Bayesian Estimation of the Univariate ACE Model With Ordinal Data

<title>Abstract</title> <p>Testing the classic univariate ACE model with ordinal data often relies on frequentist methods that face challenges with small sample sizes, zero-frequency cells in contingency tables, and quantifying uncertainty for derived variance components. While Bayesian estimation offers theoretical advantages in these scenarios, traditional data augmentation approaches are computationally intensive and scale poorly with sample size. This paper introduces an efficient marginal likelihood approach for Bayesian estimation of the ACE model with ordinal data using Stan. By modeling the sufficient statistics of the contingency table directly, this method decouples computational cost from sample size. We demonstrate that this framework effectively handles zero cells without ad-hoc adjustments, incorporates prior information to ensure admissible solutions, and provides full posterior distributions for heritability and environmental estimates. A hands-on tutorial is provided to guide researchers through the estimation process, model checking, and interpretation using R and Stan.</p>