Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series B, Pt. 3, pp. 382--396

MONOTONIC ALGORITHMS FOR MAXIMUM LIKELIHOOD ESTIMATION IN GENERALIZED LINEAR MODELS

By

MEENAKSHI DEVIDAS, University of Florida, Gainesville

and

E. OLUSEGUN GEORGE, University of Memphis, Memphis

SUMMARY. This paper proposes a modification of the Fisher--Scoring method, an algorithm which is widely used for computing maximum likelihood estimates, and one which is analogous to algorithms for computing quasi-likelihood or generalized estimating equations (GEE) estimates. Using an upper bound principle, we propose an algorithm that can be used for obtaining MLEs in GLM and GEE estimates. Generally such algorithms converge monotonically to the maximum. Details are given for the generalized exponential family, with canonical parameters modeled in terms of response functions. An iteratively reweighted least squares method that uses the above bound, is constructed for estimating regression and shape parameters of the response functions. The new algorithm is illustrated with an application to generalized logistic regression.

AMS (1991) subject classification. 62J12, 65C20

Key words and phrases. Generalized estimating equations, Generalized linear models, Loewner upper bound, Quadratic exponential models, Quasi-likelihood.

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