multispline-python 0.1.1

Nonlinear multilevel spline modeling

# MultiSpline for Python

Nonlinear multilevel spline modeling for Python.

Version: 0.1.1 License: MIT PyPI: https://pypi.org/project/multispline-python/

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Motivation

Nonlinear relationships are common in applied research, especially in education, health, and economics. While Python provides statsmodels for mixed-effects models and patsy for spline construction, combining these tools requires multiple steps and manual postestimation. multispline addresses this gap by providing a unified workflow that integrates spline construction, multilevel estimation, ICC computation, prediction, and visualization into a single interface, improving workflow efficiency and reproducibility.

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Installation

PyPI (recommended):

pip install multispline-python

Development version (GitHub):

pip install git+https://github.com/causalfragility-lab/MultiSpline-Python.git

Dependencies:

pip install numpy pandas scipy statsmodels patsy matplotlib

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Quickstart

from multispline import MultiSpline
import pandas as pd

model = MultiSpline(
    data=df,
    outcome="math",
    predictor="ses",
    cluster="school_id",
    nknots=4
)
model.fit()
model.summary()
model.plot()

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Examples

Example 1: Education - SES and math achievement

import numpy as np
import pandas as pd
from multispline import MultiSpline

np.random.seed(42)
n_schools = 20
n_per_school = 50
n = n_schools * n_per_school

school_id = np.repeat(np.arange(n_schools), n_per_school)
ses = np.random.normal(0, 1, n)
school_effect = np.random.normal(0, 3, n_schools)[school_id]
math = 50 + 0.9*ses - 0.25*ses**2 + school_effect + np.random.normal(0, 2, n)

df = pd.DataFrame({
    "math": math,
    "ses": ses,
    "school_id": school_id
})

model = MultiSpline(
    data=df,
    outcome="math",
    predictor="ses",
    cluster="school_id",
    nknots=4
)
model.fit()
model.summary()
model.plot()

Example 2: Labor economics - age and wage

np.random.seed(123)
n = 2000
n_industries = 12

industry = np.random.randint(0, n_industries, n)
age = np.random.uniform(34, 46, n)
ind_effect = np.random.normal(0, 1.5, n_industries)[industry]
wage = (8 + 0.1*age - 0.003*age**2 +
        ind_effect + np.random.normal(0, 4, n))

df = pd.DataFrame({
    "wage": wage,
    "age": age,
    "industry": industry
})

model = MultiSpline(
    data=df,
    outcome="wage",
    predictor="age",
    cluster="industry",
    nknots=4,
    autoknots=False
)
model.fit()
model.summary()
model.plot()

# Grid prediction
grid = model.predict(grid=True, n_grid=100)
print(grid.head())

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Workflow

multispline automates five steps in a single interface:

1. Knot placement at quantiles of predictor distribution
2. Natural cubic spline basis construction via patsy
3. Multilevel model estimation via statsmodels MixedLM
4. ICC computation from variance components
5. Grid-based prediction and visualization

Optimization uses robust fallback: lbfgs -> bfgs -> cg.

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Options

Parameter	Description
outcome	Outcome variable name (str)
predictor	Predictor variable name (str)
cluster	Grouping variable name (str)
nknots	Number of spline knots (default=4)
autoknots	Auto-select knots 4-7 via floor(sqrt(n))

Methods

Method	Description
.fit()	Fit the model
.summary()	Print model summary and ICC
.predict()	Return fitted values
.predict(grid=True)	Return grid DataFrame
.plot()	Visualize nonlinear fit

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Requirements

• Python 3.8 or later
• Predictor variable must be continuous
• Sufficient between-cluster variability required

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Limitations

• Predictor variable must be continuous
• Performance depends on sufficient between-cluster variability
• Not appropriate for discrete predictors or negligible random-effects variance
• Random-intercept only (no random slopes in v0.1.1)
• Continuous outcomes only

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Related Packages

Language	Package	Repository
R	MultiSpline	https://github.com/causalfragility-lab/MultiSpline
Stata	multispline	https://github.com/causalfragility-lab/MultiSpline-Stata
Python	MultiSpline-Python	this repo

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Author

Subir Hait Michigan State University [e-mail] RePEC: https://authors.repec.org/pro/pha1643 GitHub: https://github.com/causalfragility-lab

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License

MIT (c) Subir Hait

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Citation

If you use multispline in your research, please cite:

Hait, Subir. 2026. MultiSpline for Python: Nonlinear multilevel
spline modeling. Version 0.1.1.
https://github.com/causalfragility-lab/MultiSpline-Python

BibTeX:

@software{hait2026multisplinepy,
  author  = {Hait, Subir},
  title   = {MultiSpline for Python: Nonlinear multilevel
             spline modeling},
  year    = {2026},
  version = {0.1.1},
  url     = {https://github.com/causalfragility-lab/MultiSpline-Python}
}