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st: marginal vs. conditional log likelihood in GLLAMM

From   Dan MacNulty <>
Subject   st: marginal vs. conditional log likelihood in GLLAMM
Date   Wed, 18 Oct 2006 09:50:47 -0700

Dear all,
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).

Dan MacNulty
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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