Doctor of Philosophy / Department of Statistics / Shie-Shien Yang / 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
disadvantages.
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
tests.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/530 |
| Date | January 1900 |
| Creators | Liu, Ying |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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