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In detail, two distinct second-level discrete effects are considered in the model, one affecting the initial probability vector and the other affecting the transition probability matrix of the first-level ordinal latent Markov process. To model these separate effects, we consider a bi-dimensional mixture specification that allows to avoid unverifiable assumptions on the random effect distribution and to derive a two-way clustering of second-level units. Starting from a general model where the two random effects are dependent, we also obtain the independence model as a special case. The proposal is applied to data on the physical health status of a sample of elderly residents grouped into nursing homes. A simulation study assessing the performance of the proposal is also included.<\/jats:p>","DOI":"10.1007\/s11634-021-00446-7","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T16:02:43Z","timestamp":1623772963000},"page":"457-485","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6019-6605","authenticated-orcid":false,"given":"Giorgio Eduardo","family":"Montanari","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Doretti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Francesca","family":"Marino","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,6,15]]},"reference":[{"key":"446_CR1","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1198\/016214506000001086","volume":"102","author":"RM Altman","year":"2007","unstructured":"Altman RM (2007) Mixed hidden Markov models: an extension of the hidden Markov model to the longitudinal data setting. 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