{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T18:14:30Z","timestamp":1791310470023,"version":"4.3.1"},"reference-count":44,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[1992,9,1]],"date-time":"1992-09-01T00:00:00Z","timestamp":715305600000},"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":[[1992,9,1]]},"abstract":"<jats:title>SUMMARY<\/jats:title>\n               <jats:p>It is common to observe a vector of discrete and\/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables. This paper discusses a class of models for the marginal expectations of each response and for pairwise associations. The marginal models are contrasted with log-linear models. Two generalized estimating equation approaches are compared for parameter estimation. The first focuses on the regression parameters; the second simultaneously estimates the regression and association parameters. The robustness and efficiency of each is discussed. The methods are illustrated with analyses of two data sets from public health research.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1992.tb01862.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T06:27:34Z","timestamp":1544164054000},"page":"3-24","source":"Crossref","is-referenced-by-count":548,"title":["Multivariate Regression Analyses for Categorical Data"],"prefix":"10.1093","volume":"54","author":[{"given":"Kung-Yee","family":"Liang","sequence":"first","affiliation":[{"name":"Johns Hopkins University , Baltimore , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Scott L.","family":"Zeger","sequence":"additional","affiliation":[{"name":"Johns Hopkins University , Baltimore , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bahjat","family":"Qaqish","sequence":"additional","affiliation":[{"name":"University of North Carolina , Chapel Hill , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090922052074000_rssb01862-cit-0001","volume-title":"An Introduction to Multivariate Statistical Analysis","author":"Anderson","year":"1971","edition":"2nd edn."},{"key":"2024090922052074000_rssb01862-cit-0002","volume-title":"Latent Variable Models in Factor Analysis.","author":"Bartholomew","year":"1983"},{"key":"2024090922052074000_rssb01862-cit-0003","volume-title":"Discrete Multivariate Analysis: Theory and Practice.","author":"Bishop","year":"1975"},{"key":"2024090922052074000_rssb01862-cit-0004","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1093\/oxfordjournals.aje.a112994","article-title":"Chronic obstructive pulmonary disease: A challenge in genetic epidemiology","volume":"112","author":"Cohen","year":"1980","journal-title":"Am. J. Epidem."},{"key":"2024090922052074000_rssb01862-cit-0005","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1093\/biomet\/75.3.501","article-title":"Conditional logistic regression models for correlated binary data","volume":"75","author":"Connolly","year":"1988","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0006","doi-asserted-by":"crossref","first-page":"909","DOI":"10.2307\/2530704","article-title":"Global cross-ratio models for bivariate, discrete ordered responses","volume":"42","author":"Dale","year":"1986","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0007","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1111\/j.2517-6161.1990.tb01770.x","article-title":"Hierarchical interaction models","volume":"52","author":"Edwards","year":"1990","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090922052074000_rssb01862-cit-0008","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1214\/aoms\/1177705693","article-title":"An optimum property of regular maximum likelihood estimation","volume":"31","author":"Godambe","year":"1960","journal-title":"Ann. Math. Statist."},{"key":"2024090922052074000_rssb01862-cit-0009","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/0378-3758(89)90106-7","article-title":"An extension of quasi-likelihood estimation (with discussion)","volume":"22","author":"Godambe","year":"1989","journal-title":"J. Statist. Planng Inf."},{"key":"2024090922052074000_rssb01862-cit-0010","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2307\/1909757","article-title":"Dummy endogeneous variables in a simultaneous equation system","volume":"60","author":"Heckman","year":"1978","journal-title":"Econometrica"},{"key":"2024090922052074000_rssb01862-cit-0011","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1007\/BF02293808","article-title":"Structural analysis of covariance and correlation matrices","volume":"43","author":"J\u00f6reskog","year":"1978","journal-title":"Psychometrika"},{"key":"2024090922052074000_rssb01862-cit-0012","doi-asserted-by":"crossref","first-page":"991","DOI":"10.2307\/2529879","article-title":"Mixtures of continuous and categorical variables in discriminant analysis: A hypothesis testing approach","volume":"38","author":"Krzanowski","year":"1982","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0013","first-page":"33","article-title":"Topics in likelihood-based methods for longitudinal data analysis","volume":"1","author":"Laird","year":"1991","journal-title":"Statist. Sin."