تحليل المسوح المعقدة وأوزانها: تقديرات ممثلة بأخطاء معيارية صحيحة

import numpy as np
import pandas as pd

# Synthetic sample: 4 strata x 10 clusters x 15 units
rng = np.random.default_rng(7)
df = pd.DataFrame({"stratum": np.repeat(range(4), 150),
                   "psu": np.repeat(range(40), 15)})
u = rng.normal(0, 1, 40)[df.psu]  # cluster effect
df["y"] = 50 + 5 * df.stratum + 4 * u + rng.normal(0, 4, 600)
df["w"] = np.repeat(rng.uniform(50, 150, 40), 15)

# Weighted mean with Taylor-linearised standard error
m = np.average(df.y, weights=df.w)
df["z"] = df.w * (df.y - m) / df.w.sum()
t = df.groupby(["stratum", "psu"]).z.sum()
var = sum(len(g) / (len(g) - 1) * ((g - g.mean())**2).sum()
          for _, g in t.groupby(level="stratum"))

deff = var / (df.y.var() / len(df))
print(f"mean={m:.2f}  se={var**0.5:.3f}  deff={deff:.2f}")

library(survey)
data(api)

# Stratified sample: strata = school type
dstr <- svydesign(ids = ~1, strata = ~stype, weights = ~pw,
                  fpc = ~fpc, data = apistrat)
svymean(~api00, dstr, deff = TRUE)
svyby(~api00, ~stype, dstr, svymean)

# Cluster sample raked to population margins
dclus <- svydesign(ids = ~dnum, weights = ~pw, fpc = ~fpc,
                   data = apiclus1)
pop <- as.data.frame(table(stype = apipop$stype))
draked <- rake(dclus, list(~stype), list(pop))
svymean(~api00, draked)

# Jackknife replicate weights
djk <- as.svrepdesign(dclus, type = "JK1")
svymean(~api00, djk)