## 10.1 Fitting GLMs

All regression models aim to model the expected value of the response variable $$Y$$ given the observed data $$X$$, through some link function $$C$$

$E(Y|X) = C(X)$

Depending on the data type of $$Y$$, this link function takes different forms. Examples include:

• Linear regression: C = Identity function (no change)
• Logistic regression: C = logit function
• Poisson regression: C = log function

### 10.1.1 R

The general syntax is similar to lm(), with the additional required family= argument. See ?family for a list of options. Example for Logistic regression would be:

glm(y ~ x1 + x2 + x3, data=DATA, family="binomial") 

### 10.1.2 SPSS

File menu: Regression –> Binary Logistic.

Syntax:

logistic regression Y with x1 x2 x3
/categorical = x2

https://www.ibm.com/support/knowledgecenter/en/SSLVMB_26.0.0/statistics_reference_project_ddita/spss/regression/syn_logistic_regression_overview.html

### 10.1.3 Stata

logistic Y x1 x2

https://www.stata.com/features/overview/logistic-regression/