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 = "309323",
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"
}
