A Hybrid NUTS-Gibbs Sampler with State Space Marginalization for Estimation of Dynamic Structural Equation Models with Binomial Outcomes

TL;DR

This paper introduces a hybrid NUTS-Gibbs sampler for dynamic structural equation models with binomial outcomes, improving scalability and efficiency for large datasets.

Contribution

The paper presents a novel hybrid NUTS-Gibbs sampler that handles binomial responses with improved scalability and efficiency in DSEM estimation.

Findings

The proposed sampler outperforms existing algorithms in simulation experiments.

It enables feasible estimation of larger DSEM models with binomial data.

Application to panic attack prediction demonstrates practical utility.

Abstract

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 P\'olya-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.