April 25, 2006Lecture 14 Slide #1 Logits and Factor Analysis Homework Review Logit Analysis –Logit Interpretation –Logit diagnostics Factor analysis-in-brief –Scaling in factor analysis –Using scales

April 25, 2006Lecture 14 Slide #2 Homework Review Predict the choice between Quad and LD-HR –required recodes Plot the effect of the risk index and ideology on probability of a shift

April 25, 2006Lecture 14 Slide #3 Interpreting Logits (again) Logits can be used to directly calculate odds: Logits can be reversed to obtain the predicted probabilities:

April 25, 2006Lecture 14 Slide #4 Interpreting Logits, Continued How would you calculate the effect of a particular combination of independent variables on the probability of Y=1? Set all X j ’s at the appropriate values, then calculate (e= ) The result is the average probability for that “type” of respondents

April 25, 2006Lecture 14 Slide #5 Example: Effect of ideology, gender on probability of choosing the LD-HR model for standard setting Model: choice (DR_standard) as a function of: –Ideology, gender and certainty Types –A=conservative male; B=liberal female –Set certainty at the average –A: conservative, male, average level of certainty Ideology=7, gender = 1, certainty=5.865 –B: liberal, female, average level of certainty Ideology=1, gender = 0, certainty= =chose threshold, 1=choose LD-HR

April 25, 2006Lecture 14 Slide #6 Logit Model Results

April 25, 2006Lecture 14 Slide #7 Analyzing Types L = ( *(ideology)) + ( *(sex)) + ( *(certainty)) L Probability Conservative Males: (indep. vars.: 7; 1; 5.865) Liberal Females: (indep. vars.: 1; 0; 5.865) Hint: Use a spreadsheet to calculate L and P. In Excel, the formula for probability would be: P = 1/(1+EXP(-L)) Example from Scientist data

April 25, 2006Lecture 14 Slide #8 Estimates of Coefficient Strength In Excel, calculate the difference in probability for each X at its min and max, holding all other variables constant:

April 25, 2006Lecture 14 Slide #9 Estimated Logit Probabilities

April 25, 2006Lecture 14 Slide #10 Logit Diagnostics The most useful diagnostics are to match “influence” (case-wise dfbetas) with predicted probabilities:

April 25, 2006Lecture 14 Slide #11 Logit Outliers and Influence In this instance, the high influence cases are those in the mid-range on key variables (certainty, ideology). This simply makes them hard to predict.

April 25, 2006Lecture 14 Slide #12 Factor Analysis-in-Brief A means for estimating the underlying structure in a set of “indicator” variables –A reversal of regression analysis –What unobserved dependent variable would best explain the variance in the observed indicators? Multiple related approaches –Exploratory versus Confirmatory –We focus on confirmatory principal factor analysis

April 25, 2006Lecture 14 Slide #13 Indicators of Societal Risk Management Views U/E4_34: When the risk is very small, it is acceptable for the government to impose that risk on in- dividuals without their consent. U/E4_35: Even if the potential benefits to society are very large, it is wrong for the government to impose risks on individuals without their consent. U/E4_36: It is acceptable for the government to impose risks without consent if the individuals harmed by the policy are compensated for their losses. U/E4_37: For society as a whole to survive and prosper, it is necessary that risks and sacrifices be accepted by citizens.

April 25, 2006Lecture 14 Slide #14 Underlying Structure? Societal Risk Mgmt. Perspective Small risks OK to impose Wrong to impose even if benefits are large Acceptable if compensated Risks necessary for society to prosper

April 25, 2006Lecture 14 Slide #15 Factor procedure

April 25, 2006Lecture 14 Slide #16 “Rotating” Factors

April 25, 2006Lecture 14 Slide #17 Saving Factor Scores

April 25, 2006Lecture 14 Slide #18 Using Factor Scores

April 25, 2006Lecture 14 Slide #19 Summing Up Factor analysis is a means of “data reduction” Useful when you have indicators Best when used in “confirmatory” mode Has an “exploratory” side

April 25, 2006Lecture 14 Slide #20 Final (non-cumulative) Exam Will include a simple exercise in –Using factor analysis to construct a factor score –Running a logit model using that score (along with several other variables) –Plotting the influence of the independent variables Will be an extension of the homework completed for today –No new data Posted on Friday (April 28) at 5PM Due on Wednesday (May 3) at 5PM