NES: linear probability summaries

Source: NES/nes_linear.Rmd

This page uses Gaussian lapylace regressions as the linear-probability companion to the NES logistic example.

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,
    )

nes = pd.read_csv(root / "NES/data/nes.txt", sep=r"\s+", index_col=0, na_values=["NA"])
d = nes.loc[nes.year == 1992, ["rvote", "income", "female", "black"]].dropna().copy()
d["rvote"] = d["rvote"].astype(float)
d.head()

	rvote	income	female	black
32093	1.0	4	1	0
32094	1.0	2	1	0
32096	0.0	1	1	1
32097	1.0	2	0	0
32098	0.0	3	1	0

fit = fit_glm("rvote ~ income + female + black", d, seed=18101, prior_scale=2.5, intercept_scale=5, aux_scale=1)
fit.summary(["alpha", "beta", "sigma"])

	Mean	MCSE	StdDev	5%	50%	95%	N_Eff	N_Eff/s	R_hat
alpha	0.246450	0.002074	0.043692	0.171520	0.245949	0.318253	443.989000	708.117000	1.000900
beta[1]	0.044699	0.000532	0.011878	0.025663	0.044493	0.064241	497.837000	793.998000	1.001130
beta[2]	0.007528	0.000910	0.024746	-0.031872	0.008191	0.047391	740.262000	1180.640000	1.001020
beta[3]	-0.322904	0.001405	0.040291	-0.389097	-0.324131	-0.255734	822.932000	1312.490000	0.999306
sigma	0.463037	0.000293	0.008898	0.448351	0.463127	0.477993	923.011032	1472.106909	1.001635

coef_medians(fit).round(3)

Intercept    0.246
income       0.044
female       0.008
black       -0.324
dtype: float64