**2. Multilevel models**

Multilevel models partition the variance of the dependent variable at different levels of data grouping. At least two types of variance are distinguished: *intra-group variance σ*<sup>2</sup> *<sup>w</sup>*, or individual-level variance (level one), and *between-group variance σ*<sup>2</sup> *b*, which defines the variation at the group level (level two).

The dependency of the observations in the same group is measured with the *intraclass correlation coefficient* (ICC). Shrout and Fleiss in 1979 defined the ICC as the ratio of the *between-group variance* and the *total variance* (the sum of the variances between groups and in intra-groups):

$$\text{ICC} = \frac{\sigma\_b^2}{\sigma\_b^2 + \sigma\_w^2} \tag{1}$$

The ICC varies between 0 and 1, since the variance cannot be negative. Before using a multilevel model, it is necessary to determine whether the ICC is significant at each level of the data. To that end, using the null model (defined in the next section), we determine whether the variance of the residuals of each level is significant. If that occurs, the ICC is also significant, and this means that at the individual level, the observations are dependent, and therefore, it is necessary to use a multilevel model instead of an ordinary multiple regression model [2].
