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Two algorithms for fitting constrained marginal models

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  • Evans, R.J.
  • Forcina, A.

Abstract

The two main algorithms that have been considered for fitting constrained marginal models to discrete data, one based on Lagrange multipliers and the other on a regression model, are studied in detail. It is shown that the updates produced by the two methods are identical, but that the Lagrangian method is more efficient in the case of identically distributed observations. A generalization is given of the regression algorithm for modelling the effect of exogenous individual-level covariates, a context in which the use of the Lagrangian algorithm would be infeasible for even moderate sample sizes. An extension of the method to likelihood-based estimation under L1-penalties is also considered.

Suggested Citation

  • Evans, R.J. & Forcina, A., 2013. "Two algorithms for fitting constrained marginal models," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 1-7.
    • Handle: RePEc:eee:csdana:v:66:y:2013:i:c:p:1-7
    DOI: 10.1016/j.csda.2013.02.001
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    6. Monia Lupparelli & Alberto Roverato, 2017. "Log-mean linear regression models for binary responses with an application to multimorbidity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 227-252, February.
    7. Forcina, Antonio, 2023. "Marginal log-linear models and mediation analysis," Statistics & Probability Letters, Elsevier, vol. 194(C).
    8. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    9. Anna Klimova & Tamás Rudas, 2015. "Iterative Scaling in Curved Exponential Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 832-847, September.
    10. Antonoio Forcina, 2019. "Estimation and testing of multiplicative models for frequency data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 807-822, October.

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