Characteristic |
Beta |
95% CI 1 |
|---|---|---|
| muJorgensen_(Intercept) | -3.4 | -3.8, -3.0 |
| muTrump_(Intercept) | -0.22 | -0.32, -0.12 |
| muJorgensen_regionNortheast | -0.49 | -1.1, 0.16 |
| muJorgensen_regionSouth | -0.24 | -0.77, 0.30 |
| muJorgensen_regionWest | -0.36 | -0.95, 0.21 |
| muTrump_regionNortheast | -0.38 | -0.54, -0.22 |
| muTrump_regionSouth | 0.15 | 0.02, 0.28 |
| muTrump_regionWest | -0.39 | -0.54, -0.24 |
| 1
CI = Credible Interval |
||
Model
Because I had three possible outcomes, and because there is no natural ordering among the outcomes, I ended up using a categorical model.
\[ vote_i \sim Categorical(\rho_{trump}, \rho_{biden}, \rho_{jorgensen}) \]
Here is the mathematical equation I used.
\[ \begin{aligned} \rho_{biden} &=& 1 - \rho_{trump} - \rho_{jorgensen}\\ \rho_{trump} &=& \frac{e^{-0.22 - 0.38 northeast + 0.15 south - 0.39 west}}{1 + e^{-0.22 - 0.38 northeast + 0.15 south - 0.39 west}}\\ \rho_{jorgensen} &=& \frac{e^{-3.4 - 0.49 northeast -0.24 south - 0.36 west}}{1 + e^{-3.4 - 0.49 northeast -0.24 south - 0.36 west}}\\ \end{aligned} \] Now we can look at our regression table, which shows our expected values.
If we want to calculate the posterior probability, we substitute these values into the equation above.