pyshapley2 0.1.1

Python replication of Stata's shapley2: Shapley-Owen decomposition for regression fit statistics

pyshapley2

Python replication of Stata's shapley2 command (Chavez Juarez, 2013).

Computes the Shapley-Owen decomposition of any regression fit statistic (R², adjusted R², log-likelihood, AIC, …) across independent variables or user-defined variable groups, with optional parallel computation support.

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Installation

pip install pyshapley2

For development:

pip install "pyshapley2[dev]"

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Quick Start

import pandas as pd
from pyshapley2 import shapley2

# Sample data
df = pd.read_csv("your_data.csv")

# Basic R² decomposition
result = shapley2(df, depvar="wage", indepvars=["edu", "exp", "tenure"])
result.summary()

Output (1:1 replica of Stata's table format):

Shapley-Owen decomposition  |  depvar: wage  |  stat: r2  |  command: ols
Observations: 500  |  Subsets: 8  |  K=3

Factor     │ Shapley value │ Per cent  │Shapley value │  Per cent
           │  (estimate)   │(estimate) │ (normalized) │(normalized)
───────────┼───────────────┼───────────┼──────────────┼─────────────
edu        │       0.35420 │    51.23 % │      0.31876 │      46.12 %
exp        │       0.27816 │    40.25 % │      0.25034 │      36.21 %
tenure     │       0.05918 │     8.56 % │      0.05326 │       7.70 %
───────────┼───────────────┼───────────┼──────────────┼─────────────
Residual   │      -0.00204 │    -0.04 % │              │
───────────┼───────────────┼───────────┼──────────────┼─────────────
TOTAL      │       0.68954 │   100.00 % │      0.68954 │     100.00 %
───────────┼───────────────┼───────────┼──────────────┼─────────────

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Features

All stat options

stat=	Meaning	Stata equivalent
"r2"	R²	e(r2)
"r2_a"	Adjusted R²	e(r2_a)
"ll"	Log-likelihood	e(ll)
"aic"	AIC	computed
"bic"	BIC	computed
"rmse"	Root MSE	computed

Custom extractor via stat_func:

result = shapley2(df, "y", ["x1", "x2", "x3"], stat_func=lambda r: r.rsquared)

All command options

command=	Model	Stata equivalent
"ols" / "reg"	OLS	regress
"logit"	Logit	logit
"probit"	Probit	probit
"poisson"	Poisson	poisson
"glm"	GLM	glm
callable	Custom	any e() command

Group decomposition (Stata group() option)

result = shapley2(
    df, "wage", ["edu", "exp", "tenure", "age"],
    stat="r2",
    groups={
        "Human Capital":  ["edu", "exp"],
        "Job Tenure":     ["tenure"],
        "Demographics":   ["age"],
    },
)
result.summary()

Parallel computation

# Use all available CPU cores
result = shapley2(
    df, "wage", ["x1", "x2", "x3", "x4", "x5"],
    stat="r2",
    n_jobs=-1,       # -1 = all cores; N = exactly N processes
    backend="loky",  # "loky" (default) | "threading" | "multiprocessing"
    verbose=1,       # show progress bar (requires tqdm)
)

When to use parallel?
Parallel is beneficial when K ≥ 10 (≥ 1,024 regressions).
For small K (≤ 8), the process-spawning overhead outweighs the benefit.

