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Research Article Open access CC BY 4.0

Logistic Regression without Intercept

Guoping Zeng

Asian Journal of Probability and Statistics · pp. 30–42 · Published 6 Apr 2022

10.9734/ajpas/2022/v17i130414

Abstract

Logistic regression is a popular statistic modelling algorithm in predicting a binary outcome. Although logistic regression almost always has an intercept, logistic regression without intercept is sometimes appropriate or even necessary. However, logistic regression without intercept has rarely been discussed other than being used explicitly or implicitly. In this paper, we aim at filling this gap by systematically studying logistic regression without intercept. Specifically, we study the 4 most important aspects of logistic regression: (1) Maximum Likelihood Estimate, (2) data configuration (complete separation, quasi-complete separation and overlap) to categorize the existence and uniqueness of maximum likelihood estimate, (3) multicollinearity, and (4) monotonic transformations of independent variables. We adopt an extensional method in that we first present results for logistic regression with intercept and then extend the results to the case of without intercept. Our numerical examples further compare logistic regression with intercept and without intercept.

Logistic regression intercept multicollinearity variance inflation factor separation overlap

References (23)

  1. 1 UCI Machine Learning Repository
  2. 2 Statistical Methods in Cancer Research
  3. 3 Ridge Estimators in Logistic Regression [DOI]
  4. 4 Multicollinearity in Regression Analyses Conducted in Epidemiologic Studies [DOI]
  5. 5 On the existence of maximum likelihood estimates in logistic regression models [DOI]
  6. 6 An overview of techniques for dealing with large numbers of independent variables in epidemiologic studies [DOI]
  7. 7 Regression through the Origin [DOI]
  8. 8 On the Existence of Maximum Likelihood Estimates in Logistic Regression Models [DOI]
  9. 9 Ridge estimation in logistic regression [DOI]
  10. 10 On the small sample properties of norm-restricted maximum likelihood estimators for logistic regression models [DOI]
  11. 11 A Solution to Separation and Multicollinearity in Multiple Logistic Regression [DOI]
  12. 12 A Unified Definition of Mutual Information with Applications in Machine Learning [DOI]
  13. 13 Metric Divergence Measures and Information Value in Credit Scoring [DOI]
  14. 14 Notes on regression through the origin [DOI]
  15. 15 On the relationship between multicollinearity and separation in logistic regression [DOI]
  16. 16 On the existence of maximum likelihood estimates for weighted logistic regression [DOI]
  17. 17 On the analytical properties of category encodings in logistic regression [DOI]
  18. 18 A comparison study of computational methods of Kolmogorov–Smirnov statistic in credit scoring [DOI]
  19. 19 Regularized (bridge) logistic regression for variable selection based on ROC criterion [DOI]
  20. 20 Invariant properties of logistic regression model in credit scoring under monotonic transformations [DOI]
  21. 21 Comparison between Models With and Without Intercept
  22. 22 Two-sample tests for sparse high-dimensional binary data [DOI]
  23. 23 On the Existence of an Analytical Solution in Multiple Logistic Regression

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