},{"key":"2024090922052074000_rssb01862-cit-0014","doi-asserted-by":"crossref","first-page":"963","DOI":"10.2307\/2529876","article-title":"Random effects models for longitudinal data","volume":"38","author":"Laird","year":"1982","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0015","first-page":"31","article-title":"Graphical models for association between variables, some of which are qualitative and some quantitative","volume":"17","author":"Lauritzen","year":"1989","journal-title":"Ann. Statist."},{"key":"2024090922052074000_rssb01862-cit-0016","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","article-title":"Longitudinal data analysis using generalized linear models","volume":"73","author":"Liang","year":"1986","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0017","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1080\/01621459.1989.10478789","article-title":"A class of logistic regression models for multivariate binary time series","volume":"84","author":"Liang","year":"1989","journal-title":"J. Am. Statist. Ass."},{"key":"2024090922052074000_rssb01862-cit-0018","first-page":"1014","article-title":"Newton-Raphson and EM algorithms for linear mixed-effects models for repeated measures data","volume":"83","author":"Lindstrom","year":"1988","journal-title":"J. Am. Statist. Ass."},{"key":"2024090922052074000_rssb01862-cit-0019","article-title":"Generalized estimating equations for correlated binary data: using the odds ratio as a measure of association","volume-title":"Technical Report.","author":"Lipsitz","year":"1989"},{"key":"2024090922052074000_rssb01862-cit-0020","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1093\/biomet\/72.3.497","article-title":"Maximum likelihood estimation for mixed continuous and categorical data with missing values","volume":"72","author":"Little","year":"1985","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0021","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1002\/sim.4780070108","article-title":"General methods for analyzing repeated measures","volume":"7","author":"Louis","year":"1988","journal-title":"Statist. Med."},{"key":"2024090922052074000_rssb01862-cit-0022","volume-title":"Structural Analysis of Discrete Data with Econometric Applications.","author":"Manski","year":"1981"},{"key":"2024090922052074000_rssb01862-cit-0023","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1111\/j.2517-6161.1980.tb01109.x","article-title":"Regression models for ordinal data (with discussion)","volume":"42","author":"McCullagh","year":"1980","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090922052074000_rssb01862-cit-0024","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-3242-6","volume-title":"Generalized Linear Models","author":"McCullagh","year":"1989","edition":"2nd edn."},{"key":"2024090922052074000_rssb01862-cit-0025","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1093\/biomet\/74.2.247","article-title":"A generalized linear model with nested strata of extra-Poisson variation","volume":"74","author":"Morton","year":"1987","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0026","doi-asserted-by":"crossref","first-page":"523","DOI":"10.2307\/2531457","article-title":"Some comments on Rosner's multiple logistic model for clustered data","volume":"46","author":"Neuhaus","year":"1990","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0027","doi-asserted-by":"crossref","first-page":"1022","DOI":"10.2307\/2531733","article-title":"Correlated binary regression with covariate specific to each binary observation","volume":"44","author":"Prentice","year":"1988","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0028","article-title":"Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses","volume-title":"Biometrics","author":"Prentice","year":"1991"},{"key":"2024090922052074000_rssb01862-cit-0029","article-title":"Multivariate regression models using generalized estimating equations","volume-title":"Doctoral Thesis.","author":"Qaqish","year":"1990"},{"key":"2024090922052074000_rssb01862-cit-0030","article-title":"Marginal regression models for correlated responses with multiple classes and multiple levels of nesting","volume-title":"Technical Report.","author":"Qaqish","year":"1990"},{"key":"2024090922052074000_rssb01862-cit-0031","doi-asserted-by":"crossref","first-page":"961","DOI":"10.2307\/2531153","article-title":"Multivariate methods in ophthalmology with application to paired-data situations","volume":"40","author":"Rosner","year":"1984","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0032","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1093\/ajcn\/40.5.1090","article-title":"Increased risk of respiratory infection and diarrhea in children with pre-existing mild vitamin A deficiency","volume":"40","author":"Sommer","year":"1984","journal-title":"Am. J. Clin. Nutr."