Exponential Family of Distributions and Generalized Linear Models

Annette J. Dobson
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Annette J. Dobson: University of Newcastle

Chapter 3 in Introduction to Statistical Modelling, 1983, pp 21-26 from Springer

Abstract: Abstract For several decades linear models of the form (3.1) % MathType!MTEF!2!1!+- % feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iaadIfacqaHYoGycqGHRaWkcaWGLbaaaa!3C40! $$ y = X\beta + e $$ with the assumption that the elements of e are NID(0, σ2) have formed the basis of most analyses of continuous data. For instance the examples in the previous chapter, the comparison of two means (plant growth example) and the relationship between a continuous response variable and a covariate (birthweight example), are both of this form. So, too, are generalizations of these examples to comparisons of more than two means (ANOVA) and the relationship between a continuous response variable and several explanatory variables (multiple regression).

Date: 1983
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DOI: 10.1007/978-1-4899-3174-0_3

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