Award Date

5-1-2024

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.

Controlled Subject

Log-linear models; Contingency tables

Disciplines

Mathematics

File Format

pdf

File Size

727 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

Rights

IN COPYRIGHT. For more information about this rights statement, please visit http://rightsstatements.org/vocab/InC/1.0/

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Mathematics Commons

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