Variance Component Models with Binary Response: Interviewer Variability

Abstract

SUMMARY Interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non‐normal family. The maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire. This raises some interesting questions about the use of unbalanced ANOVA methods with these data.

A general maximum likelihood analysis of overdispersion in generalized linear models

“…The double summation over i and k is conveniently (if inefficiently) handled by expanding the data vector to length Kn and replicating y and x K times, and the Gaussian quadrature variable z n times (Hinde, 1982;Anderson and Aitkin, 1985). Model fitting is then identical to that of a single sample of Kn with prior weight vector w. Initial estimates for the first E-step for/3 are conveniently obtained from the ordinary GLM fit, and for cr by arbitrary specification other than zero (e.g.…”

“…Past experience (Hinde, 1982;Anderson and Aitkin, 1985) with mixture modelling for overdispersion may have left the discouraging impression that the problem is compurationally intensive. While the Gauss-Newton algorithm may give more efficient model-fitting , report on this for normal mixtures), with present CPU speeds on personal computers this no longer seems such a serious issue, and the simplicity and generality of the non-parametric model and of the EM algorithm for full NPML estimation in overdispersed exponential family models make them powerful modelling tools.…”

“…The directional derivative approach of Lesperance and Kalbfleisch (1992) may be superior for this purpose. The methods in the paper are derived from those used by Hinde and Wood (1987) for the two-level binomial logit variance component model; they generalized the normal mixing distribution approach of Anderson and Aitkin (1985). A further paper (Aitkin, 1996) gives a detailed exposition of Hinde and Wood's approach for two-level models in the exponential family, with examples.…”

Non-linear panel estimation of import quotas: The evolution of quota premiums under the ATC

“…(6). Gaussian quadrature has been applied to discrete approximation of the conditional properties of time series for asset pricing models by (Tauchen and Hussey, 1991), and also in statistics more generally for non-parametric estimation of the properties of distribution space (Anderson and Aitkin, 1985;Laird, 1978, Aitkin, 1999. Laird (1978) and Ma et al (1996) both demonstrate the usefulness of this method for approximating distribution functions (as in the distribution of our quota estimates) without assuming specific parametric forms for the distributions.…”

Developments in statistical analysis in quantitative genetics

“…During the eighties, numerical integration based on quadrature (e.g. Anderson and Aitkin 1985) and different approximations, some involving considerable computational complexity, were the tools available for inference (e.g. Harville and Mee 1984; Ochi and Prentice 1984;Foulley et al 1987).…”