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The generalized linear model and particularly the logistic model are widely used in public health, medicine, and epidemiology. Goodness-of-fit tests for these models are popularly used to describe how well a proposed model fits a set of observations. These different goodness-of-fit tests all have individual advantages and disadvantages. In this thesis, we mainly consider the performance of the "Hosmer-Lemeshow" test, the Pearson's chi-square test, the unweighted sum of squares test and the cumulative residual test. We compare their performance in a series of empirical studies as well as particular simulation scenarios. We conclude that the unweighted sum of squares test and the cumulative sums of residuals test give better overall performance than the other two. We also conclude that the commonly suggested practice of assuming that a p-value less than 0.15 is an indication of lack of fit at the initial steps of model diagnostics should be adopted. Additionally, D'Agostino et al. presented the relationship of the stacked logistic regression and the Cox regression model in the Framingham Heart Study. So in our future study, we will examine the possibility and feasibility of the adaption these goodness-of-fit tests to the Cox proportional hazards model using the stacked logistic regression.
Generalized Linear Model, Stacked Logistic Regression, Goodness-of-fit Tests, Logistic Regression
Date of Defense
August 19, 2010.
A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Includes bibliographical references.
Dan L. McGee, Professor Co-Directing Dissertation; Jinfeng Zhang, Professor Co-Directing Dissertation; Myra Hurt, University Representative; Debajyoti Sinha, Committee Member.
Florida State University
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