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st: marginal vs. conditional log likelihood in GLLAMM
I'm using GLLAMM to examine the effects of various factors on the binary
outcome hunting success (kill/no kill) of individually-known
free-ranging wolves in Yellowstone National Park, USA. I'm using the
Akaike information criteria (AIC) to select the best approximating model
among a set of candidate models. AIC = -2log likelihood + 2K, where K is
the 'degrees of freedom' correction, or number of parameters in the model.
However, Vaida & Blanchard (2005) point out that AIC in current use is
not appropriate for subject-specific inferences with mixed effects
models because it is based on the marginal log likelihood, which they
say should be reserved for population-level inferences. Thus, where the
focus of research is on the subjects rather than the population, Vaida &
Blanchard propose a conditional AIC in which the likelihood is the
conditional likelihood, and K=p+1, where p is the 'effective number of
parameters' for the mean model defined by Hodges & Sargent (2001).
My understanding is that the log likelihood displayed in the output for
GLLAMM is the marginal log likelihood. If that's the case, does anyone
know how to request a conditional log likelihood in GLLAMM? I'd also be
grateful to learn how others have calculated the 'effective number of
parameters', p, following Hodges & Sargent (2001).
University of Minnesota
Vaida, F. & Blanchard, S. 2005. Conditional Akaike information for mixed
effects models. Biometrika 92:351-370.
Hodges, J.S. & Sargent, D.J. 2001. Counting degrees of freedom in
hierarchical and other richly parameterized models. Biometrika 88:367-379.
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