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Comparing Binomial Generalized Linear Models

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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.

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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.

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Contributed by: Darren Glosemeyer (March 2011)
Open content licensed under CC BY-NC-SA

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Details

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.

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