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L OGISTIC R EGRESSION Now with multinomial support!

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A N I NTRODUCTION 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)

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H OW I T A LL W ORKS 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

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G RAPH OF THE L OGISTIC F UNCTION

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C OEFFICIENT I NTERPRETATION 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

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

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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]

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O THER M ETHODS ? Probit Very similar to logit Easier to interpret coefficients (predicted probabilities) Probabilities aren’t bounded between 0 and 1

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E XAMPLES 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

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

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