Dynamic structural equation modeling (DSEM) is widely used for analyzing intensive longitudinal data (ILD). Although many ILD have categorical (Bernoulli or binomially distributed) responses, currently available Metropolis-within-Gibbs samplers for estimating DSEMs are limited to using the probit link and the Bernoulli distribution. These samplers scale poorly with increasing model complexity and/or data size. Here, we present a hybrid sampler -- alternating between one step of the No-U-Turn Sampler (NUTS) and one Gibbs step -- which solves both of these problems: the Gibbs step naturally handles Pólya-Gamma distributed latent variables arising from binomially distributed responses with a logit link, and the NUTS step utilizes a Kalman filter to exactly marginalize over latent states, alleviating the need to sample these variables. We demonstrate in simulation experiments that the proposed sampler is more efficient than alternative algorithms, and that it makes DSEM estimation with binomial data feasible for larger data and models than what has previously been possible. We also illustrate its use in an example application of predicting panic attacks.

翻译：动态结构方程建模（DSEM）被广泛用于分析密集纵向数据（ILD）。尽管许多ILD包含分类（伯努利或二项分布）响应，但目前用于估计DSEM的Metropolis-within-Gibbs采样器仅限于使用probit链接函数和伯努利分布。这些采样器随着模型复杂度和/或数据规模的增加而扩展性不佳。本文提出一种混合采样器——在一步无转向采样器（NUTS）与一步吉布斯采样之间交替进行——这解决了上述两个问题：吉布斯步骤自然地处理由二项分布响应配合logit链接函数产生的Pólya-Gamma分布潜变量，而NUTS步骤则利用卡尔曼滤波器对潜在状态进行精确边际化，从而避免了对这些变量的采样需求。通过仿真实验证明，所提采样器比替代算法更高效，并且使基于二项数据的DSEM估计得以适用于比先前更大规模的数据和模型。我们还通过一个预测惊恐发作的应用实例展示了其实际用途。