Depression, intertwined with sleep deprivation and self-esteem, presents a significant challenge to mental health worldwide. The research shown in this paper employs advanced statistical methodologies to unravel the complex interactions among these factors. Through log-linear homogeneous association, multinomial logistic regression, and generalized linear models, the study scrutinizes large datasets to uncover nuanced patterns and relationships. By elucidating how depression, sleep disturbances, and self-esteem intersect, the research aims to deepen understanding of mental health phenomena. The study clarifies the relationship between these variables and explores reasons for prioritizing depression research. It evaluates how statistical models, such as log-linear, multinomial logistic regression, and generalized linear models, shed light on their intricate dynamics. Findings offer insights into risk and protective factors associated with these variables, guiding tailored interventions for individuals in psychological distress. Additionally, policymakers can utilize these insights to develop comprehensive strategies promoting mental health and well-being at a societal level.