Notes about ‘BAMLSS with random effects’

We tested 5 types of models to obtain faster and adequate mixing on a BAMLSS model that includes independent random effects with respect to the municipalities. See below a summary of different model types we tested.

1. Model with intercept: The identifiability of this model seems to be complicated when the variance of the groups is higher or of the same magnitud as the variance of the error. We solved this by post-processing the samples where the empirical mean of the random effects is subtracted from the random effects and added to the intercept. This is equivalent to put the restriction than the mean of the random effects is equals to zero.
2. Model without intercept: When we remove the intercept, we obtain random effects with non-zero mean. Convergence looks OK, but mixing of model 1 is better.
3. Model with intercept and binning option: The binning option uses only unique values of the variables. It is used to make computations faster. Results are quite similar to 1.
4. Model with discretized covariate: We discretized a continuous covariate to observe differences with the original model. In general, this is quite similar to model 1 in terms of results, time, and mixing.
5. Model with discretized covariate and binning option: This model discretized a covariate, but also uses binning option to reduce the computational cost. The model is faster, but the mixing is not that good. It also seems that the option binning imposes the restriction that the sum of the smooth function evaluated at the unique values is equals to zero. This means that the smooth function evaluated at all the observations does not necessarily sums to zero, indicating than the intercept estimation might be affected.