Marginally Specified Logistic‐Normal Models for Longitudinal Binary Data

Abstract

Summary.Likelihood‐based inference for longitudinal binary data can be obtained using a generalized linear mixed model (Breslow, N. and Clayton, D. G., 1993,Journal of the American Statistical Association88, 9–25; Wolfinger, R. and O'Connell, M., 1993,Journal of Statistical Computation and Simulation48, 233–243), given the recent improvements in computational approaches. Alternatively, Fitzmaurice and Laird (1993,Biometrika80, 141–151), Molenberghs and Lesaffre (1994,Journal of the American Statistical Association89, 633–644), and Heagerty and Zeger (1996,Journal of the American Statistical Association91, 1024–1036) 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.