Award Date
May 2024
Degree Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
First Committee Member
Petros Hadjicostas
Second Committee Member
Hokwon Cho
Third Committee Member
Dieudonne Phanord
Fourth Committee Member
Ashok Singh
Number of Pages
80
Abstract
Log-linear models can be used to model the joint relationship of two or more categorical variables in a multiway contingency table. In a log-linear model, the logarithm of the expected joint counts (or the logarithm of the joint probabilities) in a contingency table can be written as a linear model.
Most log-linear models used in practice are standard. Standard log-linear models include the traditional parameter terms we see in ANOVA models: an overall effect, main effects, and various kinds of interaction terms.
Standard log-linear models are divided into hierarchical and non-hierarchical. Hierarchical models satisfy the hierarchy principle: if a higher-order term is included in the log-linear model, then so are all the lower-order terms.
Most of the standard log-linear models used in practice are hierarchical models. Nonhierarchical standard models appear rarely in the literature because they are difficult to interpret.
In this thesis, we examine standard and non-standard log-linear models for 2 × 2 contingency tables. To show their application, we use a thromboembolism data set that first appeared in Vessey and Doll (1968) and was later analyzed by Worcester (1971) using a multiplicative model, which can be equivalently written as a non-standard log-linear model.
Although the above data were collected in a one-to-two matching design, Worcester (1971) analyzed them using multinomial sampling where only the total was fixed.
In this thesis, however, we also examine a product multinomial sampling design for these data, which is a more correct probability model for a matched design.
We use the free statistical software R to estimate the above log-linear models. We compare the estimated log-linear models using the Pearson chi-square test, the G-square test, and the AIC, and we discuss the results.
Disciplines
Mathematics
Degree Grantor
University of Nevada, Las Vegas
Language
English
Repository Citation
Hoque, G M Toufiqul, "Standard and Non-Standard Log-Linear Models For 2 × 2 Contingency Tables" (2024). UNLV Theses, Dissertations, Professional Papers, and Capstones. 5008.
https://digitalscholarship.unlv.edu/thesesdissertations/5008
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