階層線性模型 (Hierarchical Linear Modeling)

Overview

Hierarchical Linear Modeling (HLM), also called multilevel modeling, accounts for the nested structure of data where lower-level units (e.g., students, employees) are clustered within higher-level units (e.g., schools, firms). By partitioning variance into within-group and between-group components and allowing intercepts and slopes to vary randomly, HLM produces unbiased estimates and correct standard errors.

When to Use

• Data has a hierarchical or nested structure (individuals within groups)
• Intra-class correlation (ICC) is non-trivial (rule of thumb: ICC > 0.05)
• Research questions involve cross-level interactions (group-level moderators of individual-level effects)
• Repeated measures or longitudinal data nested within subjects (growth models)

When NOT to Use

• Data are not nested or clustering is negligible (ICC near zero)
• Number of groups is very small (fewer than 20 Level-2 units)
• Interest is purely in fixed effects with no group-level predictors
• The nesting structure is crossed, not hierarchical (use crossed random effects instead)