ECON526
University of British Columbia
\[ \def\indep{\perp\!\!\!\perp} \def\Er{\mathrm{E}} \def\R{\mathbb{R}} \def\En{{\mathbb{E}_n}} \def\Pr{\mathrm{P}} \newcommand{\norm}[1]{\left\Vert {#1} \right\Vert} \newcommand{\abs}[1]{\left\vert {#1} \right\vert} \def\inprob{{\,{\buildrel p \over \rightarrow}\,}} \def\indist{\,{\buildrel d \over \rightarrow}\,} \DeclareMathOperator*{\plim}{plim} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator*{\argmin}{arg\,min} \]
\[ CATE(x) = \Er[Y_i(1) - Y_i(0)|X_i = x] \]
import pandas as pd
import numpy as np
import patsy
from sklearn import linear_model, ensemble, base, neural_network
import statsmodels.formula.api as smf
import statsmodels.api as sm
#from sklearn.utils._testing import ignore_warnings
#from sklearn.exceptions import ConvergenceWarning
import matplotlib.pyplot as plt
import seaborn as sns| rid_panel | prov | Location_ID | dist | wave | edu | agecat | log_xp_percap | rhr031 | rhr032 | ... | hh_xp_all | tv | parabola | fridge | motorbike | car | pig | goat | cow | horse | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 1.225100e+04 | 22768.000000 | 2.277100e+04 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | ... | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.000000 | 22771.00000 | 22771.000000 | 22771.000000 |
| mean | 3.406884e+12 | 42.761156 | 4.286882e+06 | 431842.012033 | 1.847174 | 52.765799 | 4.043081 | 13.420404 | 0.675157 | 0.754908 | ... | 3.839181 | 0.754908 | 0.482148 | 0.498661 | 0.594792 | 0.470511 | 0.536691 | 0.53858 | 0.515041 | 0.470247 |
| std | 1.944106e+12 | 14.241982 | 1.423541e+06 | 143917.353784 | 0.875323 | 45.833778 | 1.280589 | 1.534089 | 0.468326 | 0.430151 | ... | 1.481982 | 0.430151 | 0.499692 | 0.500009 | 0.490943 | 0.499141 | 0.498663 | 0.49852 | 0.499785 | 0.499125 |
| min | 1.100103e+10 | 31.000000 | 3.175010e+06 | 3524.000000 | 1.000000 | 6.000000 | 0.000000 | 7.461401 | 0.000000 | 0.000000 | ... | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.00000 | 0.000000 | 0.000000 |
| 25% | 1.731008e+12 | 32.000000 | 3.210180e+06 | 323210.000000 | 1.000000 | 6.000000 | 3.000000 | 11.972721 | 0.000000 | 1.000000 | ... | 3.000000 | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.00000 | 0.000000 | 0.000000 |
| 50% | 3.491004e+12 | 35.000000 | 3.517171e+06 | 353517.000000 | 2.000000 | 12.000000 | 5.000000 | 12.851639 | 1.000000 | 1.000000 | ... | 5.000000 | 1.000000 | 0.000000 | 0.000000 | 1.000000 | 0.000000 | 1.000000 | 1.00000 | 1.000000 | 0.000000 |
| 75% | 5.061008e+12 | 53.000000 | 5.307020e+06 | 535307.000000 | 3.000000 | 99.000000 | 5.000000 | 15.018967 | 1.000000 | 1.000000 | ... | 5.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.00000 | 1.000000 | 1.000000 |
| max | 6.681013e+12 | 75.000000 | 7.571030e+06 | 757571.000000 | 3.000000 | 99.000000 | 5.000000 | 15.018967 | 1.000000 | 1.000000 | ... | 5.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.00000 | 1.000000 | 1.000000 |
