# Difference between marginal and conditional models

A marginal model accounts for the correlation within each cluster. A conditional model also takes into account the correlation within each cluster.

My questions are:

1. Does a marginal model models main effects across a population whereas a conditional model models main effects within a cluster and across a population?
2. The interpretation of the coefficients of a marginal model is basically the same as "regular model." But what about the coefficients of a conditional model?
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Yes, the interpretations are quite similar to "regular models", and the major distinction between them is whether you are comparing observations within the same cluster, or across all the clusters.

In a typical conditional model - also known as a conditionally-specified model, or a mixed model - the coefficients have cluster-specific interpretations. The coefficients of a covariate is a measure of difference in mean response, in the same cluster, at observations for which the specific covariates differ by one unit and all the other covariates are identical. Depending on the link function, the "measure of difference" can be a difference, or a log-ratio, or a log odds-ratio. An exception is the intercept, which doesn't describe a difference, but instead gives the mean response in observations for which all covariates and the random effect(s) are zero.

In a marginal model, the coefficients have population-averaged interpretations. Excepting the intercept, the coefficients describe differences in mean response, but now across all observations (and hence across all clusters). The coefficient of a covariate is the difference in mean response (or log-ratio of means, etc) per unit difference in that covariate, in observations for which all other covariates are identical. Note that this definition is agnostic about whether the comparisons are in the same cluster or not.

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