{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:41:40Z","timestamp":1790815300414,"version":"4.1.0"},"reference-count":41,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T00:00:00Z","timestamp":1141344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,4,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>For a class of latent Markov models for discrete variables having a longitudinal structure, we introduce an approach for formulating and testing linear hypotheses on the transition probabilities of the latent process. For the maximum likelihood estimation of a latent Markov model under hypotheses of this type, we outline an EM algorithm that is based on well-known recursions in the hidden Markov literature. We also show that, under certain assumptions, the asymptotic null distribution of the likelihood ratio statistic for testing a linear hypothesis on the transition probabilities of a latent Markov model, against a less stringent linear hypothesis on the transition probabilities of the same model, is of \u03c7\u00af2 type. As a particular case, we derive the asymptotic distribution of the likelihood ratio statistic between a latent class model and its latent Markov version, which may be used to test the hypothesis of absence of transition between latent states. The approach is illustrated through a series of simulations and two applications, the first of which is based on educational testing data that have been collected within the National Assessment of Educational Progress 1996, and the second on data, concerning the use of marijuana, which have been collected within the National Youth Survey 1976\u20131980.<\/jats:p>","DOI":"10.1111\/j.1467-9868.2006.00538.x","type":"journal-article","created":{"date-parts":[[2006,3,3]],"date-time":"2006-03-03T15:10:01Z","timestamp":1141398601000},"page":"155-178","source":"Crossref","is-referenced-by-count":46,"title":["Likelihood Inference for a Class of Latent Markov Models under Linear Hypotheses on the Transition Probabilities"],"prefix":"10.1093","volume":"68","author":[{"given":"Francesco","family":"Bartolucci","sequence":"first","affiliation":[{"name":"Universit\u00e0 di Perugia , Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,3,3]]},"reference":[{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/S0378-3758(02)00318-X","article-title":"Parameter estimation for hidden Markov chains","volume":"108","author":"Archer","year":"2002","journal-title":"J. Statist. Planng Inf."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1044","DOI":"10.1080\/01621459.2000.10474301","article-title":"Transmission of pneumococcal carriage in families: a latent Markov process model for binary longitudinal data","volume":"95","author":"Auranen","year":"2000","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1214\/aos\/1015956713","article-title":"A likelihood ratio test for MTP2 within binary variables","volume":"28","author":"Bartolucci","year":"2000","journal-title":"Ann. Statist."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s11336-001-0934-z","article-title":"Likelihood inference on the underlying structure of IRT models","volume":"70","author":"Bartolucci","year":"2005","journal-title":"Psychometrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1214\/aoms\/1177697196","article-title":"A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains","volume":"41","author":"Baum","year":"1970","journal-title":"Ann. Math. Statist."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1111\/1467-9574.00233","article-title":"Latent Markov modelling of recidivism data","volume":"57","author":"Bijleveld","year":"2003","journal-title":"Statist. Neerland."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1214\/aoms\/1177728725","article-title":"On the distribution of the likelihood ratio","volume":"25","author":"Chernoff","year":"1954","journal-title":"Ann. Math. Statist."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1109","DOI":"10.1111\/j.0006-341X.2000.01109.x","article-title":"Estimation of operating characteristics for dependent diagnostic tests based on latent Markov models","volume":"56","author":"Cook","year":"2000","journal-title":"Biometrics"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1112","DOI":"10.1080\/01621459.1998.10473772","article-title":"A unified approach to likelihood inference on stochastic orderings in a nonparametric context","volume":"93","author":"Dardanoni","year":"1998","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3990-9","volume-title":"Explanatory Item Response Models: a Generalized Linear and Nonlinear Approach","author":"De Boeck","year":"2004"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm (with discussion)","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Statist. Soc. B"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4613-9637-6","volume-title":"Multiple Problem Youth: Delinquency, Substance Use, and Mental Health Problems","author":"Elliot","year":"1989"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1093\/biomet\/61.2.215","article-title":"Exploratory latent structure analysis using both identifiable and unidentifiable models","volume":"61","author":"Goodman","year":"1974","journal-title":"Biometrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-1988-9","volume-title":"Item Response Theory: Principles and Applications","author":"Hambleton","year":"1985"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1177\/0049124198026003001","article-title":"The latent Markov chain with multivariate random effects\u2014an evaluation of instruments measuring labor market status in the British Household Panel Study","volume":"26","author":"Humphreys","year":"1998","journal-title":"Sociol. Meth. Res."