Abstract. The detection of community or population structure through analysis of explicit cause–effect modeling of given observations has received considerable attention. The complexity of the task is mirrored by the large number of existing approaches and methods, the applicability of which heavily depends on the design of efficient algorithms of data analysis. It is occasionally even difficult to disentangle concepts and algorithms. To add more clarity to this situation, the present paper focuses on elaborating the system analytic framework that probably encompasses most of the common concepts and approaches by classifying them as model-based analyses of latent factors. Problems concerning the efficiency of algorithms are not of primary concern here. In essence, the framework suggests an input–output model system in which the inputs are provided as latent model parameters and the output is specified by the observations. There are two types of model involved, one of which organizes the inputs by assigning combinations of potentially interacting factor levels to each observed object, while the other specifies the mechanisms by which these combinations are processed to yield the observations. It is demonstrated briefly how some of the most popular methods (Structure, BAPS, Geneland) fit into the framework and how they differ conceptually from each other. Attention is drawn to the need to formulate and assess qualification criteria by which the validity of the model can be judged. One probably indispensable criterion concerns the cause–effect character of the model-based approach and suggests that measures of association between assignments of factor levels and observations be considered together with maximization of their likelihoods (or posterior probabilities). In particular the likelihood criterion is difficult to realize with commonly used estimates based on Markov chain Monte Carlo (MCMC) algorithms. Generally applicable MCMC-based alternatives that allow for approximate employment of the primary qualification criterion and the implied model validation including further descriptors of model characteristics are suggested.

中文翻译：

---

基于模型的潜在因素分析

摘要。通过分析给定观察的显式因果模型来检测社区或人口结构已受到相当多的关注。大量现有方法和方法反映了任务的复杂性，其适用性在很大程度上取决于有效的数据分析算法的设计。有时甚至难以解开概念和算法。为了使这种情况更加清晰，本文重点阐述了系统分析框架，该框架可能包含大多数常见概念和方法，将它们归类为基于模型的潜在因素分析。与算法效率有关的问题在这里不是主要关注的问题。在本质上，该框架提出了一个输入-输出模型系统，其中输入作为潜在模型参数提供，输出由观察指定。涉及两种类型的模型，其中一种通过将潜在相互作用因子水平的组合分配给每个观察对象来组织输入，而另一种则指定处理这些组合以产生观察结果的机制。简要演示了一些最流行的方法（Structure、BAPS、Geneland）如何适应框架以及它们在概念上有何不同。提请注意需要制定和评估可以判断模型有效性的资格标准。一个可能不可或缺的标准涉及基于模型的方法的因果特征，并建议将因子水平分配和观察值之间的关联度量与其可能性（或后验概率）的最大化一起考虑。特别是似然标准很难用基于马尔可夫链蒙特卡罗 (MCMC) 算法的常用估计来实现。建议采用普遍适用的基于 MCMC 的替代方案，这些替代方案允许近似采用主要资格标准和隐含的模型验证，包括模型特征的进一步描述符。特别是似然标准很难用基于马尔可夫链蒙特卡罗 (MCMC) 算法的常用估计来实现。建议采用普遍适用的基于 MCMC 的替代方案，这些替代方案允许近似采用主要资格标准和隐含的模型验证，包括模型特征的进一步描述符。特别是似然标准很难用基于马尔可夫链蒙特卡罗 (MCMC) 算法的常用估计来实现。建议采用普遍适用的基于 MCMC 的替代方案，这些替代方案允许近似采用主要资格标准和隐含的模型验证，包括模型特征的进一步描述符。