stratindex

A nonparametric index of stratification (Zhou 2012) — a Python port of the R package strat by Xiang Zhou.

Documentation: https://promsoft.github.io/stratindex/

The index measures how strongly a set of strata (social classes, occupations, schools, …) stratifies a numeric outcome (income, test scores, …). It is the weighted excess of concordant over discordant pairs among all pairs of observations drawn from different strata with distinct outcomes — an analogue of Somers' D where strata are ordered by the average percentile rank of their members (or taken as pre-ordered). The index lies in [-1, 1]: 1 means perfect stratification (every member of a higher stratum outranks every member of a lower one), 0 means no stratification.

Zhou, Xiang. 2012. "A Nonparametric Index of Stratification." Sociological Methodology, 42(1): 365–389. doi:10.1177/0081175012452207

Installation

pip install stratindex

Requires Python ≥ 3.12. The only runtime dependency is NumPy.

Usage

from stratindex import strat, srank, load_cpsmarch2015

d = load_cpsmarch2015()  # bundled example data: March CPS 2015, 14,358 men

# stratum-specific information: population share and average percentile rank
print(srank(d["income"], d["big_class"], weights=d["weight"]))

# the stratification index with a between-/within-group decomposition
s = strat(
    d["income"], d["big_class"],
    weights=d["weight"],
    group=d["education"], group_name="education",
)
print(s.format(digits=4))

overall stratification:

 strat  std_error
0.4128    0.01296

decomposition by education:

                   weight   strat
 within education  0.2435  0.2684
between education  0.7565  0.4592

Results are plain dataclasses: s.strat, s.std_error, s.strata_info, s.decomposition, s.within_group; in Jupyter they render as HTML tables. If pandas is installed, s.to_pandas() returns the tables as DataFrames, and load_cpsmarch2015(as_pandas=True) returns a DataFrame.

A DataFrame (or any mapping of columns, like the dict above) can be passed directly — string keywords are resolved as column names, and the group label is taken from the column name:

s = strat(d, outcome="income", strata="big_class",
          weights="weight", group="education")

pandas Categorical strata keep their category order (used by ordered=True and for row order in the tables). Besides the default Goodman–Kruskal approximation, a bootstrap standard error is available: strat(..., se_method="bootstrap", n_boot=500, random_state=0).

Correspondence with the R package

R	Python
strat(outcome, strata, weights, ordered, group)	strat(outcome, strata, weights=None, ordered=False, group=None, group_name="group")
srank(outcome, strata, weights, group)	srank(outcome, strata, weights=None, group=None)
s$overall (strat, std_error)	s.strat, s.std_error (or s.overall)
s$strata_info	s.strata_info
s$decomposition	s.decomposition
s$within_group	s.within_group
data(cpsmarch2015)	load_cpsmarch2015()

Behavioral notes:

• Strata and group levels are ordered by their sorted unique values (as R's factor() does for character vectors). With ordered=True this level order is the stratum order.
• R derives the group label from the expression passed as group; Python uses the column name in data mode (or group_name= explicitly).
• The pairwise comparisons (an O(n²) C++ loop in the original) are computed in O(n log n) via weighted inversion counting; the full 14,358-row example runs in a fraction of a second.
• Numerical output is cross-validated against the original R package (see tests/data/r_golden.json, regenerated with scripts/r_golden.R).

Standard error

The reported standard error is the approximation of Goodman & Kruskal (1963), as in the R package: se = sqrt((1 - strat²) · n / deno) where deno is the total weight of comparable pairs.

License

GPL-3.0-or-later, same as the original R package (this is a derivative work). The bundled cpsmarch2015 dataset originates from the March 2015 Current Population Survey (U.S. Census Bureau / BLS public data), as distributed with the R package.