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.