TY - JOUR
T1 - Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies
AU - Agresti, Alan
AU - Caffo, Brian
AU - Ohman-Strickland, Pamela
N1 - Funding Information:
The research of Agresti and Caffo was partially supported by grants from NSF and NIH.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2004/10/1
Y1 - 2004/10/1
N2 - This note shows three cases in which a considerable loss of efficiency can result from assuming a parametric distribution for a random effect that is substantially different from the true distribution. For two simple models for binary response data, we studied the effects of assuming normality or of using a nonparametric fitting procedure for random effects, when the true distribution is potentially far from normal. Although usually the choice of random effects distribution has little effect on efficiency of predicting outcome probabilities, the normal approach suffered when the true distribution was a two-point mixture with a large variance component. Likewise, for a simple survival model, assuming a gamma distribution for the frailty distribution when the true one was a two-point mixture resulted in considerable loss of efficiency in predicting the frailties. The paper concludes with a discussion of possible ways of addressing the problem of potential efficiency loss, and makes suggestions for future research.
AB - This note shows three cases in which a considerable loss of efficiency can result from assuming a parametric distribution for a random effect that is substantially different from the true distribution. For two simple models for binary response data, we studied the effects of assuming normality or of using a nonparametric fitting procedure for random effects, when the true distribution is potentially far from normal. Although usually the choice of random effects distribution has little effect on efficiency of predicting outcome probabilities, the normal approach suffered when the true distribution was a two-point mixture with a large variance component. Likewise, for a simple survival model, assuming a gamma distribution for the frailty distribution when the true one was a two-point mixture resulted in considerable loss of efficiency in predicting the frailties. The paper concludes with a discussion of possible ways of addressing the problem of potential efficiency loss, and makes suggestions for future research.
KW - Binomial
KW - Frailty model
KW - Gamma distribution
KW - Logit model
KW - Nonparametric
KW - Odds ratio
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U2 - 10.1016/j.csda.2003.12.009
DO - 10.1016/j.csda.2003.12.009
M3 - Article
AN - SCOPUS:4944247358
SN - 0167-9473
VL - 47
SP - 639
EP - 653
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 3
ER -