1191/0962280204sm368ra",
       eprint = "http://dx.doi.org/10.1191/0962280204sm368ra",
       abstract = "Certain statistical models specify a conditional mean function, given a random
         effect and covariates of interest. On the other hand, one may instead model a marginal mean only in
         terms of the covariates. We discuss some common situations where conditional and marginal means
         coincide. In a Gaussian linear mixed effects model we have equivalent interpretations of the
         conditional and marginal regression parameter estimates. Similar results exist for more general link
         functions. In this paper we give a short overview of some models, where conditional and marginal
         results are equivalent and we illustrate this with some examples. When the conditional mean is
         additive in a random effect on the log scale, it is seen that the marginal mean equals the
         conditional mean plus a constant, such that slope parameters have the same interpretation in both
         formulations. No further distributional assumptions are needed in either of these cases. With a
         logit link and a double exponential random effect, a closed form marginal link function is derived
         from the conditional model. When a logit or probit link is used with a normal random effect, the
         marginal mean parameters become attenuated by a factor which depends on parameters of the
         distribution of the covariates. In a conditional Weibull proportional hazards model with a positive
         stable frailty, the marginal hazards are again Weibull but with slope parameters attenuated towards
         zero.",
       ad_area = "Statistics",
       ad_tools = "ADIFOR"
}


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