Abstract

Finite mixture models for an underlying Beta distribution were introduced by Elmer, Jones and Nagin (2018) and a generalization of it to time-varying variances by Noel and Schiltz (2024). The family of Beta distributions has the big advantage of containing very diverse density shapes which makes it very interesting for modeling in a lot of real-life applications.
Current versions of these models have however the problem that the data have to be strictly between 0 and 1 in order to avoid computational issues. We resolve that problem by using the zero-one inflated Beta distribution instead and present our R package trajeR which allows to calibrate the model.
We illustrate the difference between the Beta model and the zero-one inflated Beta by means of an example with simulated data and finish with presenting the results on real-life data sets, both coming from the COVID-19 pandemics where we again compare the results obtained by using the Beta and the zero-one inflated Beta distribution.

References:
• Elmer J., Jones B.L. & Nagin D.S. (2018) Using the Beta distribution in group-based trajectory models. BML Medical Research Methodology, 18 (152), 1-5.
• Noel C. & Schiltz, J. (2024) Finite Mixture Models for an underlying Beta distribution with an application to COVID-19 data. In: M. Stemmler, W. Wiedermann & F.L. Huang (eds.) Dependent Data in Social Sciences Research: Forms, Issues and Methods of Analysis Second Edition. New York: Springer.