Hierarchical Latent Space Item Response Model for Analyzing Mental Health Vulnerability of Elementary School Students in South Korea

Mental health difficulties among elementary school students represent a growing public health concern in South Korea, yet analytical tools for identifying school-specific vulnerability patterns from item response data remain limited. We propose the hierarchical latent space item response model (HLSIRM), which adds hierarchical respondent effects and an inner-product latent interaction for signed respondent-item associations, yielding a unified interaction map that separates school, individual main effects from school/individual-item interactions. We apply HLSIRM to mental health vulnerability data from 2,210 elementary school students across 35 schools in Incheon, South Korea. Clustering item vectors by directional similarity identifies four empirically derived vulnerability domains. School-level analysis reveals that the absence of counseling experience is the primary vulnerability domain aligned with most school vectors, while stress, depression, and smartphone dependency concentrate in specific schools. Within-school analysis demonstrates how individual student positions in the interaction map translate into targeted intervention strategies that address school-specific needs.