Multivariate random effects with unstructured variance-covariance matrices of large dimensions, $q$, can be a major challenge to estimate. In this paper, we introduce a new implementation of a reduced-rank approach to fit large dimensional multivariate random effects by writing them as a linear combination of $d < q$ latent variables. By adding reduced-rank functionality to the package glmmTMB, we enhance the mixed models available to include random effects of dimensions that were previously not possible. We apply the reduced-rank random effect to two examples, estimating a generalized latent variable model for multivariate abundance data and a random-slopes model.

翻译：具有大维度$q$的非结构化方差-协方差矩阵的多元随机效应，其估计可能面临重大挑战。本文介绍了一种降秩方法的新实现，通过将多元随机效应表示为$d < q$个潜变量的线性组合，来拟合大维度多元随机效应。通过为glmmTMB软件包增加降秩功能，我们扩展了可用混合模型的范围，使其能够包含以往无法处理的维度随机效应。我们将降秩随机效应应用于两个示例：估计多元丰度数据的广义潜变量模型和随机斜率模型。