On goodness-of-fit of logistic regression model

by Liu, Ying

Abstract (Summary)
Logistic regression model is a branch of the generalized linear models and is

widely used in many areas of scientific research. The logit link function and the binary

dependent variable of interest make the logistic regression model distinct from linear

regression model.

The conclusion drawn from a fitted logistic regression model could be incorrect or

misleading when the covariates can not explain and /or predict the response variable

accurately based on the fitted model- that is, lack-of-fit is present in the fitted logistic

regression model.

The current goodness-of-fit tests can be roughly categorized into four types. (1)

The tests are based on covariate patterns, e.g., Pearson's Chi-square test, Deviance D

test, and Osius and Rojek's normal approximation test. (2) Hosmer-Lemeshow's C and

Hosmer-Lemeshow's H tests are based on the estimated probabilities. (3) Score tests

are based on the comparison of two models, where the assumed logistic regression

model is embedded into a more general parametric family of models, e.g., Stukel's

Score test and Tsiatis's test. (4) Smoothed residual tests include le Cessie and van

Howelingen's test and Hosmer and Lemeshow's test. All of them have advantages and


In this dissertation, we proposed a partition logistic regression model which can

be viewed as a generalized logistic regression model, since it includes the logistic

regression model as a special case. This partition model is used to construct goodness-of-

fit test for a logistic regression model which can also identify the nature of lack-of-fit is

due to the tail or middle part of the probabilities of success. Several simulation results

showed that the proposed test performs as well as or better than many of the known


Bibliographical Information:


School:Kansas State University

School Location:USA - Kansas

Source Type:Master's Thesis

Keywords:logistic regression goodness of fit statistics 0463


Date of Publication:01/01/2007

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