pytruncreg Overview

The pytruncreg package developed by Harvard University's CausaLab is designed to estimate one-way truncated gaussian regression models. The truncreg function requires formula, data, a truncation point and direction of truncation. This python package is a translation of the original truncreg R package CRAN by Yves Croissant and Achim Zeileis.

Parameters

• formula (str): String describing the model to be fitted in format y ~ x_1 + x_2 + ... x_n
• data (DataFrame): The dataset containing the variables specified in the formula
• point (float): The point of truncation in y
• direction (str): Specifies the direction of truncation, taking values "left" or "right"
• scaled (bool, optional): Default is False. When set to True the model will use a scaled version of the dependent variable
• iterlim (int, optional): Default is 50. The maximum iterations for the optimization algorithm.

Returns

• OptimizeResult: an object containing the results of the results of the optimization algorithm
• SE an array containing the standard errors for intercept and coefficients
• vcov the hessian (variance-covariance matrix) from the optimization process

Description

The truncreg function based on the original truncreg R package CRAN by Yves Croissant and Achim Zeileis, performs maximum likelihood estimation of a truncated gaussian regression model. The function supports both left and right truncation and will extract variables inside of formula from the provided data then constructs the model matrix by supplying an intercept and fits the truncated regression model using the L-BFGS-B optimization algorithm. Internally, the function calculates the log-likelihood, gradient, and Hessian matrix for the optimization process. The initial values for beta coefficients are estimated using ordinary least squares.\ In the case of overflow, truncreg will attempt to handle potential overflow issues in calculating the Mills ratio and log-likelihood. If scaled=True, the dependent variable is scaled before estimation.

Example Usage

import pandas as pd
import numpy as np
from pytruncreg import truncreg

np.random.seed(42)
data = pd.DataFrame({
    'y': np.random.normal(0, 1, 1000),
    'x1': np.random.normal(1, 3, 1000),
    'x2': np.random.normal(10, 3, 1000)
})

result = truncreg(formula='y~x1+x2', data=data, point=-4, direction='left')
print(result)

Dependencies

• numpy
• scipy.stats
• scipy.optimize
• re