Approaches to hypothesis testing or interval construction are discussed in this chapter, from both the frequentist and Bayesian frameworks. To link to the literature on generalized linear mixed models (GLLM), the hierarchical linear model is reparametrized as a GLLM. Inferences for HGLMs using extended likelihood, an expansion of the likelihood principle to include information about both fixed and random parameters, and Bayesian approaches are next discussed. The extended likelihood imposes a constraint on the mean of the random effects, whereas in the Bayesian approach, prior distributions for the parameters governing the random effect distributions are specified. Several worked examples are detailed.