This VA reliance measure was not only bimodal but also followed a U-shaped distribution, because most veterans tended to be either mostly or entirely reliant on VA, or hardly or not at all reliant on VA; while there was a significant proportion remaining using both VA and Medicare services.
We fitted the beta-binomial model to confirm the U-shaped distribution of the VA reliance measure.
The distribution of predicted VA reliance shows that the beta-binomial model generated predictions that tracked closely with the U-shaped distribution of unadjusted VA reliance.
We illustrate the use of beta-binomial regression in this U-shaped distribution example, but beta-binomial regression is extraordinarily flexible for all types of distributions of the outcome of interest like all beta distribution-based estimation procedures.
For outcomes with bimodal or U-shaped distributions, the distribution is important to consider if our goals are to understand the actual distribution and to ensure that we can generate unbiased regression coefficients and mean values that generate reasonable predictions.