# Logistic Regression - PowerPoint PPT Presentation

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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)

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Logistic Regression

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## 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

• 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

### 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:

• 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]

### 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

• 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