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Analytical closed-form solution for binary logit regression by categorical predictors

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  • Stan Lipovetsky

Abstract

In contrast to the common belief that the logit model has no analytical presentation, it is possible to find such a solution in the case of categorical predictors. This paper shows that a binary logistic regression by categorical explanatory variables can be constructed in a closed-form solution. No special software and no iterative procedures of nonlinear estimation are needed to obtain a model with all its parameters and characteristics, including coefficients of regression, their standard errors and t -statistics, as well as the residual and null deviances. The derivation is performed for logistic models with one binary or categorical predictor, and several binary or categorical predictors. The analytical formulae can be used for arithmetical calculation of all the parameters of the logit regression. The explicit expressions for the characteristics of logit regression are convenient for the analysis and interpretation of the results of logistic modeling.

Suggested Citation

  • Stan Lipovetsky, 2015. "Analytical closed-form solution for binary logit regression by categorical predictors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(1), pages 37-49, January.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:1:p:37-49
    DOI: 10.1080/02664763.2014.932760
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    Cited by:

    1. Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2020. "Closed-form maximum likelihood estimator for generalized linear models in the case of categorical explanatory variables: application to insurance loss modeling," Computational Statistics, Springer, vol. 35(2), pages 689-724, June.
    2. Alexandre Brouste & Christophe Dutang & Tom Rohmer, 2022. "A Closed-form Alternative Estimator for GLM with Categorical Explanatory Variables," Post-Print hal-03689206, HAL.
    3. Lipovetsky, Stan, 2018. "Quantum paradigm of probability amplitude and complex utility in entangled discrete choice modeling," Journal of choice modelling, Elsevier, vol. 27(C), pages 62-73.

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