Abramowitz, M. and Stegun, I. A. (eds) (1964) *Handbook of Mathematical Functions*. National Bureau of Standards, Washington DC.

Aitkin, M. (1995) Probability model choice in single samples from exponential families using Poisson log-linear modelling, and model comparison using Bayes and posterior Bayes factors. *Statistics and Computing*, **5**, 113–20.

Aitkin, M. (1996) A general maximum likelihood analysis of variance components in generalized linear models. Submitted.

Aitkin, M. and Aitkin, I. (1996) A hybrid EM/Gauss-Newton algorithm for maximum likelihood in mixture distributions. *Statistics and Computing* (to appear).

Aitkin, M., Anderson, D. A., Francis, B. J. and Hinde, J. P. (1989) *Statistical Modelling in GLIM*. Oxford University Press.

Aitkin, M. and Francis, B. J. (1995) Fitting overdispersed generalized linear models by nonparametric maximum likelihood. *GLIM Newsletter*, **25**, 37–45.

Aitkin, M. and Tunnicliffe Wilson, G. T. (1980) Mixture models, outliers and the EM algorithm. *Technometrics*, **22**, 325–31.

Anderson, D. A. (1988) Some models for overdispersed binomial data. *Aust. J. Statist.*, **30**, 125–48.

Anderson, D. A. and Aitkin, M. (1985) Variance component models with binary response: interviewer variability. *J. Roy. Statist. Soc.*
**B 47**, 203–10.

Anderson, D. A. and Hinde, J. P. (1988) Random effects in generalized linear models and the EM algorithm. *Commun. Statist.-Theory Meth.*, **17**, 3847–56.

Barry, J. T., Francis, B. J. and Davies, R. B.(1989) SABRE: software for the analysis of binary recurrent events. In *Statistical Modelling*, Springer-Verlag, New York.

Bock, R. D. and Aitkin, M. (1981) Marginal maximum likelihood estimation of item parameters: an application of an EM algorithm. *Psychometrika*, **46**, 443–59.

Böhning, D., Schlattman, P. and Lindsay, B. (1992) Computerassisted analysis of mixtures (C.A.MAN): statistical algorithms. *Biometrics*, **48**, 285–303.

Breslow, N. (1984) Extra-Poisson variation in log-linear models. *Appl. Statist.*, **33**, 38–44.

Breslow, N. (1989) Score tests in overdispersed GLMs. In *Statistical Modelling*, Springer-Verlag, New York.

Breslow, N. (1990) Tests of hypotheses in overdispersed Poisson regression and other quasi-likelihood models. *J. Amer. Statist. Assoc.*, **85**, 565–71.

Brownlee, K. A. (1965) *Statistical Theory and Methodology in Science and Engineering* (2nd edn). Wiley, New York.

Crouch, E. A. C. and Spiegelman, D. (1990) The evaluation of integrals of the form ∫-∞/+∞(*t*) exp(-*t*
^{2})d*t*: application to logistic-normal models. *J. Amer. Statist. Assoc.*, **85**, 464–9.

Davies, R. B. (1987) Mass point methods for dealing with nuisance parameters in longitudinal studies. In: R. Crouchley, ed. *Longitudinal Data Analysis*. Avebury, Aldershot, Hants.

Dean, C. B. (1992) Testing for overdispersion in Poisson and binomial regression models. *J. Amer. Statist. Assoc.*, **87**, 451–7.

Dempster, A. P., Laird, N. M. and Rubin D. A. (1977) Maximum likelihood estimation from incomplete data via the EM algorithm (with Discussion). *J. Roy. Statist. Soc.* B, **39**, 1–38.

Dietz, E. (1992) Estimation of heterogeneity-a GLM approach. In *Advances in GLIM and Statistical Modelling*. Springer-Verlag, New York.

Dietz, E. and Böhning, D. (1995) Statistical inference based on a general model of unobserved heterogeneity. In *Statistical Modelling*. Springer-Verlag, New York.

Efron, B. (1986) Double exponential families and their use in generalized linear regression. *J. Amer. Statist. Assoc.*, **81**, 709–21.

Ezzet, F. and Davies, R. B. (1988) A manual for MIXTURE. Centre for Applied Statistics, Lancaster, UK.

Feigl, P. and Zelen, M. (1965) Estimation of exponential probabilities with concomitant information. *Biometrics*, **21**, 826–38.

Follman, D. A. and Lambert, D. (1989) Generalizing logistic regression by nonparametric mixing. *J. Amer. Statist. Assoc.*, **84**, 295–300.

Francis, B. J., Green, M. and Payne, C. (eds) (1993) *The GLIM System: Release 4 Manual*. Clarendon Press, Oxford.

Heckman, J. J. and Singer, B. (1984) A method for minimizing the impact of distributional assumptions in econometric models of duration. *Econometrica*, **52**, 271–320.

Hinde, J. P. (1982) Compound Poisson regression models. In R. Gilchrist, ed. *GLIM 82* Springer-Verlag, New York.

Hinde, J. P. and Wood, A. T. A. (1987) Binomial variance component models with a non-parametric assumption concerning random effects. In R. Crouchley, ed. *Longitudinal Data Analysis*. Avebury, Aldershot, Hants.

Kiefer, J. and Wolfowitz, J. (1956) Consistency of the maximum likelihood estimator in the presence of infinitely many nuisance parameters. *Ann. Math. Statist.*, **27**, 887–906.

Laird, N. M. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. *J. Amer. Statist. Assoc.*, **73**, 805–11.

Lesperance, M. L. and Kalbfleisch, J. D. (1992) An algorithm for computing the non-parametric MLE of a mixing distribution. *J. Amer. Statist. Assoc.*, **87**, 120–6.

Lindsay, B. G. (1983) The geometry of mixture likelihoods, part I: a general theory. *Ann. Statist.*, **11**, 86–94.

Louis, T. A. (1982) Finding the observed information matrix when using the EM algorithm. *J. Roy. Statist. Soc.*, B, **44**, 226–33.

McCullagh, P. and Nelder, J. A. (1989) *Generalized Linear Models*. Chapman & Hall, London.

Moore, D. F. (1987) Modelling the extraneous variance in the presence of extrabinomial variation. *Appl. Statist.*, **36**, 8–14.

Nelder, J. A. (1985) Quasi-likelihood and GLIM. In R. Gilchrist, B. Francis and J. Whittaker, eds, *Generalized Linear Models* Springer-Verlag, Berlin.

Williams, D. A. (1982) Extra-binomial variation in logistic linear models. *Appl. Statist;.*, **31**, 144–8.