Hierarchical Linear Model (HLM)
Hierarchical Linear Model · Also known as: HLM, multilevel linear model, nested data model, random coefficient model
The Hierarchical Linear Model (HLM) is a multilevel regression method designed for data in which lower-level units (e.g., students, patients) are nested within higher-level groups (e.g., schools, hospitals). It simultaneously models within-group relationships and between-group variation, producing unbiased estimates and correct standard errors that ordinary regression cannot provide for nested data.
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When to use it
Use HLM whenever observations are nested within groups and you expect (or detect) non-trivial intraclass correlation (ICC > 0.05 is a common rule of thumb). Classic applications include students in schools, employees in organisations, patients in clinics, and repeated measures within individuals. HLM is also appropriate when you want to model cross-level interactions — for example, whether a student-level effect varies with school policy. Do not use HLM when all observations are truly independent (ICC ≈ 0), when group sizes are very small (fewer than 5–10 per group), or when you have fewer than about 20–30 groups at the highest level, as variance components become unreliable.
Strengths & limitations
- Correctly accounts for non-independence of observations within clusters, yielding valid standard errors and p-values.
- Partitions variance into within-group and between-group components, revealing how much context matters.
- Models cross-level interactions: how group-level variables moderate individual-level relationships.
- Borrows statistical strength across groups through partial pooling, stabilising estimates for small or sparse groups.
- Handles unbalanced group sizes and missing data at the individual level naturally within the ML/REML framework.
- Requires sufficient sample size at every level: typically at least 20–30 higher-level units for stable variance-component estimates.
- More complex to specify, estimate, and interpret than standard OLS, especially when random slopes are included.
- Variance-component estimates can be biased or fail to converge when the model is over-specified relative to the data.
- Assumes normality of random effects; serious departures can distort variance estimates and shrinkage.
- Does not handle non-continuous outcomes directly — logistic or Poisson variants (GLMM) are needed for binary or count outcomes.
Frequently asked
How many groups do I need to run HLM reliably?
A commonly cited minimum is 20–30 higher-level units for stable variance-component estimates. With fewer groups the between-group variance estimate becomes unreliable and random-effect standard errors are severely underestimated. Group size also matters: very small groups (fewer than 5 units) contribute little information about within-group slopes.
What is the ICC and when does it justify HLM?
The intraclass correlation coefficient (ICC) is the proportion of total outcome variance attributable to group membership. An ICC above roughly 0.05 indicates meaningful clustering that, if ignored, will inflate Type I error rates in standard regression. A formal likelihood-ratio test comparing the null HLM to OLS is more reliable than any fixed ICC threshold.
Should I use REML or ML estimation?
Use REML when estimating variance components or making inferences about fixed effects in a final model — REML produces less biased variance estimates. Switch to ML when comparing two models that differ only in their fixed effects using a likelihood-ratio test, because REML likelihoods are not comparable across models with different fixed structures.
What is group-mean versus grand-mean centring and why does it matter?
Grand-mean centring subtracts the overall predictor mean, leaving within- and between-group effects confounded in the Level-1 slope. Group-mean centring subtracts each group's own mean, isolating the pure within-group effect. The choice changes what the slope estimates and must be driven by the research question.
Can HLM be extended to non-continuous outcomes?
Yes. Generalised linear mixed models (GLMMs) extend HLM to binary outcomes (multilevel logistic regression), count outcomes (multilevel Poisson or negative binomial), ordinal outcomes, and survival data. The random-effects logic and estimation approach follow the same principles as standard HLM.
Sources
- Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Sage Publications. ISBN: 978-0761919049
- Snijders, T. A. B., & Bosker, R. J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling (2nd ed.). Sage Publications. ISBN: 978-1849202015
How to cite this page
ScholarGate. (2026, June 3). Hierarchical Linear Model. ScholarGate. https://scholargate.app/en/statistics/hierarchical-linear-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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