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On a Likelihood‐Based Goodness‐of‐Fit Test of the Beta‐Binomial Model
Author(s) -
Garren Steven T.,
Smith Richard L.,
Piegorsch Walter W.
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.947_1.x
Subject(s) - goodness of fit , beta binomial distribution , binomial distribution , statistics , binomial test , negative binomial distribution , mathematics , binomial (polynomial) , binomial proportion confidence interval , beta (programming language) , continuity correction , likelihood ratio test , econometrics , computer science , poisson distribution , programming language
Summary. When faced with proportion data that exhibit extra‐binomial variation, data analysts often consider the beta‐binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta‐binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness‐of‐fit test proposed by Brooks et al. (1997, Biometrics 53 , 1097–1115) but find that it lacks the ability to distinguish between the beta‐binomial model and some severely non‐beta‐binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.