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


Rufibach, K (2010). An active set algorithm to estimate parameters in generalized linear models with ordered predictors. Computational Statistics and Data Analysis, 54(6):1442-1456.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:1 June 2010
Deposited On:10 Mar 2010 08:56
Last Modified:17 Feb 2018 16:57
Publisher:Elsevier
ISSN:0167-9473
OA Status:Green
Publisher DOI:https://doi.org/10.1016/j.csda.2010.01.014

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