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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)

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Logistic Regression

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  1. Logistic Regression Now with multinomial support!

  2. 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)

  3. 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

  4. Graph of the Logistic Function

  5. 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

  6. SPSS • Standard Logistic Regression: • logistic regression [dep. var] with [ind. vars] • Multinomial Logistic Regression: • nomreg [dep. var] with [ind. vars]

  7. 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]

  8. Other Methods? • Probit • Very similar to logit • Easier to interpret coefficients (predicted probabilities) • Probabilities aren’t bounded between 0 and 1

  9. 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

  10. Examples • 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.

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