Extended redundancy analysis (ERA) is used to reduce multiple sets of predictors to a smaller number of components and examine the effects of these components on a response variable. In various social and behavioural studies, auxiliary covariates (e.g., gender, ethnicity) can often lead to heterogeneous subgroups of observations, each of which involves distinctive relationships between predictor and response variables. ERA is currently unable to consider such covariate-dependent heterogeneity to examine whether the model parameters vary across subgroups differentiated by covariates. To address this issue, we combine ERA with model-based recursive partitioning in a single framework. This combined method, MOB-ERA, aims to partition observations into heterogeneous subgroups recursively based on a set of covariates while fitting a specified ERA model to data. Upon the completion of the partitioning procedure, one can easily examine the difference in the estimated ERA parameters across covariate-dependent subgroups. Moreover, it produces a tree diagram that aids in visualizing a hierarchy of partitioning covariates, as well as interpreting their interactions. In the analysis of public data concerning nicotine dependence among US adults, the method uncovered heterogeneous subgroups characterized by several sociodemographic covariates, each of which yielded different directional relationships between three predictor sets and nicotine dependence.

中文翻译：

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基于模型的递归分割扩展冗余分析，并应用于美国成年人的尼古丁依赖

扩展冗余分析 (ERA) 用于将多组预测变量减少到较少的分量，并检查这些分量对响应变量的影响。在各种社会和行为研究中，辅助协变量（例如性别、种族）通常会导致观察的异质亚组，每个亚组都涉及预测变量和响应变量之间的独特关系。ERA 目前无法考虑这种依赖于协变量的异质性来检查模型参数是否因协变量区分的亚组而异。为了解决这个问题，我们将 ERA 与基于模型的递归分区结合在一个框架中。这种组合方法，MOB-ERA，旨在基于一组协变量递归地将观察划分为异构子组，同时将指定的 ERA 模型拟合到数据。分区过程完成后，可以轻松检查估计的 ERA 参数在协变量依赖子组之间的差异。此外，它生成一个树状图，有助于可视化划分协变量的层次结构，以及解释它们的相互作用。在分析有关美国成年人尼古丁依赖的公共数据时，该方法揭示了以几个社会人口统计学协变量为特征的异质亚组，每个亚组都产生了三个预测因子集与尼古丁依赖之间的不同方向关系。人们可以很容易地检查估计的 ERA 参数在协变量依赖子组之间的差异。此外，它生成一个树状图，有助于可视化划分协变量的层次结构，以及解释它们的相互作用。在分析有关美国成年人尼古丁依赖的公共数据时，该方法揭示了以几个社会人口统计学协变量为特征的异质亚组，每个亚组都产生了三个预测因子集与尼古丁依赖之间的不同方向关系。人们可以很容易地检查估计的 ERA 参数在协变量依赖子组之间的差异。此外，它生成一个树状图，有助于可视化划分协变量的层次结构，以及解释它们的相互作用。在分析有关美国成年人尼古丁依赖的公共数据时，该方法揭示了以几个社会人口统计学协变量为特征的异质亚组，每个亚组都产生了三个预测因子集与尼古丁依赖之间的不同方向关系。