Comparing Binomial Generalized Linear Models

link function	residual deviance
logit	1.51743

Generalized linear models are models of the form



y

i

=

-1

g

(

β

0

+

β

1

f

1i

+

β

2

f

2i

+…)

, where

g

is an invertible function called the link function and the

f

j

are basis functions of one or more predictor variables. The term

β

0

+

β

1

f

1i

+

β

2

f

2i

+…

is linear in the

β

i

and is referred to as the linear predictor. The value



y

i

is the predicted response for the

th

i

observed response

y

i

, and the

y

i

are assumed to be independent observations from the same exponential family of distributions. When the exponential family is the binomial family, the success probability

p

is modeled.

This Demonstration fits binomial models with various common link functions. Check the boxes next to the named link functions to fit models with those links. Select a linear predictor to choose the argument of

-1

g

in the model. The linear predictors are taken to be polynomials in a single predictor variable

x

, so for instance, with a quadratic linear predictor, the model is

-1

g



β

0

+

β

1

x+

β

2

x



.

Mouse over a fitted curve to see the functional form of the model. The residual deviances for the models are included in a table for comparison.