Avoiding Boundary Estimates in Linear Mixed Models Through Weakly Informative Priors

Variance parameters in mixed or multilevel models can be difficult to estimate, especially when the number of groups is small. Here we address the problem that the group-level variance estimate is often on the boundary. We propose a maximum penalized likelihood approach which is equivalent to estimating the variance by its marginal posterior mode, given a weakly informative prior distribution. By choosing the prior from the gamma family with at least 1 degree of freedom, we ensure that the prior density is zero at the boundary and thus the marginal posterior mode of the group-level variance will be positive. The use of a weakly informative prior allows us to stabilize our estimates while remaining faithful to the data.