{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:18:11Z","timestamp":1760239091881,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,9,29]],"date-time":"2020-09-29T00:00:00Z","timestamp":1601337600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Lifebrain project","award":["732592 - H2020-SC1-2016-2017\/ 492 H2020-SC1-2016-RTD"],"award-info":[{"award-number":["732592 - H2020-SC1-2016-2017\/ 492 H2020-SC1-2016-RTD"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In accordance with the theme of this special issue, we present a model that indirectly discovers symmetries and asymmetries between past and present assessments within continuous sequences. More specifically, we present an alternative use of a latent variable version of the Mixture Transition Distribution (MTD) model, which allows for clustering of continuous longitudinal data, called the Hidden MTD (HMTD) model. We compare the HMTD and its clustering performance to the popular Growth Mixture Model (GMM), as well as to the recently introduced GMM based on individual case residuals (ICR-GMM). The GMM and the ICR-GMM contrast with HMTD, because they are based on an explicit change function describing the individual sequences on the dependent variable (here, we implement a non-linear exponential change function). This paper has three objectives. First, it introduces the HMTD. Second, we present the GMM and the ICR-GMM and compare them to the HMTD. Finally, we apply the three models and comment on how the conclusions differ depending on the clustering model, when using a specific dataset in psychology, which is characterized by a small number of sequences (n = 102), but that are relatively long (for the domains of psychology and social sciences: t = 20). We use data from a learning experiment, in which healthy adults (19\u201380 years old) were asked to perform a perceptual\u2013motor skills over 20 trials.<\/jats:p>","DOI":"10.3390\/sym12101618","type":"journal-article","created":{"date-parts":[[2020,9,29]],"date-time":"2020-09-29T08:43:27Z","timestamp":1601369007000},"page":"1618","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Use of a Hidden Mixture Transition Distribution Model in Clustering Few but Long Continuous Sequences: An Illustration with Cognitive Skills Data"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3798-757X","authenticated-orcid":false,"given":"Zhivko","family":"Taushanov","sequence":"first","affiliation":[{"name":"Faculty of Psychology and Educational Sciences, University of Geneva, 1205 Geneva, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7731-2406","authenticated-orcid":false,"given":"Paolo","family":"Ghisletta","sequence":"additional","affiliation":[{"name":"Faculty of Psychology and Educational Sciences, University of Geneva, 1205 Geneva, Switzerland"},{"name":"Faculty of Psychology, Swiss Distance University Institute, 3900 Brig, Switzerland"},{"name":"Swiss National Centre of Competence in Research LIVES, University of Geneva, 1205 Geneva, Switzerland"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,29]]},"reference":[{"key":"ref_1","unstructured":"Nesselroade, J., and Baltes, P. 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