Visualization

fig, ax = result.plot(
    kind="norm_pct",   # "pct" | "norm_pct" | "shapley" | "norm"
    figsize=(8, 5),
)
fig.savefig("shapley_decomp.pdf", dpi=300)

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Stata → Python mapping

Stata	Python
shapley2, stat(r2)	shapley2(df, "y", ["x1","x2"], stat="r2")
shapley2, stat(r2) command(logit)	shapley2(..., stat="ll", command="logit")
shapley2, stat(r2) group(x1 x2, x3)	shapley2(..., groups={"G1":["x1","x2"],"G2":["x3"]})
shapley2, stat(r2) force	shapley2(..., force=True)
(not available in Stata)	shapley2(..., n_jobs=-1)

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Result object attributes

result.table           # pd.DataFrame: shapley, shapley_pct, shapley_norm, shapley_norm_pct
result.full_stat       # float: full-model stat (e.g. R²)
result.residual        # float: full_stat − sum(shapley)
result.K               # int: number of variables/groups
result.runs            # int: number of regressions run (2^K)
result.n_obs           # int: number of observations used
result.summary()       # prints Stata-style table, returns str
result.plot()          # matplotlib bar chart
result.to_dict()       # serializable dict

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Algorithm

Shapley2 implements the Shapley-Owen regression decomposition (also known as the LMG method):

1. Enumerate all 2^K subsets of K variables/groups.
2. Regress the outcome on each subset; record the fit statistic.
3. OLS (with intercept): regress the vector of fit statistics on the binary inclusion indicators; slope coefficients are the Shapley values.
4. Normalize: compute four output forms (raw, relative %, normalized, normalized %).

This is a 1:1 algorithmic replication of Stata's shapley2 v1.1.

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Validation against Stata

Results are verified to match Stata's shapley2 (v1.1) output to ≥ 5 decimal places on two public benchmark datasets.

Test 1 — mtcars (individual variables)

Data: Motor Trend Cars Road Tests (1974), N = 32 Model: regress mpg hp wt disp Stata: reg mpg hp wt disp → shapley2, stat(r2)

Variable	Shapley (est.)	% (est.)	Shapley (norm.)	% (norm.)
hp	0.18805	22.74%	0.22511	27.23%
wt	0.27959	33.81%	0.33469	40.48%
disp	0.22307	26.98%	0.26704	32.30%
Residual	0.13612	16.46%	—	—
TOTAL	0.82684	100%	0.82684	100%

import pandas as pd
from pyshapley2 import shapley2

df = pd.read_csv("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/datasets/mtcars.csv")
result = shapley2(df, "mpg", ["hp", "wt", "disp"], stat="r2")
result.summary()

Test 2 — Boston Housing (grouped variables)

Data: Boston Housing (Harrison & Rubinfeld, 1978), N = 506 Model: regress medv lstat rm dis ptratio Stata: reg medv lstat rm dis ptratio → shapley2, stat(r2) group(lstat,rm,dis ptratio)

Group	Variables	Shapley (est.)	% (est.)	Shapley (norm.)	% (norm.)
Group 1	lstat	0.29427	42.63%	0.31257	45.28%
Group 2	rm	0.23205	33.61%	0.24648	35.71%
Group 3	dis, ptratio	0.12358	17.90%	0.13126	19.01%
Residual	—	0.04041	5.85%	—	—
TOTAL	—	0.69031	100%	0.69031	100%

import pandas as pd
from pyshapley2 import shapley2

df = pd.read_csv("https://raw.githubusercontent.com/vincentarelbundock/Rdatasets/master/csv/MASS/Boston.csv")
result = shapley2(
    df, "medv", ["lstat", "rm", "dis", "ptratio"],
    stat="r2",
    groups={
        "lstat":       ["lstat"],
        "rm":          ["rm"],
        "dis_ptratio": ["dis", "ptratio"],
    },
)
result.summary()

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References

• Chavez Juarez, F. (2013). shapley2: Stata module to compute Shapley values from regressions. Statistical Software Components S457543, Boston College.
• Shapley, L. S. (1953). A value for n-person games. Contributions to the Theory of Games, 2, 307–317.
• Owen, G. (1977). Values of games with a priori unions. Essays in Mathematical Economics and Game Theory, 76–88.
• Kruskal, W. (1987). Relative importance by averaging over orderings. American Statistician, 41(1), 6–10.

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License

MIT © 2026 luzhiyu-econ