In statistics, the generalized linear model (GLM) is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
The GAUSS function glm is used to solve generalized linear model problems. GAUSS provides the following combinations from exponential family and related link function.
| Normal | Binomial | Poisson | Gamma | |
| identity | * | * | * | * |
| inverse | * | * | * | * |
| ln | * | * | * | * |
| logit | * | |||
| probit | * |
Format
// Read data matrix from a '.csv' file and start from the second row
data = csvReadM("binary.csv", 2);
// Read headers from first row
vnames = csvReadSA("binary.csv", 1|1);
// Specify dependent variable
y = data[.,1];
// Specify independent variable
x = data[.,2:4];
// Specify link function
link = "logit";
// Call glm function
call glm(y, x, "binomial", vnames, 3, link);Output
Generalized Linear Model
Valid cases: 400 Dependent Variable: admit
Degrees of freedom: 394 Distribution: binomial
Deviance: 458.5 Link function: logit
Pearson Chi-square: 397.5 AIC: 470.5
Log likelihood: -229.3 BIC: 494.5
Dispersion: 1 Iterations: 4
Standard Prob
Variable Estimate Error z-value >|z|
---------------- ------------ ------------ ------------ ------------
CONSTANT -3.99 1.14 -3.5001 0.000465027
rank 2 -0.67544 0.31649 -2.1342 0.0328288
3 -1.3402 0.34531 -3.8812 0.000103942
4 -1.5515 0.41783 -3.7131 0.000204711
gre 0.0022644 0.001094 2.0699 0.0384651
gpa 0.80404 0.33182 2.4231 0.0153879
Note: Dispersion parameter for BINOMIAL distribution taken to be 1