{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T19:57:00Z","timestamp":1781294220144,"version":"3.54.1"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,11,11]],"date-time":"2009-11-11T00:00:00Z","timestamp":1257897600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2011,4]]},"DOI":"10.1007\/s11222-009-9157-4","type":"journal-article","created":{"date-parts":[[2009,11,9]],"date-time":"2009-11-09T23:38:58Z","timestamp":1257809938000},"page":"173-183","source":"Crossref","is-referenced-by-count":11,"title":["Restricted likelihood inference for generalized linear mixed models"],"prefix":"10.1007","volume":"21","author":[{"given":"Ruggero","family":"Bellio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandra R.","family":"Brazzale","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2009,11,11]]},"reference":[{"key":"9157_CR1","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1093\/biomet\/70.2.343","volume":"70","author":"O.E. Barndorff-Nielsen","year":"1983","unstructured":"Barndorff-Nielsen, O.E.: On a formula for the distribution of the maximum likelihood estimator. Biometrika 70, 343\u2013365 (1983)","journal-title":"Biometrika"},{"key":"9157_CR2","doi-asserted-by":"crossref","first-page":"991","DOI":"10.2307\/2530970","volume":"41","author":"P.J. Beitler","year":"1985","unstructured":"Beitler, P.J., Landis, J.R.: A mixed-effects model for categorical data. Biometrics 41, 991\u20131000 (1985)","journal-title":"Biometrics"},{"key":"9157_CR3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1191\/1471082X03st058oa","volume":"3","author":"J.G. Booth","year":"2003","unstructured":"Booth, J.G., Casella, G., Friedl, H., Hobert, J.P.: Negative binomial loglinear mixed models. Stat. Model. 3, 179\u2013191 (2003)","journal-title":"Stat. Model."},{"key":"9157_CR4","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1198\/000313006X110203","volume":"60","author":"B. Caffo","year":"2006","unstructured":"Caffo, B., Griswold, M.: A user-friendly tutorial on link-probit-normal models. Am. Stat. 60, 139\u2013145 (2006)","journal-title":"Am. Stat."},{"key":"9157_CR5","doi-asserted-by":"crossref","first-page":"639","DOI":"10.1198\/106186002439","volume":"11","author":"D.B. Clarkson","year":"2002","unstructured":"Clarkson, D.B., Zhan, Y.: Using spherical-radial quadrature to fit generalized linear mixed effects models. J. Comput. Graph. Stat. 11, 639\u2013659 (2002)","journal-title":"J. Comput. Graph. Stat."},{"key":"9157_CR6","doi-asserted-by":"crossref","DOI":"10.1002\/0471728438","volume-title":"Mixed Models: Theory and Applications","author":"E. Demidenko","year":"2004","unstructured":"Demidenko, E.: Mixed Models: Theory and Applications. Wiley, New York (2004)"},{"key":"9157_CR7","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198502784.001.0001","volume-title":"Approximating Integrals via Monte Carlo and Deterministic Methods","author":"M. Evans","year":"2000","unstructured":"Evans, M., Swartz, T.: Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford University Press, Oxford (2000)"},{"key":"9157_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3095-8","volume-title":"Number-Theoretic Methods in Statistics","author":"K.-T. Fang","year":"1994","unstructured":"Fang, K.-T., Wang, Y.: Number-Theoretic Methods in Statistics. Chapman & Hall, London (1994)"},{"key":"9157_CR9","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1016\/j.csda.2006.05.003","volume":"51","author":"J. Gonzalez","year":"2006","unstructured":"Gonzalez, J., Tuerlinckx, F., De Boeck, P., Cools, R.: Numerical integration in logistic-normal models. Comput. Stat. Data Anal. 51, 1535\u20131548 (2006)","journal-title":"Comput. Stat. Data Anal."},{"key":"9157_CR10","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s11222-006-6890-9","volume":"16","author":"W. Jank","year":"2006","unstructured":"Jank, W.: Efficient simulated maximum likelihood with an application to online retailing. Stat. Comput. 16, 111\u2013124 (2006)","journal-title":"Stat. Comput."