The implementation of an universal R package able to treat and cluster all kind of longitudinal data using any specification of the HMTD model (including HMM, DCMM, MTD, Mixture models etc.) will be a very useful tool. As this thesis has shown, HMTD may be a very good alternative to GMM and the other clustering methods. The package for continuous data will be released soon.
On the basis of preliminary trials (that are not included in this thesis), the HMTD model seems to copes well with discrete data too. However, it would be interesting to compare more extensively the performance of the HMTD with DCMM (R package MARCH) when clustering discrete data. Even though DCMM is a model that is specif-ically designed for discrete data, chances are that HMTD could be as good as it for this type of data, because many discrete distributions can be approximated by continuous ones.
The estimation procedure remains demanding in terms of computational time. Ac-celerating the convergence of the model in its full form could open new possibilities for treating larger datasets with higher number of covariates.
Another interesting point is the further study of the di↵erent flexible clustering possibilities, as well as their application using latent level covariates together with the visible ones. The combination of simultaneous clustering and modelling may be very attractive for many social studies involving di↵erent life course trajectories as discussed before. The possibility to identify general groups of persons that evolve di↵erently by simultaneously estimating and modelling di↵erently their latent trajectories, may represent an innovative and useful tool in various domains.
Finally, it would be interesting to see how the HMTD model performs in various
7.6. FURTHER DEVELOPMENTS 171 other fields and for di↵erent purposes. An interesting application may be to identify sequences whose distribution may not be appropriate according to the nature of the phenomenon of interest. As a small illustration in social sciences, we can imagine a longitudinal study that concerns a sensible subject to which the respondents may be afraid to answer and prefer to conform to the norm. In this case, one cluster of the model may capture the trajectories whose auto-dependence structure deviates from the others (randomly or incorrectly answered questions). In other fields, one may similarly identify errors due to the person in charge of collecting survey data, or a faulty measurement tool for instance. Besides ordinary clustering, these are only a few of the many possible applications of the HMTD model.
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Glossary
AIC Akaike Information Criterion. 108 BIC Bayesian Information Criterion. 108 CI Confidence Interval. 97
DE Di↵erential Evolution. 61
EM Expectation-Maximization algorithm. 41 GA Genetic Algorithm. 60
GEM Generalized Expectation-Maximization algorithm. 46 GM M Gaussian Mixture Models. 9
GM M Growth Mixture Models. 34 HM M Hidden Markov Model. 13
HM T D Hidden Mixture Transition Distributions. 15 ICL Integrated Complete Likelihood. 109
M LE Maximum Likelihood Estimate. 97 M T D Mixture Transition Distributions. 9 N M Nelder-Mead optimisation. 61
P SO Particle Swarm Optimization. 60 SA Simulated Annealing. 59
189