Comparing Binomial Generalized Linear Models

Generalized linear models are models of the form , where is an invertible function called the link function and the are basis functions of one or more predictor variables. The term is linear in the and is referred to as the linear predictor. The value is the predicted response for the observed response , and the are assumed to be independent observations from the same exponential family of distributions. When the exponential family is the binomial family, the success probability 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 in the model. The linear predictors are taken to be polynomials in a single predictor variable , so for instance, with a quadratic linear predictor, the model is .
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.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The logit link function is .
The probit link is the inverse CDF for a standard normal distribution, and the cauchit link is the inverse CDF for a standard Cauchy distribution.
The identity function for is .
The log-log and complementary log-log links are and , respectively.
The log and log complement links are and , respectively.
The odds power link is the odds power link , with taken to be 1.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students. »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+