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

中文翻译：

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纵向二进制和连续结果的半可变联合模型。

半变量模型通过允许一些回归系数相对于基础协变量恒定而扩展了可变系数模型。在本文中，我们开发了一个半变量联合建模框架，用于估计两个密集测量的纵向响应之间的时变关联：连续响应和二进制响应。为了克服对这些响应进行联合建模的主要挑战，即缺乏自然的多元分布，我们引入了二进制响应背后的高斯潜变量。然后，我们将模型分解为两个部分：连续响应的边际模型和给定连续响应的二元响应的条件模型。我们开发了一个两阶段的估计程序，并讨论了所得估计量的渐近正态性。加拿大统计杂志44：44-57；2016©2015加拿大统计学会