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/BF02295181","article-title":"Loglinear multidimensional IRT models for polytomously scored items","volume":"59","author":"Kelderman","year":"1994","journal-title":"Psychometrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1177\/014662169401800308","article-title":"State mastery learning: dynamic models for longitudinal data","volume":"18","author":"Langeheine","year":"1994","journal-title":"Appl. Psychol. Measmnt"},{"key":"2023040707474172200_","volume-title":"Latent Structure Analysis","author":"Lazarsfeld","year":"1968"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1002\/j.1538-7305.1983.tb03114.x","article-title":"An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition","volume":"62","author":"Levinson","year":"1983","journal-title":"Bell Syst. Tech. J."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1080\/01621459.1991.10475008","article-title":"Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis","volume":"86","author":"Lindsay","year":"1991","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474172200_","volume-title":"Hidden Markov and Other Models for Discrete-valued Time Series","author":"MacDonald","year":"1997"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1191\/0962280203sm323ra","article-title":"Latent mixed Markov modelling of smoking transitions using Monte Carlo bootstrapping","volume":"12","author":"Mannan","year":"2003","journal-title":"Statist. Meth. Med. Res."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF02296300","article-title":"Efficient estimation and local identification in latent class analysis","volume":"21","author":"McHugh","year":"1956","journal-title":"Psychometrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","DOI":"10.1002\/0471721182","volume-title":"Finite Mixture Models","author":"McLachlan","year":"2000"},{"key":"2023040707474172200_","volume-title":"Latent Structure Analysis with Choice Modeling Applications","author":"Poulsen","year":"1982"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/0167-8116(90)90028-L","article-title":"Mixed Markov and latent Markov modelling applied to brand choice behaviour","volume":"7","author":"Poulsen","year":"1990","journal-title":"Int. J. Res. Marktng"},{"key":"2023040707474172200_","first-page":"321","volume-title":"Proc. 4th Berkeley Symp. Mathematical Statistics and Probability","author":"Rasch","year":"1961"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"577","DOI":"10.2307\/1913267","article-title":"Identification in parametric models","volume":"39","author":"Rothenberg","year":"1971","journal-title":"Econometrica"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"17","DOI":"10.2333\/bhmk.23.17","article-title":"Evaluation of mathematical models for ordered polytomous responses","volume":"23","author":"Samejima","year":"1996","journal-title":"Behaviormetrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1214\/aos\/1176344136","article-title":"Estimating the dimension of a model","volume":"6","author":"Schwarz","year":"1978","journal-title":"Ann. Statist."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1198\/016214502753479464","article-title":"Bayesian methods for hidden Markov models: recursive computing in the 21st century","volume":"97","author":"Scott","year":"2002","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"605","DOI":"10.1080\/01621459.1987.10478472","article-title":"Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions","volume":"82","author":"Self","year":"1987","journal-title":"J. Am. Statist. Ass."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1093\/biomet\/72.1.133","article-title":"Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints","volume":"72","author":"Shapiro","year":"1985","journal-title":"Biometrika"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"49","DOI":"10.2307\/1403361","article-title":"Towards a unified theory of inequality constrained testing in multivariate analysis","volume":"56","author":"Shapiro","year":"1988","journal-title":"Int. Statist. Rev."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S0047-259X(03)00134-9","article-title":"The restricted EM algorithm under inequality restrictions on the parameters","volume":"92","author":"Shi","year":"2005","journal-title":"J. Multiv. Anal."},{"key":"2023040707474172200_","volume-title":"Constrained Statistical Inference: Inequality, Order, and Shape Restrictions","author":"Silvapulle","year":"2004"},{"key":"2023040707474172200_","first-page":"213","volume-title":"Sociological Methodology","author":"Van de Pol","year":"1990"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1017\/CBO9780511542411.016","volume-title":"Methods in Human Growth Research","author":"Vermunt","year":"2004"},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"179","DOI":"10.2307\/1165200","article-title":"Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates","volume":"24","author":"Vermunt","year":"1999","journal-title":"J. Educ. Behav. Statist."},{"key":"2023040707474172200_","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1155\/2002\/874560","article-title":"Fitting hidden Markov models to psychological data","volume":"10","author":"Visser","year":"2002","journal-title":"Scient. Programmng"},{"key":"2023040707474172200_","volume-title":"Panel Analysis: Latent Probability Models for Attitude and Behavior Processes","author":"Wiggins","year":"1973"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1467-9868.2006.00538.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/2\/155\/49794558\/jrsssb_68_2_155.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/68\/2\/155\/49794558\/jrsssb_68_2_155.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T22:39:49Z","timestamp":1736289589000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/68\/2\/155\/7110605"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,3]]},"references-count":41,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2006,3,3]]},"published-print":{"date-parts":[[2006,4,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.1467-9868.2006.00538.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2006,4]]},"published":{"date-parts":[[2006,3,3]]}}}