Elections and the economy: hills of uncertainty

Source: ElectionsEconomy/hills.Rmd

This page visualizes posterior draws for the intercept and slope in the Hibbs regression, fitted through lapylace.

Setup

from pathlib import Path
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import lapylace as lp

root = Path("../../ROS-Examples")

def coef_medians(fit):
    return pd.Series(
        [np.median(fit.alpha_draws()), *np.median(fit.beta_draws(), axis=0)],
        index=["Intercept", *fit.columns],
    )

def fit_glm(formula, data, family=None, seed=1, prior_scale=2.5, intercept_scale=5, aux_scale=10, **kwargs):
    return lp.stan_glm(
        formula,
        data=data,
        family=family or lp.gaussian(),
        prior=lp.normal(0, prior_scale),
        prior_intercept=lp.normal(0, intercept_scale),
        prior_aux=lp.exponential(aux_scale),
        chains=2,
        parallel_chains=2,
        iter_warmup=300,
        iter_sampling=500,
        seed=seed,
        refresh=100,
        **kwargs,
    )

hibbs = pd.read_csv(root / "ElectionsEconomy/data/hibbs.dat", sep=r"\s+")
fit = fit_glm("vote ~ growth", hibbs, seed=17901, prior_scale=10, intercept_scale=100, aux_scale=10)
coef_medians(fit).round(2)

Intercept    46.33
growth        3.02
dtype: float64

draws = pd.DataFrame({"intercept": fit.alpha_draws(), "growth": fit.beta_draws()[:,0]})
fig, axes = plt.subplots(1, 2, figsize=(8, 3))
axes[0].hist(draws.intercept, bins=30, color="0.6")
axes[0].set_title("Intercept")
axes[1].hist(draws.growth, bins=30, color="0.6")
axes[1].set_title("Growth slope")
fig.tight_layout()