Likelihood inference in a correlated probit regression model

Correlated binary observations arise in a variety of applications. For example, in animal studies the term 'litter effect' is used to describe the greater alikeness of responses within a litter as compared to that between litters, at a given set of experimental conditions. In a setting that motivated this work, cells on individual atomic bomb survivors were scored as to the presence or absence of chromosomal aberrations. The number of aberrant cells varied among subjects at a specified radiation exposure estimate, age at exposure, city of exposure and sex, in a manner that substantially exceeds that consistent with a binomial error structure (Otake & Prentice, 1984). This extra-binomial variation, or overdispersion, reflects the fact that the binary response of cells from a given survivor tend to be more alike than are the responses of cells from distinct survivors having the same estimated radiation exposure level and other covariate values. Such overdispersion may result from individual differences in susceptibility to radiation damage, from omitted covariates, or, most plausibly in this setting, from substantial random errors in the estimated radiation exposure levels. Failure to acknowledge overdispersion may lead to serious underestimation of the standard errors associated with regression parameter estimates and to unduly precise inferences.