ERIC Number: EJ1458201
Record Type: Journal
Publication Date: 2025-Feb
Pages: 14
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0049-1241
EISSN: EISSN-1552-8294
Available Date: N/A
Linear Probability Model Revisited: Why It Works and How It Should Be Specified
Sociological Methods & Research, v54 n1 p173-186 2025
A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the ordinary least squares estimator (OLS) to LPM estimate? This article shows that the OLS estimates a weighted average of the X-conditional heterogeneous effect plus a bias. Under the condition that E(D|X) is equal to the linear projection of D on X, the bias becomes zero, and the OLS estimates the "overlap-weighted average" of the X-conditional effect. Although the condition does not hold in general, specifying the X-part of the LPM such that the X-part predicts D well, not Y, minimizes the bias counter-intuitively. This article also shows how to estimate the overlap-weighted average without the condition by using the "propensity-score residual" D-E(D|X). An empirical analysis demonstrates our points.
Descriptors: Probability, Least Squares Statistics, Regression (Statistics), Causal Models, Predictor Variables, Statistical Bias, Error of Measurement, Randomized Controlled Trials, Test Validity, Models
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
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Data File: URL: https://sites.google.com/view/gelee/codes-data
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