},{"key":"9157_CR11","doi-asserted-by":"crossref","first-page":"963","DOI":"10.2307\/2529876","volume":"38","author":"N.M. Laird","year":"1982","unstructured":"Laird, N.M., Ware, J.H.: Random-effects models for longitudinal data. Biometrics 38, 963\u2013974 (1982)","journal-title":"Biometrics"},{"key":"9157_CR12","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011340","volume-title":"Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood","author":"Y. Lee","year":"2006","unstructured":"Lee, Y., Nelder, J.A., Pawitan, Y.: Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood. Chapman & Hall\/CRC Press, Boca Raton (2006)"},{"key":"9157_CR13","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1093\/biomet\/89.2.401","volume":"89","author":"J.G. Liao","year":"2002","unstructured":"Liao, J.G., Lipsitz, S.R.: A type of restricted maximum likelihood estimator of variance components in generalised linear mixed models. Biometrika 89, 401\u2013409 (2002)","journal-title":"Biometrika"},{"key":"9157_CR14","first-page":"624","volume":"90","author":"Q. Liu","year":"1994","unstructured":"Liu, Q., Pierce, D.A.: A note on Gauss-Hermite quadrature. Biometrika 90, 624\u2013629 (1994)","journal-title":"Biometrika"},{"key":"9157_CR15","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1111\/j.2517-6161.1990.tb01790.x","volume":"52","author":"P. McCullagh","year":"1990","unstructured":"McCullagh, P., Tibshirani, R.: A simple method for the adjustment of profile likelihoods. J. R. Stat. Soc., Ser. B 52, 325\u2013344 (1990)","journal-title":"J. R. Stat. Soc., Ser. B"},{"key":"9157_CR16","volume-title":"Generalized, Linear, and Mixed Models","author":"C.E. McCulloch","year":"2001","unstructured":"McCulloch, C.E., Searle, R.E.: Generalized, Linear, and Mixed Models. Wiley, New York (2001)"},{"key":"9157_CR17","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1111\/j.2517-6161.1994.tb01959.x","volume":"56","author":"C.A. McGilchrist","year":"1994","unstructured":"McGilchrist, C.A.: Estimation in generalized mixed models. J. R. Stat. Soc., Ser. B 56, 61\u201369 (1994)","journal-title":"J. R. Stat. Soc., Ser. B"},{"key":"9157_CR18","volume-title":"Models for Discrete Longitudinal Data","author":"G. Molenberghs","year":"2005","unstructured":"Molenberghs, G., Verbeke, G.: Models for Discrete Longitudinal Data. Springer, New York (2005)"},{"key":"9157_CR19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511812231","volume-title":"Numerical Methods of Statistics","author":"J.F. Monahan","year":"2001","unstructured":"Monahan, J.F.: Numerical Methods of Statistics. Cambridge University Press, Cambridge (2001)"},{"key":"9157_CR20","doi-asserted-by":"crossref","first-page":"664","DOI":"10.2307\/2965714","volume":"92","author":"J. Monahan","year":"1997","unstructured":"Monahan, J., Genz, A.: Spherical-radial integration rules for Bayesian computation. J. Am. Stat. Assoc. 92, 664\u2013674 (1997)","journal-title":"J. Am. Stat. Assoc."},{"key":"9157_CR21","doi-asserted-by":"crossref","first-page":"1787","DOI":"10.1016\/j.jspi.2005.06.010","volume":"137","author":"L. Nie","year":"2007","unstructured":"Nie, L.: Convergence rate of MLE in generalized linear and nonlinear mixed-effects models: theory and applications. J. Stat. Plann. Inference 137, 1787\u20131804 (2007)","journal-title":"J. Stat. Plann. Inference"},{"key":"9157_CR22","doi-asserted-by":"crossref","first-page":"896","DOI":"10.1016\/j.jmva.2006.11.009","volume":"98","author":"M. Noh","year":"2007","unstructured":"Noh, M., Lee, Y.: REML estimation for binary data in GLMMs. J. Multivar. Anal. 98, 896\u2013915 (2007)","journal-title":"J. Multivar. Anal."},{"key":"9157_CR23","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1198\/016214501753168389","volume":"96","author":"M.K. Olsen","year":"2001","unstructured":"Olsen, M.K., Schafer, J.L.: A two-part random-effects model for semicontinuous longitudinal data. J. Am. Stat. Assoc. 96, 730\u2013745 (2001)","journal-title":"J. Am. Stat. Assoc."},{"key":"9157_CR24","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s001800300132","volume":"18","author":"J. Pan","year":"2003","unstructured":"Pan, J., Thompson, R.: Gauss-Hermite quadrature approximation for estimation in generalised linear mixed models. Comput. Stat. 18, 57\u201378 (2003)","journal-title":"Comput. Stat."},{"key":"9157_CR25","doi-asserted-by":"crossref","first-page":"5765","DOI":"10.1016\/j.csda.2006.10.003","volume":"51","author":"J. Pan","year":"2007","unstructured":"Pan, J., Thompson, R.: Quasi-Monte Carlo estimation in generalized linear mixed models. Comput. Stat. Data Anal. 51, 5765\u20135775 (2007)","journal-title":"Comput. Stat. Data Anal."