Predicting the Impact of AI Tools on Learning and Academic Performance: A Categorical Data Analysis Approach

Abstract

Understanding complex interrelationships within categorical data is essential across various research domains, particularly when traditional regression assumptions are not met. This study aimed to identify and model significant associations and predictive relationships among a set of exclusively categorical variables using advanced statistical techniques. Initially, five distinct log-linear models were developed to explore multidimensional dependencies among variables. These models were systematically evaluated and compared using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to determine the most parsimonious and best-fitting model structure. To further examine predictive relationships with a specified categorical outcome variable, binary, ordinal, and multinomial logistic regression models were applied. These models were assessed using key goodness-of-fit metrics, including pseudo R-squared, AIC, and BIC. Results revealed a statistically significant and interpretable log-linear model that captured critical interaction effects among the predictors. Among the logistic models, binary logistic regression consistently demonstrated superior performance, providing the most robust and accurate predictions. This study underscores the value of integrating log-linear and logistic regression techniques for comprehensive analysis of categorical data. The combined approach enhances the understanding of complex variable interactions and supports informed decision-making for future research, policy formulation, and intervention strategies.