Abstract #301987

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JSM 2003 Abstract #301987
Activity Number: 29
Type: Contributed
Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #301987
Title: Generalized Linear Models Using the NEF6 Distribution
Author(s): David N. Esch*+ and Carl N. Morris
Companies: Harvard University and Harvard University
Address: 1 Oxford St., Cambridge, MA, 02138,
Keywords: generalized linear models ; exponential families ; natural exponential families ; skewness
Abstract:

The NEF6 Distribution is the Natural Exponential Family (NEF) generated by the Generalized Hyperbolic Secant Distribution. It is the sixth NEF with Quadratic Variance Function, the other five being Normal, Poisson, Gamma, Binomial, and Negative Binomial. The NEF6 distribution ranges from a symmetric bell-shaped distribution to skewed, the extreme case of skewness being a Gamma limit law. Its variance function is a quadratic with no real roots. We propose a generalized linear model using such a distribution to model conditionally or unconditionally skewed data, regressing on covariates. Model properties, fitting techniques, simulated examples, and applicability to real data will be disucssed. We believe this model could form a useful compromise between Gamma (constant coefficient of variation) and normal (constant variance) models, for situations when the variance does not vanish entirely when the linear predictor is zero, yet variance grows as the square of the linear predictor.

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