Finite Mixture Models in the sense of Nagin ([2]) are fuzzy logic cluster analysis models for time series. Starting from a sample of trajectories, the aim is to detect a number of subgroups of the sample, so that subjects in the same group exhibit quite similar data trajectories, whereas two subjects from two different groups have trajectories that differ in some sense. These models have been generalized by Schiltz ([4]) and are part of a larger strand of models that analyze latent evolutions in longitudinal data.We introduce an extension of Nagin’s finite mixture model to underlying Beta distributions and present our R package ([3]) trajeR which allows to calibrate the model. Then, we test the model and illustrate some of the possibilities of trajeR by means of an example with simulated data.In a second part of the paper, we use this model to analyze COVID-19 related data ([1]) during the first part of the pandemic. We identify a classification of the world into five groups of countries with respect to the evolution of the contamination rate and show that the median population age is the main predictor of group membership. We do however not see any sign of efficiency of the sanitary measures taken by the different countries against the propagation of the virus.

References

[1] Hasell J. et al., A cross-country database of COVID-19 testing, Scientific Data, 7(2020), pp. 345.[2] Nagin D.S., Group-Based Modeling of Development, Harvard University Press, 2005.[3] Noel C., Schiltz J., trajeR, an R package for cluster analysis of time series, WorkingPaper, University of Luxembourg, Luxembourg, 2022.[4] Schiltz J., A generalization of Nagin’s finite mixture model, In: Stemmler M., Von Eye A. & Wiedermann W. (eds.), Dependent Data in Social Sciences Research, Springer. 2015, pp. 107-126.