I am researching beta regression models to decide if they are appropriate for my data.
My very first search yielded this basic introduction, that also describes the zero-one inflated beta regression. It gives an example of using it to measure the percent of days patients take their medicine, stating "there is something qualitatively different about people who always take their medication than those who do sometimes or never." I think that this is an interesting conceptual interpretation, and I would like to find some academic literature that discusses this technique from that angle. However, most of the papers that I can find address purely the mathematical underpinnings of beta regression and why it must be bounded between 0 and 1.
Are there any academic papers that discuss the technique of modeling zeros, ones, and in-betweens separately because of inherent differences in underlying structure? I understand that this will vary with application/domain; I am interested in learning generally from any sector.