UC Riverside

Semivarying models extend varying coefficient models by allowing some regression coefficients to be constant with respect to the underlying covariate(s). In this paper we develop a semivarying joint modelling framework for estimating the time-varying association between two intensively measured longitudinal response: a continuous one and a binary one. To overcome the major challenge of jointly modelling these responses, namely, the lack of a natural multivariate distribution, we introduce a Gaussian latent variable underlying the binary response. Then we decompose the model into two components: a marginal model for the continuous response, and a conditional model for the binary response given the continuous response. We develop a two-stage estimation procedure and discuss the asymptotic normality of the resulting estimators. We assess the finite-sample performance of our procedure using a simulation study, and we illustrate our method by analyzing binary and continuous responses from the Women's Interagency HIV Study.