1. Statistics Sweden September 2004 Dan Hedlin
Logistic Regression
Statistics Sweden
September 2004
Dan Hedlin

2. Binary Y variable (0 or 1)
Contract cancer or not, over or under a poverty line, response or nonresponse
Y is not limited in ordinary regression
Trick:
p is probability for cancer, etc.

3. Alternative expressions
Common notation
Equivalent:

4. Different scales Log-odds (additive effects)
Odds p/(1-p) (multiplicative effects)
Probability p
Another difference to ’ordinary’ regression:
Iterative computation and numerical issues

5. Interpretation of parameters
’Base probability’ for and
Maybe most interpretable when x are interval scaled variables and the zero point is meaningful

6. Interpretation of ß One auxiliary variable: So
Hence additive one-step-increment of x gives multiplicative effect on odds with

7. Classical example
Bliss (1935), also in Agresti (1990) ’Catergorical Data Analysis’, Wiley, section
Beetles, two interval-scaled variables y = dead/survived, x = log(dose carbon disulphide)
There are other models for a binary y that in some cases may be better. Logistic reg most common.

8. Model fitting Table low-high risk vs each variable separately
Are there cells with zero observations?
First selection with e.g. Forward selection 0.25 significance level
Test each remaining variable separately
For continuous variables: examine linearity by dividing the continuous variable in groups and compute log-odds within group
Test interaction effects
Consider subject matter knowledge