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Restricted Estimation of Generalized Linear Models

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  • Hans Nyquist

Abstract

Maximum likelihood estimation of the generalized linear model under linear restrictions on the parameters is considered. Using a penalty function approach an iterative procedure for obtaining the estimates is proposed. The likelihood ratio test, the Wald test and the Lagrange multiplier test are considered as alternatives for testing a hypothesis about linear restrictions on the parameters. An application of the estimator and the tests is illustrated in a numerical example. The approach extends to a definition of a ridge estimator for generalized linear models and to a definition of piecewise regressions, including cubic spline functions and a nonparametric smoother.

Suggested Citation

  • Hans Nyquist, 1991. "Restricted Estimation of Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 40(1), pages 133-141, March.
    • Handle: RePEc:bla:jorssc:v:40:y:1991:i:1:p:133-141
    DOI: 10.2307/2347912
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    Cited by:

    1. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 393-416, December.
    2. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.
    3. Jeremias Leão & Francisco Cysneiros & Helton Saulo & N. Balakrishnan, 2016. "Constrained test in linear models with multivariate power exponential distribution," Computational Statistics, Springer, vol. 31(4), pages 1569-1592, December.
    4. Jamshidian, Mortaza, 2004. "On algorithms for restricted maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 137-157, March.
    5. Cysneiros, Francisco Jose A. & Paula, Gilberto A., 2005. "Restricted methods in symmetrical linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 689-708, June.
    6. Faisal M. Zahid & Shahla Ramzan, 2012. "Ordinal ridge regression with categorical predictors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(1), pages 161-171, March.
    7. M. Revan Özkale & Hans Nyquist, 2021. "The stochastic restricted ridge estimator in generalized linear models," Statistical Papers, Springer, vol. 62(3), pages 1421-1460, June.
    8. Gerhard Tutz & Gunther Schauberger, 2015. "A Penalty Approach to Differential Item Functioning in Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 21-43, March.
    9. Faisal Maqbool Zahid & Gerhard Tutz, 2013. "Proportional Odds Models with High‐Dimensional Data Structure," International Statistical Review, International Statistical Institute, vol. 81(3), pages 388-406, December.
    10. Devriendt, Sander & Antonio, Katrien & Reynkens, Tom & Verbelen, Roel, 2021. "Sparse regression with Multi-type Regularized Feature modeling," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 248-261.
    11. Faisal Zahid & Gerhard Tutz, 2013. "Ridge estimation for multinomial logit models with symmetric side constraints," Computational Statistics, Springer, vol. 28(3), pages 1017-1034, June.
    12. M. Pardo, 2011. "Testing equality restrictions in generalized linear models for multinomial data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 73(2), pages 231-253, March.
    13. Paula, Gilberto A., 1999. "One-sided tests in generalized linear dose-response models," Computational Statistics & Data Analysis, Elsevier, vol. 30(4), pages 413-427, June.
    14. Reinaldo Arellano-Valle & Silvia Ferrari & Francisco Cribari-Neto, 1999. "Bartlett and Bartlett-type corrections for testing linear restrictions," Applied Economics Letters, Taylor & Francis Journals, vol. 6(9), pages 547-549.
    15. Fikriye Kurtoğlu & M. Revan Özkale, 2016. "Liu estimation in generalized linear models: application on gamma distributed response variable," Statistical Papers, Springer, vol. 57(4), pages 911-928, December.
    16. Tutz, Gerhard & Leitenstorfer, Florian, 2006. "Response shrinkage estimators in binary regression," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2878-2901, June.
    17. Ding, Jieli & Tian, Guo-Liang & Yuen, Kam Chuen, 2015. "A new MM algorithm for constrained estimation in the proportional hazards model," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 135-151.
    18. Månsson, Kristofer, 2012. "On ridge estimators for the negative binomial regression model," Economic Modelling, Elsevier, vol. 29(2), pages 178-184.

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