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Biometrika 1982 69(1):123-136; doi:10.1093/biomet/69.1.123
© 1982 by Biometrika Trust
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Penalized maximum likelihood estimation in logistic regression and discrimination

J. A. ANDERSON and V. BLAIR

Department of Statistics, University of Newcastle upon Tyne Manchester
Department of Statistical Unit, Statistical Unit, Christie Hospital Manchester

Maximum likelihood estimation of the parameters of the binary logistic regression model for pr(H|x) is discussed with separate discussion of sampling from (i) the conditional distribution of H given x, (ii) the joint distribution of H and x, and (iii) the conditional distribution of x given H. Difficulties associated with continuous x in the latter sampling scheme are discussed. To avoid these, penalized maximum likelihood estimates are introduced, which give estimates of the logistic parameters and a nonparametric spline estimate of the marginal distribution of x. Extensions to multinomial logistic regression are outlined.

Key Words: Binary logistic regression • Discrimination • Maximum likelihood estimation • Multinomial logistic regression • Nonparametric density estimation • Penalized maximum likelihood estimation • Spline function


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