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Logistic Regression

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Logistic Regression

Now with multinomial support!

- 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)

- Binary outcome: standard logistic regression

- 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

- 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

- Standard Logistic Regression:
- logistic regression [dep. var] with [ind. vars]

- Multinomial Logistic Regression:
- nomreg [dep. var] with [ind. vars]

- Standard Logistic Regression:
- logit [dep. var] [ind. vars]

- Multinomial Logistic Regression:
- mlogit [dep. var] [ind. vars]

- Odds-Ratio Coefficients
- [regression], or

- Predicted Probability Estimates (new to Stata 11)
- margins [ind. var to analyze], at[value of other ind. vars]

- Probit
- Very similar to logit
- Easier to interpret coefficients (predicted probabilities)
- Probabilities aren’t bounded between 0 and 1

- Stata:
- use http://www.ats.ucla.edu/stat/stata/dae/binary.dta
- logit admit gre gpa i.rank
- logit, or
- odds-ratio (instead of log odds-ratio) interpretation of the coefficients

- margins rank, atmeans
- 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

- SPSS
- Download binary.sav from http://www.ats.ucla.edu/stat/spss/dae/logit.htm
- After opening the file:
- logistic regression admit with gregpa rank
/categorical = rank.

- logistic regression admit with gregpa rank