Table 1

 Hypothetical multilevel regression analysis of systolic blood pressure (SBP) (mm Hg) in 25 000 people aged 35 to 64 from 39 neighbourhoods of a city

Empty modelModel with individual variablesModel with individual variables and random slopesModel with individual variables, random slopes, and non-constant individual variance
Model 1Model 2Model 3Model 4
“Fixed effects” and “random effects” are expressions that are often used in MLRA. In very simple terms, fixed effects are used to model means, whereas random effects are used to model variances. BMI, body mass index; ICC, intraclass correlation; VPC, variance partition coefficient. *As the variance is a function of individual BMI, the values in the table are for the intercepts (people with BMI equal to 25 kg/m2). †When performing statistical modelling, you try to find a function that predicts SBP as well as possible and, therefore, decrease unexplained variance. The goodness of this fit is measured by different statistical techniques. One very common technique that we used in our study model is the reduction in “deviance”. This technique is used to evaluate the fit of consecutive models with additional terms.6–8 Table 1 shows that in our study model, as compared with the empty model, every consecutive model significantly decreases the deviance and improves the goodness of the fit of the model.
Fixed effects
Mean SBP of the city (intercept)130.2128.1128.0127.9
Regression coefficients (β), 95% confidence intervals (CI)β (95% CI)β (95% CI)β (95% CI)β (95% CI)
    Age in years0.81 (0.78, 0.87)0.80 (0.77, 0.86)0.80 (0.77, 0.86)
    BMI (1 unit kg/m2)0.88 (0.86, 0.92)0.89 (0.83, 1.01)0.91 (0.85, 1.03)
    Antihypertensive medication14.7 (14.3, 15.3)14.7 (14.3, 15.3)15.5 (14.8, 15.8)
Random effects
Components of varianceVariance (SE)Variance (SE)Variance (SE)*Variance (SE)*
Variance between neighbourhood intercepts36.2 (8.1)27.6 (6.4)27.6 (6.4)27.5 (6.4)
Variance between individuals433.4 (3.9)307.6 (2.8)305.1 (2.8)298.5 (3.5)
BMI–SBP slope variance between neighbourhoods0.11 (0.03)0.11 (0.03)
BMI related individual SBP variance0.16 (0.08)
Neighbourhood covariance (intercept slope)0.93 (0.34)0.92 (0.34)
Individual level covariance5.16 (0.31)
Proportional change in variance (PCV) by the new modelPCVPCVPCV*PCV*
    Between neighbourhoodsReference24%24%24%
    Between individualsReference29%30%30%
ICC–VPCICC = 0.08ICC = 0.08VPC = 0.08*VPC = 0.08*
Deviance†222 764 (Reference)211 585211 443211 058