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Better predicted probabilities from linear probability models with applications to multiple imputation

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  • Paul Allison

    (Statistical Horizons LLC)

Abstract

Although logistic regression is the most popular method for regression analysis of binary outcomes, there are still many attractions to using least-squares regression to estimate a linear probability model. A major downside, however, is that predicted “probabilities” from a linear model are often greater than 1 or less than 0. That can be problematic for many real-world applications. As a solution, we propose to generate predicted probabilities based on a linear discriminant model, which Haggstrom (1983) showed could be obtained by rescaling coefficients from OLS regression. We offer a new Stata command, predict_ldm, that can be used after the regress command to generate predicted values that always fall within the (0,1) interval. We show that, for many applications, these values are very close to those produced by logistic regression. We also explore applications where there are substantial differences between logistic predictions and those produced by predict_ldm. Finally, we show that the linear discriminant method can be used to substantially improve multiple imputations of categorical data based on the multivariate normal model. We are currently developing a new mi impute command to implement this method.

Suggested Citation

  • Paul Allison, 2020. "Better predicted probabilities from linear probability models with applications to multiple imputation," 2020 Stata Conference 1, Stata Users Group.
  • Handle: RePEc:boc:scon20:1
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    File URL: http://fmwww.bc.edu/repec/scon2020/us20_Allison.pdf
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    References listed on IDEAS

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    1. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    2. Westin, Richard B., 1974. "Predictions from binary choice models," Journal of Econometrics, Elsevier, vol. 2(1), pages 1-16, May.
    3. Haggstrom, Gus W, 1983. "Logistic Regression and Discriminant Analysis by Ordinary Least Squares," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 229-238, July.
    4. Mroz, Thomas A, 1987. "The Sensitivity of an Empirical Model of Married Women's Hours of Work to Economic and Statistical Assumptions," Econometrica, Econometric Society, vol. 55(4), pages 765-799, July.
    5. Ottar Hellevik, 2009. "Linear versus logistic regression when the dependent variable is a dichotomy," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(1), pages 59-74, January.
    6. ., 2017. "Econometric analysis: loopholes and shortcomings," Chapters, in: Econometrics as a Con Art, chapter 5, pages 88-105, Edward Elgar Publishing.
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    Cited by:

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    2. Marshall L. White & William J. Sabol, 2021. "Legal Financial Obligations and Probation: Findings from the 1995 Survey of Adults on Probation," Social Sciences, MDPI, vol. 10(12), pages 1-22, November.
    3. Didier, Nicolás, 2021. "Does the expansion of higher education reduce gender gaps in the labor market? Evidence from a natural experiment," International Journal of Educational Development, Elsevier, vol. 86(C).

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