In Section 13.5.1 and Problem 13.42 we saw that for Poisson GLMMs, the marginal effects are the
Question:
In Section 13.5.1 and Problem 13.42 we saw that for Poisson GLMMs, the marginal effects are the same as the cluster-specific effects. This does not imply that ML estimates of effects are the same for a Poisson GLMM and a Poisson GLM. Explain why. (For the GLMM, is the marginal distribution Poisson?)
Data from Problem 13.42:
Consider the loglinear random effects model
log[E(Yit | ui)] = x’it β + z’it ui,
where {µi} are independent N(0, ∑). Show that this implies the marginal loglinear model
with the same fixed effects but with offset term. For the random-intercept case, indicate the role of σ on the size of the offset. Explain what happens when σ = 0.
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