Application of Log-Linear Analysis and Logistic Regression Analysis on a Four-way Contingency Table

• Activity Number: 180
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Seo-Eun Choi* and Amy Shollenbarger
• Companies: and Arkansas State University
• Keywords: categorical data analysis ; contingency table ; log-linear model ; logistic regression

Abstract

Log-linear models have been used to analyze association among categorical variables. As the number of variables increases, the complexity of the corresponding model also grows. Two log-linear models for a four-way contingency table are developed and compared using multinomial distribution and Poisson distribution, respectively. Logistic regression is to explain the relationship between explanatory variables and the response variable which is categorical. First, a log-linear model is applied to explain first grade students' awareness of final consonant clusters in monomorphemic words, by analyzing associations among four categorical variables: dialect - African-American English (AAE) or Mainstream American English (MAE), the ways of pronunciation, presentations of stimuli, and tasks of rhyming or segmentation. Once the structure of associations is confirmed, we move to the next step. With justification of possible causation relationship, a logistic regression model is applied to analyze causation relationship from three categorical variables: dialect, presentations of stimuli, and tasks, to a response variable, the ways of pronunciation, which is also categorical.