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An active set algorithm to estimate parameters in generalized linear models with ordered predictors

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  • Rufibach, Kaspar

Abstract

In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may be continuous, binary, or represent censored survival times. In the absence of precise knowledge of the response function, using monotonicity constraints on the ordinal variables improves efficiency in estimating parameters, especially when sample sizes are small. An active set algorithm that can efficiently compute such estimators is proposed, and a characterization of the solution is provided. Having an efficient algorithm at hand is especially relevant when applying likelihood ratio tests in restricted generalized linear models, where one needs the value of the likelihood at the restricted maximizer. The algorithm is illustrated on a real life data set from oncology.

Suggested Citation

  • Rufibach, Kaspar, 2010. "An active set algorithm to estimate parameters in generalized linear models with ordered predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1442-1456, June.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1442-1456
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    References listed on IDEAS

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    1. Piet Groeneboom & Geurt Jongbloed & Jon A. Wellner, 2008. "The Support Reduction Algorithm for Computing Non‐Parametric Function Estimates in Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 385-399, September.
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    4. van der Kooij, Anita J. & Meulman, Jacqueline J. & Heiser, Willem J., 2006. "Local minima in categorical multiple regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 446-462, January.
    5. David B. Dunson & Amy H. Herring, 2003. "Bayesian Inferences in the Cox Model for Order-Restricted Hypotheses," Biometrics, The International Biometric Society, vol. 59(4), pages 916-923, December.
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    Cited by:

    1. Gerhard Tutz & Jan Gertheiss, 2014. "Rating Scales as Predictors—The Old Question of Scale Level and Some Answers," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 357-376, July.
    2. Baojiang Chen & Ao Yuan & Jing Qin, 2022. "Pool adjacent violators algorithm–assisted learning with application on estimating optimal individualized treatment regimes," Biometrics, The International Biometric Society, vol. 78(4), pages 1475-1488, December.

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