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We focus on hierarchical, multivariate, binary data organized in a three-way data structure, where rows correspond to first-level units, columns to variables, and layers to second-level units within which the first-level units are nested. In this framework, model-based clustering methods can be effectively employed for dimensionality reduction purposes, facilitating a clear understanding of the phenomenon under investigation. In this work, we propose a novel modeling tool for a hierarchical clustering of first- and second-level units. We extend the Mixture of Latent Trait Analyzers (MLTA) with concomitant variables by letting prior component probabilities depend also on second-level-specific random effects. Parameter estimation is performed by means of a double EM algorithm based on a variational approximation of the model log-likelihood function, along with a nonparametric maximum likelihood estimation of the second-level-specific random effect distribution. This latter approach allows to estimate a discrete distribution which directly provides a clustering of second-level units. Within (conditional on) each of such clusters, first-level units are partitioned thanks to the MLTA specification. The proposal is applied to data from the European Social Survey to partition countries (second-level units) according to the baseline attitude of their residents (first-level units) toward digital technologies (variables). Within these clusters, residents are partitioned on the basis of their attitude toward specific digital skills. The influence of socio-economic factors on the identification of digitalization profiles is also taken into consideration via a concomitant variable approach.<\/jats:p>","DOI":"10.1007\/s11222-025-10697-5","type":"journal-article","created":{"date-parts":[[2025,8,28]],"date-time":"2025-08-28T16:09:39Z","timestamp":1756397379000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchical Mixtures of Latent Trait Analyzers with concomitant variables for multivariate binary data"],"prefix":"10.1007","volume":"35","author":[{"given":"Dalila","family":"Failli","sequence":"first","affiliation":[]},{"given":"Maria Francesca","family":"Marino","sequence":"additional","affiliation":[]},{"given":"Bruno","family":"Arpino","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,28]]},"reference":[{"key":"10697_CR1","unstructured":"Abendroth, A., L\u00fckemann, L., Hargittai, E., Billari, F., Treas, J., Van Der Lippe, T.: Digital Social Contacts in Work and Family Life Topline results From Round 10 of the European Social Survey, ESS Topline Results Series, Issue 12 (2023). https:\/\/europeansocialsurvey.org\/sites\/default\/files\/2023-10\/TL012_Digital-Social-Contacts-English.pdf"},{"key":"10697_CR2","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"M Abramowitz","year":"1964","unstructured":"Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th edn. 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