Abstract
This paper introduces a new approach, based on dependent univariate GLMs, for fitting multivariate mixture models. This approach is a multivariate generalization of the method for univariate mixtures presented by Hinde (1982). Its accuracy and efficiency are compared with direct maximization of the log-likelihood. Using a simulation study, we also compare the efficiency of Monte Carlo and Gaussian quadrature methods for approximating the mixture distribution. The new approach with Gaussian quadrature outperforms the alternative methods considered. The work is motivated by the multivariate mixture models which have been proposed for modelling changes of employment states at an individual level. Similar formulations are of interest for modelling movement between other social and economic states and multivariate mixture models also occur in biostatistics and epidemiology.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, D. A. and Hinde, J. (1988) Random effects in generalised linear models and the EM algorithm. Communications in Statistics, 17, 3847–56.
Clayton, D. (1994) Generalised linear mixed models. In Markov Chain Monte Carlo in Practice. W. Gilks, S. Richardson, and D Spiegelhalter (eds). Chapman & Hall, London.
Davies, R. B. (1984) A generalised beta-logistic model for longitudinal data with an application to residential mobility. Environment and Planning, 16, 1375–86.
Davies, R. B.(1993) Nonparametric control for residual heterogeneity in modelling recurrent behaviour. Computational Statistics and Data Analysis, 16, 143–60
Davies, R. B. and Pickles, A. R. (1987) A joint trip timing, store choice model including feedback effects and nonparametric control for omitted variables. Transportation Research A, 21, 345–61.
Fahrmeir, L. and Tutz, G. (1994) Multivariate Statistical Modelling Based on Generalised Linear Models. Springer-Verlag, New York.
Flinn, C. and Heckman, J. J. (1982) New methods for analysing individual event histories. In Sociological Methodology 1982, S. Leinhardt (ed.), pp. 99–140, Jossey Bass, San Francisco.
Fotouhi, A. and Davies, R. B. (1995) The initial condition problem for discrete-time, discrete-response data. Working paper of the Centre for Applied Statistics, Lancaster University.
Gaus 3.0 Applications (1992) Maximum likelihood. Aptech Systems, Maple Valley, WA.
Heckman, J. J. and Singer, B. (1984) A method for minimising the impact of distributional assumptions in econometric models for duration data. Econometrica, 52, 271–320.
Hinde, J. (1982) Compound Poisson regression models. In GLIM 82, Proceedings of the International Conference on Generalised Linear Models, R. Gilchrist (ed.), pp. 109–121. Springer-Verlag, Berlin.
Laird, N. (1978) Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73, 805–11.
Pickles, A. R. and Davies R. B., (1985) The longitudinal analysis of housing careers. Journal of Regional Science, 25, 85–101.
Stiratelli, R., Laird, N. and Ware, J. H. (1984) Random-effects models for serial observation with binary response. Biometrics, 40, 961–71.
Wood, A. and Hinde, J. (1987) Binomial variance component models with nonparametric mixing distributions: a GLIM approach. In Longitudinal Data Analysis, R. Crouchley (ed.), pp. 110–28, Avebury, Aldershot, UK.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Oskrochi, G.R., Davies, R.B. An EM-type algorithm for multivariate mixture models. Statistics and Computing 7, 145–151 (1997). https://doi.org/10.1023/A:1018525800226
Issue Date:
DOI: https://doi.org/10.1023/A:1018525800226