Four Parameters: Categorical

We’ve taken data from the 1992 American National Election Studies survey to see the relation between sex and voter preference among 1992 voters. We’re treating all voters as having voted at effectively the same time, and the representativeness of the survey is unknown. We modeled voter preference using a categorical regression model. The model states that men are more likely to vote for Perot than women are. Men are between 14% and 71% percent more likely to support Perot (using a 95% confidence interval)

\[\begin{aligned} \rho_{clinton} &=& \frac{e^{\beta_{0, clinton} + \beta_{1, clinton} male}}{1 + e^{\beta_{0, clinton} + \beta_{1, clinton} male}}\\ \rho_{perot} &=& \frac{e^{\beta_{0, perot} + \beta_{1, perot} male}}{1 + e^{\beta_{0, perot} + \beta_{1, perot} male}}\\ \rho_{bush} &=& 1 - \rho_{clinton} - \rho_{perot} \end{aligned}\]

Characteristic	Beta	95% CI1
muClinton_(Intercept)	0.45	0.31, 0.60
muPerot_(Intercept)	-0.85	-1.1, -0.64
muClinton_sexMale	-0.25	-0.48, -0.03
muPerot_sexMale	0.42	0.14, 0.69
1 CI = Credible Interval