},{"key":"2024090922052074000_rssb01862-cit-0033","doi-asserted-by":"crossref","first-page":"961","DOI":"10.2307\/2531147","article-title":"Random-effects models for serial observations with binary response","volume":"40","author":"Stiratelli","year":"1984","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0034","doi-asserted-by":"crossref","first-page":"585","DOI":"10.1093\/biomet\/66.3.585","article-title":"Testing the goodness-of-fit of the binomial distribution","volume":"66","author":"Tarone","year":"1979","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0035","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1111\/j.2517-6161.1989.tb01756.x","article-title":"Model specification in multivariate time series (with discussion)","volume":"51","author":"Tiao","year":"1989","journal-title":"J. R. Statist. Soc. B"},{"key":"2024090922052074000_rssb01862-cit-0036","article-title":"Sociodemographic risk factors for blindness and visual impairment: the Baltimore Eye Survey","volume-title":"Arch. Ophthalmol.","author":"Tielsch","year":"1989"},{"key":"2024090922052074000_rssb01862-cit-0037","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1080\/01621459.1984.10477073","article-title":"Regression models with time series errors","volume":"79","author":"Tsay","year":"1984","journal-title":"J. Am. Statist. Ass."},{"key":"2024090922052074000_rssb01862-cit-0038","first-page":"439","article-title":"Quasi-likelihood functions, generalized linear models, and the Gauss\u2013Newton method","volume":"61","author":"Wedderburn","year":"1974","journal-title":"Biometrika"},{"key":"2024090922052074000_rssb01862-cit-0039","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1002\/sim.4780070117","article-title":"The analysis of discrete longitudinal data: commentary","volume":"7","author":"Zeger","year":"1987","journal-title":"Statist. Med."},{"key":"2024090922052074000_rssb01862-cit-0040","doi-asserted-by":"crossref","first-page":"121","DOI":"10.2307\/2531248","article-title":"Longitudinal data analysis for discrete and continuous outcomes","volume":"42","author":"Zeger","year":"1986","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0041","first-page":"51","article-title":"Feedback models for discrete and continuous time series","volume":"1","author":"Zeger","year":"1991","journal-title":"Statist. Sin."},{"key":"2024090922052074000_rssb01862-cit-0042","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.2307\/2531734","article-title":"Models for longitudinal data: A generalized estimating equation approach","volume":"44","author":"Zeger","year":"1988","journal-title":"Biometrics"},{"key":"2024090922052074000_rssb01862-cit-0043","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1080\/01621459.1962.10480664","article-title":"An efficient method for estimating seemingly unrelated regression equations and tests for aggregation bias","volume":"57","author":"Zellner","year":"1962","journal-title":"J. Am. Statist. Ass."},{"key":"2024090922052074000_rssb01862-cit-0044","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1093\/biomet\/77.3.642","article-title":"Correlated binary regression using a quadratic exponential model","volume":"77","author":"Zhao","year":"1990","journal-title":"Biometrika"}],"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.2517-6161.1992.tb01862.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/54\/1\/3\/49173384\/jrsssb_54_1_3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/54\/1\/3\/49173384\/jrsssb_54_1_3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T22:38:44Z","timestamp":1725921524000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/54\/1\/3\/7035849"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,9,1]]},"references-count":44,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1992,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1992.tb01862.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1992,9]]},"published":{"date-parts":[[1992,9,1]]}}}