Published on Oct 1, 2013in Psychometrika2.74
· DOI :10.1007/s11336-013-9328-2
Yeojin Chung4
Estimated H-index: 4
(Kookmin University),
Sophia Rabe-Hesketh55
Estimated H-index: 55
(University of California, Berkeley)
+ 2 AuthorsJingchen Liu14
Estimated H-index: 14
(Columbia University)
Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance will be positive. We suggest a default log-gamma(2,λ) penalty with λ→0, which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the data while being nondegenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior.
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