this model provides information about intraclass correlations, which are helpful in determining whether multilevel models are required in the first place. Random slopes model A random slopes model is a model in which slopes are allowed to vary according to a correlation matrix, and therefore, the slopes are different across grouping variable such as time or individuals. This model assumes that intercepts are fixed (the same across different contexts). Random intercepts and slopes model A model that includes both random intercepts and random slopes is likely the most realistic type of model, although it is also the most complex. In this model, both intercepts and slopes are allowed to vary across groups, meaning that they are different in different contexts. Developing a multilevel model In order to conduct a multilevel model analysis, one would start with fixed coefficients (slopes and intercepts). One aspect would be allowed to vary at a time (that is, would be changed), and compared with the previous model in order to assess better model fit. There are three different questions that a researcher would ask in assessing a model. First, is it a good model? Second, is a more complex model better? Third, what contribution do individual predictors make to the model? In order to assess models, different model fit statistics would be examined. One such statistic is the chi-square likelihood-ratio test, which assesses the difference between models. The likelihood-ratio test can be employed for model building in general, for examining what happens when effects in a model are allowed to vary, and when testing a dummy-coded categorical variable as a single effect. However, the test can only be used when models are nested (meaning that a more complex model includes all of the effects of a simpler model). When testing non-nested models, comparisons between models can be made using the Akaike information criterion (AIC) or the Bayesian information criterion (BIC), among others. See further Model selection. Assumptions Multilevel models have the same assumptions as other major general linear models (e.g., ANOVA, regression), but some of the assumptions are modified for the hierarchical nature of the design (i.e., nested data). Linearity The assumption of linearity states that there is a rectilinear (straight-line, as opposed to non-linear or U-shaped) relationship between variables. However, the model can be extended to nonlinear relationships. Particularly, when the mean part of the level 1 regression equation is replaced with a non-linear