Premium
A semi‐parametric estimate of extra‐Poisson variation for vital rates
Author(s) -
Fay Michael P.,
Feuer Eric J.
Publication year - 1997
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/(sici)1097-0258(19971115)16:21<2389::aid-sim683>3.0.co;2-j
Subject(s) - overdispersion , pointwise , statistics , poisson distribution , confidence interval , smoothness , mathematics , quasi likelihood , parametric statistics , poisson regression , variance (accounting) , econometrics , parametric model , count data , population , mathematical analysis , demography , accounting , sociology , business
We introduce a method for estimating overdispersion in Poisson models for vital rates. We assume smoothness conditions on the counts to obtain pointwise variance estimates that we combine to obtain an estimate of the overdispersion parameter. We create confidence intervals about the observed rates using this estimate and an approximation based on the gamma distribution. The advantage of this method is that the estimates of the superpopulation rates do not depend on the smoothness assumption, yet when this assumption is met we obtain approximately unbiased estimates of the overdispersion parameter. Thus, we may calculate confidence intervals for vital rates under an overdispersed Poisson model without making parametric assumptions on the mean rates. © 1997 John Wiley & Sons, Ltd.