First Advisor

Schaffer, Jay Ryan, 1969-

Second Advisor

Lalonde, Trent L.

Document Type

Dissertation

Date Created

5-1-2013

Department

College of Education and Behavioral Sciences, Applied Statistics and Research Methods, ASRM Student Work

Abstract

Mixed effects logistic regression models have become widely used statistical models to model clustered binary responses. However, assessing the goodness of fit (GOF) in these models, when the cluster sizes and the number of clusters are small, is not clear. In this research, three GOF statistics are proposed, and their performance in terms of Type I error rate and power is examined via simulation study. The proposed GOF statistics are the logit residual, log-transformed residual and the absolute residual GOF statistics. The simulation study was applied on different cases of number of clusters, cluster sizes and types of predictors. The simulation results showed the performance of the logit residual and the log-transformed residual GOF statistics to be poor. The absolute residual GOF statistic performed well over most cases of the simulation. It gave proper Type I error rates and high power for most cases and it is recommended to use for mixed effects logistic regression models as long as the number of clusters is at least 10 and the cluster sizes are 10 or more. However, the absolute residual GOF statistic can be affected by extremely small or large estimated probabilities and further research is recommended to avoid or reduce this restriction.

Abstract Format

html

Keywords

Goodness of fit; Statistics; Mixed effects logistic regression

Extent

105 pages

Local Identifiers

Saaid_unco_0161D_10224

Rights Statement

Copyright is held by author.

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