LOGISTIC REGRESSION
Now with multinomial support!
AN INTRODUCTION

Logistic regression is a method for analyzing
relative probabilities between discrete outcomes
(binary or categorical dependent variables)

Binary outcome: standard logistic regression


ie. Dead (1) or NonDead (0)
Categorical outcome: multinomial logistic regression

ie. Zombie (1) or Vampire (2) or Mummy (3) or Rasputin (4)
HOW IT ALL WORKS

The logistic equation is written as a function of z,
where z is a measure of the total contribution of
each variable x used to predict the outcome



Coefficients determined by maximum likelihood
estimation (MLE), so larger sample sizes are
needed than for OLS
GRAPH OF THE LOGISTIC FUNCTION
COEFFICIENT INTERPRETATION


Standard coefficients (untransformed) report the
change in the log odds of one outcome relative to
another for a one-unit increase of the independent
variable (positive, negative)
Exponentiating the coefficients reports the change in
the odds-ratio (greater than, less than one)


By evaluating all other values at particular levels (ie.
their means) it is possible to obtain predicted
probability estimates
SPSS

Standard Logistic Regression:


logistic regression [dep. var] with [ind. vars]
Multinomial Logistic Regression:

nomreg [dep. var] with [ind. vars]
STATA

Standard Logistic Regression:


Multinomial Logistic Regression:


mlogit [dep. var] [ind. vars]
Odds-Ratio Coefficients


logit [dep. var] [ind. vars]
[regression], or
Predicted Probability Estimates (new to Stata 11)

margins [ind. var to analyze], at[value of other ind.
vars]
OTHER METHODS?

Probit
Very similar to logit
 Easier to interpret coefficients (predicted
probabilities)
 Probabilities aren’t bounded between 0 and 1

EXAMPLES

Stata:
use http://www.ats.ucla.edu/stat/stata/dae/binary.dta
 logit admit gre gpa i.rank
 logit, or



margins rank, atmeans


odds-ratio (instead of log odds-ratio) interpretation of the
coefficients
predicted probability of rank with gre and gpa at their
means
margins, at(gre=(200(100)800))

start with gre=200, increase by steps of 100, end at 800
EXAMPLES

SPSS
Download binary.sav from
http://www.ats.ucla.edu/stat/spss/dae/logit.htm
 After opening the file:


logistic regression admit with gre gpa rank
/categorical = rank.