| model | equation | Stata | English |
|---|---|---|---|
| Intercept Only | \(y = \beta_0 + e_{ij}\) | mixed y |
We estimated the mean of [outcome] |
| Intercept Independent Variable(s) |
\(y =
\beta_0 +
\beta_1 x
+ e_{ij}\) \(y = \beta_0 + \beta_1 x + \beta_2 z + e_{ij}\) |
mixed y x mixed y x z |
We estimated the relationship of [independent variable(s)] with [outcome] |
| Intercept Random variation of the intercept |
\(y = \beta_0 + e_{ij} + u_{0j}\) | mixed y || groupid: |
We estimated the mean of [outcome]. We allowed the intercept of the model to vary by [groupid]. |
| Unconditional intraclass correlation coefficient (ICC) | \(\frac{var(u_{0j})}{var(u_{0j}) + var(e_{ij})}\) | mixed y || groupid: estat icc |
XX% of the variation in [outcome] was explained by clustering of participants in [groupid] |
| Intercept Independent variable(s) Random variation of the intercept |
\(y =
\beta_0 +
\beta_1x +
e_{ij} +
u_{0j}\) \(y = \beta_0 + \beta_1 x + \beta_2 z + e_{ij} + u_{0j}\) |
mixed y x || groupid: mixed y x z || groupid: |
We estimated the relationship of [independent variable(s)] with [outcome]. We allowed the intercept of the model to vary by group. |
| Intercept Independent variable Random intercept Random slope |
\(y = \beta_0 + \beta_1 x + e_{ij} + u_{0j} + u_{1j} x\) | mixed y x || groupid: x |
We estimated the relationship of [independent variable] with [outcome]. We allowed the intercept of the model to vary by group. We also allowed the relationship of [independent variable] with [outcome] to vary by group. |
| We can estimate multilevel models with more than 1 random slope. | \(y =
\beta_0 +
\beta_1 x
+ \beta_2
z +\) \(e_{ij} + u_{0j} + u_{1j} x + u_{2j} z\) |
mixed y x z || groupid: x z |