8 rows × 121 columns
# some data prep for later
formula = """
bw ~ pkh_kec_ever +
C(edu)*C(agecat) + log_xp_percap + hh_land + hh_home + C(dist) +
hh_phone + hh_rf_tile + hh_rf_shingle + hh_rf_fiber +
hh_wall_plaster + hh_wall_brick + hh_wall_wood + hh_wall_fiber +
hh_fl_tile + hh_fl_plaster + hh_fl_wood + hh_fl_dirt +
hh_water_pam + hh_water_mechwell + hh_water_well + hh_water_spring + hh_water_river +
hh_waterhome +
hh_toilet_own + hh_toilet_pub + hh_toilet_none +
hh_waste_tank + hh_waste_hole + hh_waste_river + hh_waste_field +
hh_kitchen +
hh_cook_wood + hh_cook_kerosene + hh_cook_gas +
tv + fridge + motorbike + car + goat + cow + horse
"""
bw, X = patsy.dmatrices(formula, df, return_type="dataframe")
# some categories are empty after dropping rows with Null, drop now
X = X.loc[:, X.sum() > 0]
bw = bw.iloc[:, 0]
treatment_variable = "pkh_kec_ever"
treatment = X["pkh_kec_ever"]
Xl = X.drop(["Intercept", "pkh_kec_ever", "C(dist)[T.313175]"], axis=1)
loc_id = df.loc[X.index, "Location_ID"].astype("category")
import re
# remove [ ] from names for compatibility with lightgbm
Xl = Xl.rename(columns = lambda x:re.sub('[^A-Za-z0-9_]+', '', x))from statsmodels.iolib.summary2 import summary_col
tmp = pd.DataFrame(dict(birthweight=bw,treatment=treatment,assisted_delivery=df.loc[X.index, "good_assisted_delivery"]))
usage = smf.ols("assisted_delivery ~ treatment", data=tmp).fit(cov_type="cluster", cov_kwds={'groups':loc_id})
health= smf.ols("bw ~ treatment", data=tmp).fit(cov_type="cluster", cov_kwds={'groups':loc_id})
summary_col([usage, health])| assisted_delivery | bw | |
|---|---|---|
| Intercept | 0.7827 | 3173.4067 |
| (0.0124) | (10.2323) | |
| treatment | 0.0235 | -14.8992 |
| (0.0192) | (24.6304) | |
| R-squared | 0.0004 | 0.0001 |
| R-squared Adj. | 0.0002 | -0.0001 |
Regression with sample-splitting
BLP: \[ y_i = \alpha_0 + \alpha_1 \widehat{B}(x_i) + \beta_0 (d_i-P(d=1)) + \beta_1 (d_i-P(d=1))(\widehat{CATE}(x_i) - \overline{\widehat{CATE}(x_i)}) + \epsilon_i \]
GATE: \[ y_i = \alpha_0 + \alpha_1 \widehat{B}(x_i) + \sum_k \gamma_k (d_i-P(d=1)) 1(G_k(x_i)) + u_i \]
Estimates asymptotically normal with usual standard errors
def generic_ml_model(x, y, treatment, model, n_split=10, n_group=5, cluster_id=None):
nobs = x.shape[0]
blp = np.zeros((n_split, 2))
blp_se = blp.copy()
gate = np.zeros((n_split, n_group))
gate_se = gate.copy()
baseline = np.zeros((nobs, n_split))
cate = baseline.copy()
lamb = np.zeros((n_split, 2))
for i in range(n_split):
main = np.random.rand(nobs) > 0.5
rows1 = ~main & (treatment == 1)
rows0 = ~main & (treatment == 0)
mod1 = base.clone(model).fit(x.loc[rows1, :], (y.loc[rows1]))
mod0 = base.clone(model).fit(x.loc[rows0, :], (y.loc[rows0]))
B = mod0.predict(x)
S = mod1.predict(x) - B
baseline[:, i] = B
cate[:, i] = S
ES = S.mean()
## BLP
# assume P(treat|x) = P(treat) = mean(treat)
p = treatment.mean()
