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
| Model with individual variables and complex variance (iv0) | Model with neighbourhood variables (v) | Model with neighbourhood variables (v°) | |
|---|---|---|---|
| Fixed effects and random effects are expressions often used in MLRA. In very simple terms, fixed effects are used to model means, whereas random effects are used to model variances. *Regression coefficients (β) and 95% confidence intervals (95% CI). BMI, body mass index centred on the mean; PCV, proportional change in variance; VPC, variance partition coefficient. †The reference group is people living in advantaged neighbourhoods and with BMI = 25 kg/m2. ‡In people with BMI = 25 kg/m2. | |||
| Fixed effects(Traditional measures of association) | |||
| Mean SBP of the city (intercept) | 119 mm Hg | 116 mm Hg | 116 mm Hg |
| β* (95% CI) | β * (95% CI) | β * (95% CI) | |
| Individual level variables | |||
| Age (years) | 0.76 (0.70 to 0.82) | 0.76 (0.70 to 0.82) | 0.76 (0.70 to 0.82) |
| Use of blood pressure lowering drugs (yes v no) | 0.89 (0.77 to 1.01) | 0.88 (0.76 to 1.00) | 1.02 (0.88 to 1.16) |
| BMI (kg/m2) | 15.12 (14.43 to 15.81) | 15.12 (14.43 to 15.81) | 15.12 (14.43 to 15.81) |
| Individual low income (low v high) | 2.27 (1.72 to 2.82) | 2.27 (1.72 to 2.82) | 2.26 (1.71 to 2.81) |
| Area level variables | |||
| Neighbourhood low income (low v high) | 5.23 (3.19 to 7.27) | 4.47 (2.49 to 6.45) | |
| Cross level interactions | |||
| Neighbourhood low income × BMI† | 0.35 (0.15 to 0.55) | ||
| Random effects(Multilevel measures of health variation) | |||
| Components of variance | Variance‡(SE) | Variance‡(SE) | Variance‡(SE) |
| Neighbourhood intercept variance | 27.09 (6.26) | 21.11 (4.7) | 21.02 (4.9) |
| Individual level variance | 298.22 (3.34) | 298.03 (3.34) | 298.02 (3.34) |
| BMI-SBP slope variance | 0.11 (0.03) | 0.11 (0.03) | 0.09 (0.03) |
| BMI related individual SBP variance | 0.16 (0.08) | 0.16 (0.08) | 0.16 (0.08) |
| Neighbourhood intercept-slope covariance | 0.99 (0.35) | 0.62 (0.29) | 0.58 (0.27) |
| Individual level covariance | 5.24 (0.31) | 5.24 (0.31) | 5.25 (0.31) |
| Proportional change in variance (PCV) | PCV | PCV | PCV |
| PCV between neighbourhoods | Ref. | 22% | 22% |
| PCV between individuals | Ref. | 0% | 0% |
| Variance partition coefficient (VPC) | VPC = 0.08 | VPC = 0.07 | VPC = 0.07 |
| 2×log-likelihood value | 211,024 | 211,006 | 210,996 |