×

zbMATH — the first resource for mathematics

Marginally specified logistic-normal models for longitudinal binary data. (English) Zbl 1059.62566
Summary: Likelihood-based inference for longitudinal binary data can be obtained using a generalized linear mixed model [N. E. Breslow and D. G. Clayton, J. Am. Stat. Assoc. 88, No. 421, 9–25 (1993; Zbl 0775.62195); R. Wolfinger and M. O’Connell, J. Stat. Comput. Simulation 48, No. 3–4, 233–243 (1993; Zbl 0833.62067)], given the recent improvements in computational approaches. Alternatively, G. A. Fitzmaurice and N.M. Laird [Biometrika 80, No. 1, 141–151 (1993; Zbl 0775.62296)], G. Molenberghs and E. Lesaffre [J. Am. Stat. Assoc. 89, No. 426, 633–644 (1994; Zbl 0802.62063)], and P. J. Heagerty and S. L. Zeger [J. Am. Stat. Assoc. 91, No. 435, 1024–1036 (1996; Zbl 0882.62061)] have developed a likelihood-based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and/or marginal higher moment assumptions. Each of these marginal approaches is computationally intense and currently limited to small cluster sizes. In this manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation approaches to parameter estimation are studied. A key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual-level predictions or contrasts. An example is presented where scientific interest is in both the mean response and the covariance among repeated measurements.

MSC:
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramowitz, Handbook of Mathematical Functions (1972)
[2] Booth, Standard errors of prediction in generalized linear mixed models, Journal of the American Statistical Association 93 pp 262– (1998) · Zbl 1068.62516
[3] Breslow, Approximate inference in generalized linear mixed models, Journal of the American Statistical Association 88 pp 9– (1993) · Zbl 0775.62195
[4] Carey, Modelling multivariate binary data with alternating logistic regressions, Biometrika 80 pp 517– (1993) · Zbl 0800.62446
[5] Deming, On a least squares adjustment of a sampled frequency table when the expected marginal totals are known, Annals of Mathematical Statistics 11 pp 427– (1940) · Zbl 0024.05502
[6] Drum, REML estimation with exact covariance in the logistic mixed model, Biometrics 49 pp 677– (1993) · Zbl 0800.62697
[7] Fitzmaurice, A likelihood-based method for analysing longitudinal binary responses, Biometrika 80 pp 141– (1993) · Zbl 0775.62296
[8] Fitzmaurice, Regression models for discrete longitudinal responses (with discussion), Statistical Science 8 pp 284– (1993) · Zbl 0955.62614
[9] Glonek, Multivariate logistic models, Journal of the Royal Statistical Society, Series B 57 pp 533– (1995) · Zbl 0827.62059
[10] Graubard, Regression analysis with clustered data, Statistics in Medicine 13 pp 509– (1994)
[11] Heagerty, Marginal regression models for clustered ordinal measurements, Journal of the American Statistical Association 91 pp 1024– (1996) · Zbl 0882.62061
[12] Laird, Missing data in longitudinal studies, Statistics in Medicine 7 pp 305– (1988)
[13] Lang, Simultaneously modeling joint and marginal distributions of multivariate categorical responses, Journal of the American Statistical Association 89 pp 625– (1994) · Zbl 0799.62063
[14] Liang, Longitudinal data analysis using generalized linear models, Biometrika 73 pp 13– (1986) · Zbl 0595.62110
[15] Lipsitz, Generalized estimating equations for correlated binary data: Using odds ratios as a measure of association, Biometrika 78 pp 153– (1991)
[16] Louis, Estimating a population of parameter values using Bayesian and empirical Bayesian methods, Journal of the American Statistical Association 79 pp 393– (1984)
[17] Mancl, Efficiency of regression estimates for clustered data, Biometrics 52 pp 500– (1996) · Zbl 0925.62303
[18] McCulloch, Maximum likelihood algorithms for generalized linear mixed models, Journal of the American Statistical Association 92 pp 162– (1997) · Zbl 0889.62061
[19] Molenberghs, Marginal modeling of correlated ordinal data using a multivariate Plackett distribution, Journal of the American Statistical Association 89 pp 633– (1994) · Zbl 0802.62063
[20] Monahan, Handbook of the Logistic Distribution pp 529– (1992)
[21] Neuhaus, A comparison of cluster-specific and population-averaged approaches for analyzing correlated binary data, International Statistical Review 59 pp 25– (1991)
[22] Pendergast, A survey of methods for analyzing clustered binary response data, International Statistical Review 64 pp 89– (1996) · Zbl 0900.62382
[23] Pepe, A cautionary note on inference for marginal regression models with longitudinal data and general correlated response data, Communications in Statistics 23 pp 939– (1994) · Zbl 04522389
[24] Pierce , D. A. Sands , B. R. 1975 Extra-Bernoulli variation in binary data Oregon State University
[25] Prentice, Correlated binary regression with co-variates specific to each binary observation, Biometrics 44 pp 1033– (1988) · Zbl 0715.62145
[26] Qu, Latent variable models for clustered dichotomous data with multiple subclusters, Biometrics 48 pp 1095– (1992)
[27] Stiratelli, Random effects models for serial observations with binary responses, Biometrics 40 pp 961– (1984)
[28] Thara, Ten year course of schizophrenia- The Madras longitudinal study, Acta Psychiatrica Scandinavica 90 pp 329– (1994)
[29] Wolfinger, Generalized linear mixed models: A pseudo-likelihood approach, Journal of Statistical Computation and Simulation 48 pp 233– (1993) · Zbl 0833.62067
[30] Zeger, Models for longitudinal data: A generalized estimating equation approach, Biometrics 44 pp 1049– (1988) · Zbl 0715.62136
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.