Marginally specified logistic-normal models for longitudinal binary data

Likelihood-based inference for longitudinal binary data can be obtained usi ng a generalized linear mixed model (Breslow, N. and Clayton, D. G., 1993, journal of the American Statistical Association 88, 9-25; Wolfinger, El. an d O'Connell, M., 1993, Journal of Statistical Computation and Simulation 48 , 233-243), given the recent improvements in computational approaches. Alte rnatively, Fitzmaurice and Laird (1993, Biometrika. 80, 141-151), Molenberg hs and. Lesaffre (1994, Journal of the American Statistical Association 89, 633-644), and Heagerty and Zeger (1996, Journal of the American Statistica l Association 91, 1024-1036) have developed a likelihood-based inference th at adopts a marginal mean regression parameter and completes full specifica tion of the joint multivariate distribution through either canonical and/or marginal higher moment assumptions. Each of these marginal approaches is c omputationally intense and currently limited to small cluster sizes. In the manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation appro aches to parameter estimation are studied. A key feature of the proposed ap proach is that marginal regression parameters are adopted that still permit individual-level predictions or contrasts. An example is presented where s cientific interest is in both the mean response and the covariance among re peated measurements.