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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

Logistic Regression

Now with multinomial support!

an introduction
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
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
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
slide6
SPSS
  • Standard Logistic Regression:
    • logistic regression [dep. var] with [ind. vars]
  • Multinomial Logistic Regression:
    • nomreg [dep. var] with [ind. vars]
stata
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
Other Methods?
  • Probit
    • Very similar to logit
    • Easier to interpret coefficients (predicted probabilities)
    • Probabilities aren’t bounded between 0 and 1
examples
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
examples1
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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