Dates Presentations Wed / Fri Ex. 4, logistic regression, Monday Dec 7 th Final Tues. Dec 8 th, 3:30

ps366 logistic regression

First, questions from Friday? Recoding Transforming variables Pew Survey – Form A vs. Form B (grrr)

Exercise 4 Build a model that predicts how people respond to a survey question (Obama v Romney – Think casually – Y = dichotomous (yes or no; agree or disagree) X1 (party ID....what rank / order?) X2 X3

Group data analysis Likely, you will use cross-tabs and Chi-square tests for most / many hypotheses Also, build one multi-var model in.... – Logistic regression if dichotomous variable – Linear regression if ordinal / interval

Logistic Regression Going a bit beyond Cross-tabulation – Dichotomous dependent variable regression – Cross-tabs & Chi Square are ‘bivariate’ tests Is X1 associated with Y? This does not control for effect X2, X3, etc. on Y

Binary logistic regression Dichotomous dependent variable – Test for effects of multiple independent variables Interval (age) Ordinal (party, education) Nominal (gender)

Binary logistic regression Dichotomous dependent variable, multiple independent variables – Y = Romney or Obama X1 = Party ID (0= others, 1= Democrat; or 1=D, 2=I, 3=R) X2 = Age X3 = Education

Logistic regression Several different estimators – Logit – Probit – Scobit – Similar in practice, choice depends on distribution of Y (Dependent variable)

Logistic regression

Logistic vs. Linear Regression

Logistic Regression

Maximum Likelihood Estimation (MLE) – Identifies model that predicts if Y – Initial ML function is estimated – Repeated iterations until the Log Likelihood (LL) does not change – We don’t do this by hand

Logistic Regression Dependent variable is a ‘logit’ Natural log of the odds

Logistic Regression You are estimating the probability of an event occurring Prob (event) = 1 / [ 1+e (-BO + B1X) ] Where X is the independent variable, 0 is a constant, and e is the natural log (2.718)

Logistic Regression With more than one independent variable: Prob(event) = e z / (1+ e z ); or 1 / (1 + e -z ) where Z= Bo + B 1 X 1 + B 2 X B n X n

Logistic Regression Fit: Pseudo R 2 – Various types, all imperfect Model Chi Square / Likelihood Ratio Test – Difference between LR for “baseline model” and the final model

Logistic regression So, – Substantive meaning of logit estimations not easy to interpret

Logistic Regression UCLA example Interpreting output – Classification table

Logistic Regression Interpreting output – Lots of stuff we don’t need – Variables not in the equation Ignore this, info about generating the ‘baseline model’ Skip to Block 1 Method = Enter

Logistic Regression Interpreting output – Model Summary These are “pseudo R2” value Another way to assess fit – Classification table Helps assess ‘fit’ of model Key: What % correctly classified? compares predictions of model to reality – (in this example......)

Logistic Regression Interpreting output – Variables in the Equation Similar to regression analysis – B (like slope estimate) – S.E. (error of estimate) – Wald (ratio of B to S.E.) – Sig (how significant is effect of X on Y?) – Exp(B)

Logistic Regression Interpreting output – B Estimates the odds of Y occurring... “the log of the odds.” (Yuck). The change in the log odds associated with a one unit change in the independent variable (Yuck x2) Is it significantly different than 0?

Logistic Regression Interpreting output – Wald test and sig. Is it significantly different than 0, Holding constant the effects of other X variables?

Logistic Regression Interpreting output – Exp(B) Substantive meaning of effect of X on Y If X changes from 0 to 1 (1 unit), the odds of Y being 1 increases by a factor of this. – if positive effect, larger than 1.0 – if negative effect, less than 1.0 (odds lower)

Exp(B), Odds ratio Ratio of y = 1 to y = 0 if probability of y =.5, odds ratio is /.5 = odds ratio of 1

Exp(B), Odds ratio Example – y = 1 if vote, 0 = not – Prob. of vote is.8; of not voting, 1-.8, or.2 – Odds = are ratio of prob. of y=1 to prop. y = 0 – odds of vote =.8/.2 = 4

Odds and probability

Logistic Regression Hypothesis testing – Overall, SPSS doesn’t give good information about the real effect of change in X on probability of being 0 or 1 on Y – It does let us test if effect of X on Y holds up when other X’s accounted for – It does tell us how well X’s predict Y