Restricted ridge estimator in generalized linear models: Monte Carlo simulation studies on Poisson and binomial distributed responses

ABSTRACT

It is known that collinearity among the explanatory variables in generalized linear models (GLMs) inflates the variance of maximum likelihood estimators. To overcome multicollinearity in GLMs, ordinary ridge estimator and restricted estimator were proposed. In this study, a restricted ridge estimator is introduced by unifying the ordinary ridge estimator and the restricted estimator in GLMs and its mean squared error (MSE) properties are discussed. The MSE comparisons are done in the context of first-order approximated estimators. The results are illustrated by a numerical example and two simulation studies are conducted with Poisson and binomial responses.

KEYWORDS:

• Generalized linear models
• Mean squared error
• Multicollinearity
• Poisson distribution
• Restricted ridge estimation

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J12
• 62J07

Notes

1 b shows any estimator.

2 (i), (ii), (iii), (v) and (iv) in tables show respectively the restrictions corresponding to κ = 1, κ = 1.05, κ = 1.5, κ = 0.95 and κ = 0.5.