A Bayesian framework is proposed for modeling continuous or ordered categorical measurements taken at different points (or times) and whose expected trajectories lie on one or more underlying curves. Prior information about the shape of the curves relative to a reference point is incorporated through a probability distribution for their second derivative. A flexible factor analytic model accommodates covariate effects as well as heterogeneity among subjects and among curves from a given subject. Heterogeneity is assessed separately with respect to different components of the underlying mean function. Priors are chosen for the factor analytic parameters and for the distribution of the unknown reference point. A Markov chain Monte Carlo approach is described for posterior computation. The methods are applied to a study of changes in cervical mucus throughout the menstrual cycle.
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