# SIMSTAT: Generalized Linear Models

Generalized Linear Models (GLM)
This option is often the technique of choice when it can be assumed that the errors follow either a normal, binomial, Poisson or gamma distribution and there is a link function giving a good fit, e.g. binary logistic regression assuming a binomial distribution and logistic link. Appropriate links such as power, identity, reciprocal, square root, log, logistic, probit or complementary log-log are provided and the canonical links are indicated as defaults. There are many options for controlling the Simfit GLM interface. Try the test files glm.tf1 (normal), glm.tf2 (binomial), glm.tf3 (Poisson) and glm.tf4 (gamma). The data format is as for multilinear regression, except that an extra column is needed for the sample sizes when binomial errors are assumed. In the case of binary logistic regression, the y values would all be 0 (failure) or 1 (success), and the extra column for the number of trials would be set equal to 1. If a factor with m levels is represented in a logistic regression by m (0,1) dummy indicator variables x_1, x_2, ..., x_m, and a constant term is permitted in the regression but x_1 is suppressed, then the estimated coefficients can be interpreted as log odds ratios for the factor levels with respect to level 1. There is a simplified interface to GLM which should be used for logistic regression, binary logistic regression, polynomial logistic regression, survival analysis (using exponential, Weibull or Cox models), and dose response curves (using probits, logits or log-logs).

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