Hi All,
Regarding Robert's original question, others have answered this clearly. Think of a very narrow normal distribution. The area under the thing has to be 1, so the peak may need to be very tall. In a simple case, the likelihood might be a product of such densities, and so can be arbitrarily large. More generally the likelihood is always positive, and can be above 1 if the corresponding density is sufficiently concentrated. The log can therefore be positive or negative, as can -2 times the log.
Nikita's comment needs some clarification. If you are using the default REML algorithm in PROC MIXED to estimate the variance components (i.e., if you have not overridden it with something like METHOD=ML in the PROC statement), then variance components and the likelihood are based on pseudo-data that depends on the fixed effects. Variance components and likelihoods from models with different fixed
effects (i.e., different MODEL terms) are therefore based on different pseudo-data and are NOT comparable. However, models with the same fixed effects produce likelihoods on the same pseudo-data, and comparisons of variance structures using information criteria
can be made.
If you use full maximum likelihood (METHOD=ML), then you
can use information criteria to compare models that differ in fixed and/or random effects. However, the estimates of the variance components from these models are potentially somewhat biased.
This book (
http://www.amazon.com/Mixed-Models-Second-Ramon-Littell/dp/1590475003) is indispensable if you want to do modeling using mixed models in SAS.
-Tom.
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Thomas Loughin
Simon Fraser University
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Original Message:
Sent: 05-02-2013 17:50
From: Nikita Tuzov
Subject: Negative -2 log likelihood in Proc Mixed
Robert:
I agree with Michael. In addition, you may have another problem. If you use random effects, you can employ AIC and similar model selection criteria only to compare models that differ by a fixed effect. E.g., you can't compare a model where Factor A is fixed to a model where Factor A is assumed random using AIC/AICc/BIC and such like. For more, check out my review of this book:
http://www.amazon.com/Model-Selection-Multi-Model-Inference-Information-Theoretic/product-reviews/1441929738/ref=cm_cr_pr_top_recent?ie=UTF8&showViewpoints=0&sortBy=bySubmissionDateDescending
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Nikita Tuzov
Ph D Student
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