Semi-Parametric Generalized Linear Models.

Abstract

This document considers generalized linear models in which the linear predictor is of additive semi-parametric form, linear in most of the explanatory variables but with an arbitrary functional dependence on the remainder. Estimation of the parameters and the non-parametric curve in the model is approached by maximizing a penalized likelihood. Two explicit iterative algorithms are presented. The first, which operates in O(n) time per iteration, applies where there is just one variable entering the model in a non-parametric fashion, and an integrated squared second derivative penalty is used. An example in logistic regression of tumour prevalence is given. The second algorithm is for the much more general case of a regression model specified as an arbitrary composite log-likelihood function, permitting nonlinear dependence and several splined variables. Keywords: Maximum penalized likelihood estimation; Nonlinear regression; Splines. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1985
Accession Number
ADA160958

Entities

People

  • Brian S. Yandell
  • Peter J. Green

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Automatic
  • Binomials
  • Composite Materials
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Data Science
  • Equations
  • Factor Analysis
  • Information Science
  • Iterations
  • Mathematics
  • Probability
  • Regression Analysis
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Statistical inference.