13 Research methods, statistics, critical review and evidence-based practice13.10 Correlation and regression
13.10.13 Multilevel regression
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Written by Resident Doctor Committee · Published
New in the 2027 syllabus
The College added this topic for exams from January 2027.
What it is
Multilevel regression models data organised in groups, such as patients within wards or repeated assessments within people.
Example | Lower level | Higher level |
|---|---|---|
Ward study | Patients | Wards |
Longitudinal study | Assessments | People |
Service study | Clinicians | Teams |
Why the grouping matters
Observations in the same group may resemble each other more than observations from different groups. This is within-group dependence.
Ignoring it can give misleading standard errors. When within-group correlation is positive, intervals are often too narrow, so results look more precise than they are.
Fixed and random effects
Fixed effects describe associations common to the modelled population, such as the average relationship between age and symptom score.
Term | What varies between groups |
|---|---|
Random intercept | Baseline level of the outcome |
Random slope | Association between a predictor and the outcome |
Residual | Remaining variation at the level of single observations |
Random-intercept model: wards can have different baseline means but share the same age slope.
Random-slope model: the rate of symptom change can differ between people.
Partial pooling: each group's estimate uses both its own observations and information across groups. This reduces extreme estimates from small groups.
Worked example: splitting the variance
Take a simple random-intercept linear model with these estimated variances.
Component | Variance |
|---|---|
Between wards | 4 |
Within wards | 16 |
Total variance = 4 + 16 = 20.
Intraclass correlation coefficient (the share of variance between groups) = 4 / 20 = 0.20.
So in this model, 20% of outcome variance lies between wards. The calculation does not apply unchanged to every multilevel model.
Traps in interpretation
Group-level and individual-level effects can differ. Do not read ward averages as individual associations.
With few groups, between-group variance and random-slope estimates can be unreliable, even when the total number of observations is large.
The model assumes a chosen nesting structure, mean relationship and random-effect distribution. Multilevel modelling does not automatically remove confounding.