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

VL - 47

SP - 639

EP - 653

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

SN - 0167-9473

IS - 3

ER -