**6. Conclusions**

In certain clinical research designs, the data have a nested structure (in other words, a hierarchical structure). The data that make up a nested structure are modeled using multilevel models because they simultaneously estimate the effects of the variables at the individual level and the effects of the contextual variables or variables at the group level. A significant ICC determines whether it is necessary to use a multilevel model. If the ICC is not significant, an ordinary regression model is sufficient to model the nested data. A disadvantage of multilevel models is that they easily contain a large number of parameters to be estimated. On the other hand, modeling the data levels separately incurs a large type 1 error even when the ICC is small. This fact causes the inferences to be incorrect. The maximum likelihood estimation of the parameters of a multilevel model requires that the assumptions of the distribution are satisfied. More general methods such as Bayesian estimation make it possible to estimate the parameters without requiring that the assumptions of the multilevel models be satisfied. In addition, the Bayesian estimation is robust to a small sample size, a situation that is more likely to occur in higher level observations, and in general, it is able to deal with technical problems such as multicollinearity of the data.

In this chapter, we adapted the bottom-up strategy to specify a multilevel model in the frequentist approach to the Bayesian approach. Our proposal was to use the Bayesian LOO-CV between the different steps for the comparison of models. Deviance information criterion (DIC) could also be used instead of Bayesian LOO-CV.

Two factors had a significant association with probing depth. Bleeding (site-level covariate) and dental calculus (patient-level covariate). At the tooth level, a factor associated with the probing depth was not found.

The methodology set out in this chapter can be applied to other areas of the health sciences with data with a hierarchical structure and numerical response variable.
