Abstract:
:Multinomial data arise in many areas of the life sciences, such as mark-recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi-likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet-multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X2 or the deviance D. For many types of study, such as mark-recapture, the data will be sparse. The estimator based on X2 can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X2 , the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark-recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are very sparse.
journal_name
Biometricsjournal_title
Biometricsauthors
Afroz F,Parry M,Fletcher Ddoi
10.1111/biom.13194subject
Has Abstractpub_date
2020-09-01 00:00:00pages
834-842issue
3eissn
0006-341Xissn
1541-0420journal_volume
76pub_type
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