Date of Graduation

7-2026

Document Type

Thesis

Degree Name

Master of Science in Statistics and Analytics (MS)

Degree Level

Graduate

Department

Statistics and Analytics

Advisor/Mentor

Robinson, Samantha

Committee Member

Chakraborty, Avishek

Second Committee Member

Petris, Giovanni

Keywords

Statistics and Analytics

Abstract

Mental health is an essential part of overall well-being. Accurate measurement of constructs such as loneliness, anxiety, depression, and life satisfaction is extremely important in research and practice. Traditional approaches based on Classical Test Theory (CTT) are limited. They rely on total test scores and assume constant measurement error across individuals. They may not reflect true variability in measurement precision (Zein & Akhtar, 2025; Marvianto, 2023). In contrast, Item Response Theory (IRT) provides an advanced approach by examining item-level performance. It models the relationship between latent traits and responses (Zein & Akhtar, 2025 ). To address these limitations, this study applies the Graded Response Model (GRM) to evaluate the psychometric properties of four mental health scales: UCLA Loneliness Scale, GAD-7, PHQ-9, and SWLS. The study used a sample of 1,600 respondents with an 80/20 validation framework. The results from exploratory and confirmatory factor analyses support the unidimensional structure of the scales. GRM findings show strong item discrimination and properly ordered threshold parameters. It indicates that the instruments perform well across different levels of the latent traits. Measurement precision is higher in the moderate range, while lower at extreme levels. This is consistent with previous IRT-based research (Mielenz et al., 2016 ; Vaganian et al., 2022 ). Overall, the findings highlight the advantages of IRT over CTT in providing detailed insights into item performance and improving the quality of psychological measurement.

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