# 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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