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A NONDEGENERATE PENALIZED LIKELIHOOD ESTIMATOR FOR VARIANCE PARAMETERS IN MULTILEVEL MODELS

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)
Abstract
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.
  • References (57)
  • Citations (92)
References57
Newest
#1Julian P. T. Higgins (Medical Research Council)H-Index: 99
#2Simon G. Thompson (Medical Research Council)H-Index: 102
Last.David J. Spiegelhalter (Medical Research Council)H-Index: 80
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#1Andrew Gelman (Columbia University)H-Index: 79
#2Boris Shor (U of C: University of Chicago)H-Index: 9
Last.David Park (GW: George Washington University)H-Index: 11
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#1Erin L Sauer (UW: University of Wisconsin-Madison)
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#1Simon Mats Breil (WWU: University of Münster)H-Index: 2
#2Boris Forthmann (WWU: University of Münster)H-Index: 7
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#1Michael A. Tabak (USDA: United States Department of Agriculture)H-Index: 6
#2Kerri Pedersen (USDA: United States Department of Agriculture)H-Index: 13
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#1Terence Purkiss (JCU: James Cook University)H-Index: 1
#2Lori Lach (JCU: James Cook University)H-Index: 21
#1Cassandra E. Benkwitt (Lancaster University)H-Index: 9
#2Shaun K. Wilson (UWA: University of Western Australia)H-Index: 46
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