#### Logistic Regression

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Logistic Regression

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.