Beautiful Data

Example 2: Time Series of Estimates

Figure 19-2 illustrates a problem with classical logistic regression (a standard statistical tool for predicting yes/no outcomes) and how it can be resolved using a so-called weakly informative Bayesian approach. Using polling data in each presidential election from 1952 through 2000, we fit a separate logistic regression model to each year's data, predicting Republican vote choice given race, income, and several other variables.

Within each of the little graphs, each dot displays a logistic regression coefficient with a vertical line indicating the uncertainty in the estimate. The series of dots shows separate estimates for each election, and the two rows of graphs show the time series of estimated coefficients for race and income. (For simplicity, we do not display the other coefficients here.) The left column of the display shows classical estimates, and the two right columns show different Bayesian estimates (which in this case give essentially identical answers).

The estimates in Figure 19-2 look fine except in 1964, where there is complete separation, with all black respondents supporting the Democrats. As a result, the coefficient for race is estimated at negative infinity—that is, an inference that being black results in a 0% chance of voting Republican that year. 1964 was indeed a year in which Republicans did not do well among black voters (the Republican candidate that year was Barry Goldwater, who had opposed the Civil Rights Act), but ...