ABSTRACT
Our focus in this chapter was on models designed for use situations in which individuals are nested together within clusters (e.g., students within schools). Standard statistical models are not appropriate in such cases because they don't take account of the correlations among members of the sample who are grouped within the same cluster. Ignoring this nesting can lead to biased parameter and standard error estimates. However, multilevel models, which take account of this structure, can be used to unbiased parameter estimates for a wide variety of dependent variable types. As we saw, common models such as regression, logistic regression, and Poisson regression, can all be extended for use in the multilevel context. Furthermore, we saw that regularized estimators can also be easily applied to multilevel models such as these, using functions in the R software package. To aid with inference, we have written a bootstrap sampling script that is available on the website for this book, www.routledge.com/9780367408787.
The general principles are applicable in the context of multilevel modeling, just as they were for the other model types described in this chapter. We will need to identify the optimal value of the regularization tuning parameter for a given model, typically using information indices such as AIC and BIC. In the multilevel context, there is also the added complexity associated with decisions around whether to include a random intercept only term or also a random coefficient. This is not a concern when using single-level models, and thus adds an additional layer of decision-making to go along with determining the optimal tuning parameter value. However, as we saw in this chapter such decisions can be made using information indices.
