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A semivarying joint model for longitudinal binary and continuous outcomes
Author(s) -
Kürüm Esra,
Hughes John,
Li Runze
Publication year - 2015
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11273
Subject(s) - covariate , estimator , binary number , statistics , multivariate statistics , asymptotic distribution , binary data , latent variable , mathematics , marginal model , computer science , latent variable model , multivariate normal distribution , marginal distribution , constant (computer programming) , econometrics , regression analysis , random variable , arithmetic , programming language
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 responses: 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. We then 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. The Canadian Journal of Statistics 44: 44–57; 2016 © 2015 Statistical Society of Canada