Finite mixture models have come to play a very prominent role in modelling data. The finite mixture model is predicated on the assumption that distinct latent groups exist in the population. The finite mixture model therefore is based on a categorical latent variable that distinguishes the different groups. Often in practice, distinct sub-populations do not actually exist. For example, disease severity (e.g., depression) may vary continuously and therefore, a distinction of diseased and non-diseased may not be based on the existence of distinct sub-populations. Thus, what is needed is a generalization of the finite mixture’s discrete latent predictor to a continuous latent predictor. We cast the finite mixture model as a regression model with a latent Bernoulli predictor. A latent regression model is proposed by replacing the discrete Bernoulli predictor by a continuous latent predictor with a beta distribution. Motivation for the latent regression model arises from applications where distinct latent classes do not exist, but instead individuals vary according to a continuous latent variable. The shapes of the beta density are very flexible and can approximate the discrete Bernoulli distribution. Examples and a simulation are provided to illustrate the latent regression model. In particular, the latent regression model is used to model placebo effect among drug-treated subjects in a depression study.

中文翻译：

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潜在回归分析

有限混合模型在数据建模中发挥了非常突出的作用。有限混合模型基于群体中存在不同潜在组的假设。因此，有限混合模型基于区分不同组的分类潜在变量。通常在实践中，不同的亚群实际上并不存在。例如，疾病严重程度（例如，抑郁症）可能不断变化，因此，患病和未患病的区别可能不是基于不同亚群的存在。因此，需要的是将有限混合的离散潜在预测器推广到连续潜在预测器。我们将有限混合模型转换为具有潜在伯努利预测器的回归模型。通过用具有 beta 分布的连续潜在预测器替换离散伯努利预测器来提出潜在回归模型。潜在回归模型的动机来自不存在不同潜在类别的应用程序，而是个体根据连续潜在变量而变化。beta 密度的形状非常灵活，可以近似离散伯努利分布。提供了示例和模拟来说明潜在回归模型。特别是，潜在回归模型用于模拟抑郁症研究中药物治疗受试者的安慰剂效应。而是个体根据连续的潜在变量而变化。beta 密度的形状非常灵活，可以近似离散伯努利分布。提供了示例和模拟来说明潜在回归模型。特别是，潜在回归模型用于模拟抑郁症研究中药物治疗受试者的安慰剂效应。而是个体根据连续的潜在变量而变化。beta 密度的形状非常灵活，可以近似离散伯努利分布。提供了示例和模拟来说明潜在回归模型。特别是，潜在回归模型用于模拟抑郁症研究中药物治疗受试者的安慰剂效应。