reg_df = pd.DataFrame(dict(
y=y, B=B, treatment=treatment, S=S, main=main, excess_S=S-ES
))
reg = smf.ols("y ~ B + I(treatment-p) + I((treatment-p)*(S-ES))", data=reg_df.loc[main, :])
reg_fit = reg.fit()
blp[i, :] = reg_fit.params.iloc[2:4]
blp_se[i, :] = get_treatment_se(reg_fit, cluster_id, main)[2:]
lamb[i, 0] = reg_fit.params.iloc[-1]**2 * S.var()
## GATEs
cutoffs = np.quantile(S, np.linspace(0,1, n_group + 1))
cutoffs[-1] += 1
for k in range(n_group):
reg_df[f"G{k}"] = (cutoffs[k] <= S) & (S < cutoffs[k+1])
g_form = "y ~ B + " + " + ".join([f"I((treatment-p)*G{k})" for k in range(n_group)])
g_reg = smf.ols(g_form, data=reg_df.loc[main, :])
g_fit = g_reg.fit()
gate[i, :] = g_fit.params.values[2:] #g_fit.params.filter(regex="G").values
gate_se[i, :] = get_treatment_se(g_fit, cluster_id, main)[2:]
lamb[i, 1] = (gate[i,:]**2).sum()/n_group
out = dict(
gate=gate, gate_se=gate_se,
blp=blp, blp_se=blp_se,
Lambda=lamb, baseline=baseline, cate=cate,
name=type(model).__name__
)
return out
def generic_ml_summary(generic_ml_output):
out = {
x: np.nanmedian(generic_ml_output[x], axis=0)
for x in ["blp", "blp_se", "gate", "gate_se", "Lambda"]
}
out["name"] = generic_ml_output["name"]
return outdef generate_report(results):
summaries = list(map(generic_ml_summary, results))
df_plot = pd.DataFrame({
mod["name"]: np.median(mod["cate"], axis=1)
for mod in results
})
corrfig=sns.pairplot(df_plot, diag_kind="kde", kind="reg")
df_cate = pd.concat({
s["name"]: pd.DataFrame(dict(blp=s["blp"], se=s["blp_se"]))
for s in summaries
}).T.stack()
df_groups = pd.concat({
s["name"]: pd.DataFrame(dict(gate=s["gate"], se=s["gate_se"]))
for s in summaries
}).T.stack()
return({"corr":df_plot.corr(), "pairplot":corrfig, "BLP":df_cate,"GATE":df_groups})import lightgbm as lgb
import io
from contextlib import redirect_stdout, redirect_stderr
models = [
linear_model.LassoCV(cv=10, n_alphas=25, max_iter=500, tol=1e-4, n_jobs=20),
ensemble.RandomForestRegressor(n_estimators=200, min_samples_leaf=20, n_jobs=20),
lgb.LGBMRegressor(n_estimators=200, max_depth=4, reg_lambda=1.0, reg_alpha=0.0, n_jobs=20),
neural_network.MLPRegressor(hidden_layer_sizes=(20, 10), max_iter=500, activation="logistic",
solver="adam", tol=1e-3, early_stopping=True, alpha=0.0001)
]
kw = dict(x=Xl, treatment=treatment, n_split=11, n_group=5, cluster_id=loc_id)
def evaluate_models(models, y, **other_kw):
all_kw = kw.copy()
all_kw["y"] = y
all_kw.update(other_kw)
# hide many warnings while fitting
with io.StringIO() as obuf, redirect_stdout(obuf):
with io.StringIO() as ebuf, redirect_stderr(ebuf):
results=list(map(lambda x: generic_ml_model(model=x, **all_kw), models))
sout = obuf.getvalue()
serr = ebuf.getvalue()
return([results,sout,serr])| LassoCV | RandomForestRegressor | LGBMRegressor | MLPRegressor | ||
|---|---|---|---|---|---|
| gate | 0 | -15.107964 | 28.766155 | 12.303861 | -14.803722 |
