Many ecological data sets are proportional, representing mixtures of constituent elements such as species, populations, or strains. Analyses of proportional data are challenged by categories with zero observations (zeros), all observations (ones), and overdispersion. In lieu of ad hoc data adjustments, we describe and evaluate a zero-and-one inflated Dirichlet regression model, with its corresponding R package (zoid), capable of handling observed data $x$ consisting of three possible categories: zeros, proportions, or ones. Instead of fitting the model to observations of single biological units (e.g., individual organisms) within a sample, we sum proportional contributions across units and estimate mixture proportions using one aggregated observation per sample. Optional estimation of overdispersion and covariate influences expand model applications. We evaluate model performance, as implemented in Stan, using simulations and two ecological case studies. We show that zoid successfully estimates mixture proportions using simulated data with varying sample sizes and is robust to overdispersion and covariate structure. In empirical case studies, we estimate the composition of a mixed-stock Chinook salmon (Oncorhynchus tshawytscha) fishery and analyze the stomach contents of Atlantic cod (Gadus morhua). Our implementation of the model as an R package facilitates its application to varied ecological data sets composed of proportional observations.

中文翻译：

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介绍 zoid：混合模型和 R 包，用于在生态学中用 0 和 1 对比例数据进行建模

许多生态数据集是成比例的，代表物种、种群或品系等组成元素的混合。比例数据的分析受到具有零观测值 (zeros)、所有观测值 (ones) 和过度分散的类别的挑战。代替临时数据调整，我们描述和评估一个零和一个膨胀的 Dirichlet 回归模型，及其相应的 R 包（zoid），能够处理观察到的数据$X$由三个可能的类别组成：零、比例或一。我们不是将模型拟合到样本中单个生物单位（例如，个体生物）的观察结果，而是将各单位的比例贡献相加，并使用每个样本的一个聚合观察结果来估计混合比例。过度离散和协变量影响的可选估计扩展了模型应用。我们使用模拟和两个生态案例研究来评估在 Stan 中实施的模型性能。我们表明 zoid 使用具有不同样本大小的模拟数据成功地估计了混合比例，并且对过度分散和协变量结构具有鲁棒性。在实证案例研究中，我们估计了混合种群的奇努克鲑鱼（Oncorhynchus tshawytscha) 渔业并分析大西洋鳕鱼 ( Gadus morhua ) 的胃内容物。我们将该模型作为 R 包实施，有助于将其应用于由比例观察组成的各种生态数据集。