Modeling time-dependent population proportions in a finite mixture model setting

Abstract This paper focuses on modeling population proportions with finite mixtures of Dirichlet distributions in a time-sensitive setting. Specifically, we assume that the proportions are observed in blocks or sequences so that all data points in a block need to be classified together in the resulting clustering solution. The example motivating our model comes from the United Nations’ demographic database that records the proportions of single, married, widowed, etc., participants at different ages for over 200 countries. Our methodology provides a way to distinguish several patterns that exist among the countries when it comes to changes in marital status at different ages. Conducting separate analyses by gender, we observe that the most pronounced split appears between the countries with more traditional gender roles versus those where respondents of both genders tend to get married later in life.