| 1 | 0.000000 | -5.597018 | -27.188081 | -39.727837 | |
| 2 | -38.984004 | 4.517445 | 44.632153 | 9.425064 | |
| 3 | 0.000000 | -70.189623 | -27.755634 | -21.896826 | |
| 4 | 31.866970 | 13.401602 | 14.202997 | -49.620175 | |
| se | 0 | 63.652213 | 70.625370 | 64.111149 | 79.281024 |
| 1 | 67.955345 | 69.897550 | 71.962947 | 71.820829 | |
| 2 | 65.390581 | 62.163274 | 71.329630 | 73.301360 | |
| 3 | 69.870602 | 65.344575 | 70.870277 | 67.341561 | |
| 4 | 65.380544 | 75.116098 | 79.947862 | 59.451484 |
| LassoCV | RandomForestRegressor | LGBMRegressor | MLPRegressor | ||
|---|---|---|---|---|---|
| gate | 0 | -0.059084 | -0.031245 | -0.039293 | -0.001797 |
| 1 | 0.002495 | 0.010683 | 0.024503 | -0.029182 | |
| 2 | 0.017177 | -0.017908 | 0.069366 | -0.015868 | |
| 3 | 0.075722 | 0.080367 | 0.092914 | 0.084406 | |
| 4 | 0.188141 | 0.201042 | 0.164819 | 0.159647 | |
| se | 0 | 0.047587 | 0.052874 | 0.050695 | 0.029302 |
| 1 | 0.040549 | 0.046888 | 0.042594 | 0.041753 | |
| 2 | 0.045916 | 0.045945 | 0.045443 | 0.047819 | |
| 3 | 0.046337 | 0.043092 | 0.047277 | 0.050591 | |
| 4 | 0.050327 | 0.047977 | 0.050126 | 0.053681 |
def cov_mean_by_group(y, res, cluster_id):
n_group = res["gate"].shape[1]
gate = res["gate"].copy()
gate_se = gate.copy()
dat = y.to_frame()
for i in range(res["cate"].shape[1]):
S = res["cate"][:, i]
cutoffs = np.quantile(S, np.linspace(0, 1, n_group+1))
cutoffs[-1] += 1
for k in range(n_group):
dat[f"G{k}"] = ((cutoffs[k] <= S) & (S < cutoffs[k+1])) * 1.0
g_form = "y ~ -1 + " + " + ".join([f"G{k}" for k in range(n_group)])
g_reg = smf.ols(g_form, data=dat.astype(float))
g_fit = g_reg.fit()
gate[i, :] = g_fit.params.filter(regex="G").values
rows = ~y.isna()
gate_se[i, :] = get_treatment_se(g_fit, cluster_id, rows)
out = pd.DataFrame(dict(
mean=np.nanmedian(gate, axis=0),
se=np.nanmedian(gate_se, axis=0),
group=list(range(n_group))
))
return out
def compute_group_means_for_results(results, variables, df2):
to_cat = []
for res in results:
for v in variables:
to_cat.append(
cov_mean_by_group(df2[v], res, loc_id)
.assign(method=res["name"], variable=v)
)
group_means = pd.concat(to_cat, ignore_index=True)
group_means["plus2sd"] = group_means.eval("mean + 1.96*se")
group_means["minus2sd"] = group_means.eval("mean - 1.96*se")
return group_means
def groupmeanfig(group_means):
g = sns.FacetGrid(group_means, col="variable", col_wrap=min(3,group_means.variable.nunique()), hue="method", sharey=False)
g.map(plt.plot, "group", "mean")
g.map(plt.plot, "group", "plus2sd", ls="--")
g.map(plt.plot, "group", "minus2sd", ls="--")
g.add_legend();
return(g)df2 = df.loc[X.index, :]
df2["edu99"] = df2.edu == 99
df2["educ"] = df2["edu"]
df2.loc[df2["edu99"], "educ"] = np.nan
variables1 = ["log_xp_percap","agecat","educ"]
variables2 =["tv","goat","cow",
"motorbike", "hh_cook_wood","hh_toilet_own"]
group_means_ad = compute_group_means_for_results(results_ad[0], variables1, df2)