},{"key":"9157_CR26","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1093\/biomet\/58.3.545","volume":"58","author":"H.D. Patterson","year":"1971","unstructured":"Patterson, H.D., Thompson, R.: Recovery of inter-block information when block sizes are unequal. Biometrika 58, 545\u2013554 (1971)","journal-title":"Biometrika"},{"key":"9157_CR27","doi-asserted-by":"crossref","first-page":"12","DOI":"10.2307\/1390625","volume":"4","author":"J.C. Pinheiro","year":"1995","unstructured":"Pinheiro, J.C., Bates, D.M.: Approximation to the log-likelihood function in the nonlinear mixed-effects model. J. Comput. Graph. Stat. 4, 12\u201335 (1995)","journal-title":"J. Comput. Graph. Stat."},{"key":"9157_CR28","volume-title":"R: A Language and Environment for Statistical Computing","author":"R Development Core Team","year":"2009","unstructured":"R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2009)"},{"key":"9157_CR29","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1093\/biomet\/85.2.403","volume":"85","author":"T.A. Severini","year":"1998","unstructured":"Severini, T.A.: An approximation to the modified profile likelihood function. Biometrika 85, 403\u2013411 (1998a)","journal-title":"Biometrika"},{"key":"9157_CR30","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1093\/biomet\/85.3.507","volume":"85","author":"T.A. Severini","year":"1998","unstructured":"Severini, T.A.: Likelihood functions for the elimination of nuisance parameters. Biometrika 85, 507\u2013522 (1998b)","journal-title":"Biometrika"},{"key":"9157_CR31","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198506508.001.0001","volume-title":"Likelihood Methods in Statistics","author":"T.A. Severini","year":"2000","unstructured":"Severini, T.A.: Likelihood Methods in Statistics. Oxford University Press, Oxford (2000)"},{"key":"9157_CR32","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1198\/106186002760180617","volume":"11","author":"H.J. Skaug","year":"2002","unstructured":"Skaug, H.J.: Automatic differentiation to facilitate maximum likelihood estimation in nonlinear random effects models. J. Comput. Graph. Stat. 11, 458\u2013470 (2002)","journal-title":"J. Comput. Graph. Stat."},{"key":"9157_CR33","doi-asserted-by":"crossref","first-page":"961","DOI":"10.2307\/2531147","volume":"40","author":"R. Stiratelli","year":"1984","unstructured":"Stiratelli, R., Laird, N.M., Ware, J.H.: Random effects models for serial observations with binary responses. Biometrics 40, 961\u2013971 (1984)","journal-title":"Biometrics"},{"key":"9157_CR34","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1191\/0962280202sm291ra","volume":"11","author":"J.A. Tooze","year":"2002","unstructured":"Tooze, J.A., Grunwald, G.K., Jones, R.H.: Analysis of repeated measures data with clumping at zero. Stat. Methods Med. Res. 11, 341\u2013355 (2002)","journal-title":"Stat. Methods Med. Res."},{"key":"9157_CR35","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511753930","volume-title":"Discrete Choice Methods with Simulation","author":"K. Train","year":"2003","unstructured":"Train, K.: Discrete Choice Methods with Simulation. Cambridge University Press, New York (2003)"},{"key":"9157_CR36","doi-asserted-by":"crossref","first-page":"971","DOI":"10.2307\/2533557","volume":"53","author":"L.A. Waller","year":"1997","unstructured":"Waller, L.A., Zelterman, D.: Log-linear modeling with the negative binomial multinomial distribution. Biometrics 53, 971\u2013982 (1997)","journal-title":"Biometrics"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-009-9157-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11222-009-9157-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-009-9157-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T04:22:21Z","timestamp":1739420541000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11222-009-9157-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11,11]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,4]]}},"alternative-id":["9157"],"URL":"https:\/\/doi.org\/10.1007\/s11222-009-9157-4","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11,11]]}}}