Hierarchical Linear Modeling (HLM)

Hierarchical linear modeling (HLM) is a regression approach for nested data, such as students within schools, that estimates fixed effects together with random variation across higher-level clusters.

위계적 선형모형(HLM)은 학교 안의 학생처럼 내포된 자료에 대해 고정효과와 상위 수준 군집 간의 무선 변동을 함께 추정하는 회귀 접근이다.

How do I analyze data where individuals are nested within groups such as schools or hospitals?

학교나 병원 같은 집단 안에 개인이 내포된 자료는 어떻게 분석하나요?

Hierarchical linear modeling, also called multilevel or mixed-effects modeling, accounts for the dependence among observations within the same cluster by adding random intercepts and slopes. It fits nested data where you want correct standard errors and to separate within-cluster and between-cluster effects.

When to use Hierarchical Linear Modeling (HLM)

• Students nested in classrooms or schools, patients in hospitals, employees in firms
• Repeated measurements nested within individuals
• Predictors measured at both the individual and the group level

When to use something else

• Very few clusters are available: use cluster fixed effects (dummies), with small-sample corrections such as CR2 standard errors or the wild cluster bootstrap if clustered inference is needed
• Interest is only in population-averaged effects: use generalized estimating equations (GEE)

Assumptions and requirements

• Normally distributed residuals at each level
• Random effects independent of predictors
• Correctly specified fixed and random effects
• Enough clusters to estimate between-cluster variance

What the analysis reports

• Fixed-effect coefficients with standard errors
• Variance components
• Intraclass correlation coefficient (ICC)
• Likelihood-ratio tests or AIC/BIC for model comparison

How to report it

The intraclass correlation was [value], and [predictor] significantly predicted [outcome], γ = [value], SE = [value], t([df]) = [value], p = [value].

Related methods

• Linear Mixed Model
• Generalized Estimating Equations (GEE)
• Latent Growth Modeling (LGM)

Run Hierarchical Linear Modeling (HLM) on Quorant