Tree-Structured Methods for Prediction and Data Visualization

虽然文献中存在许多递归划分算法，但大多数不适合模型解释，因为它们倾向于比其他类型更频繁地选择某些类型的预测变量。因此，这样的树状结构可能产生关于预测变量的作用和相对重要性的误导性结论。该研究的主要目的是将研究者的GUIDE和QUEST策略分别扩展到回归和分类。该方法有效地解决了选择偏差问题，大大减少了计算时间。节省的计算量使得构建迄今为止无法构建的树状结构模型成为可能。第二个目标是使用这些方法对设计实验中未复制和部分复制的数据进行建模。树状结构模型的层次结构及其变量选择能力使其成为传统方法的一个有吸引力的选择。第三个目标是扩展研究者的LOTUS算法，以适应具有多项响应变量的数据的逻辑回归树。从高维数据构建的统计模型通常很难或不直观地解释。这甚至适用于最简单的模型，即多元线性回归模型，其中参数估计的解释充满了由非线性、多重共线性和数据中的相互作用引起的困难。图形可视化可能是解释模型最有效的方法。但是这种技术不适用于二维或三维以上的空间。提出的研究使可视化技术应用于高维数据，通过使用树状结构的方法来划分数据空间，这样最多需要一个，两个或三个预测变量来建模每个分区中的数据。结果是一个图形模型，其广泛的特征可以用树形结构表示，而其精细的特征可以通过二维和三维图形显示来可视化。

Though many recursive partitioning algorithms exist in the literature, most are unsuitable for model interpretation because they tend to select some types of predictor variables more frequently than others. As a result, such tree structures can yield misleading conclusions about the roles and relative importance of the predictor variables. The main thrust of the proposed research is to extend the investigator's GUIDE and QUEST strategies to regression and classification, respectively. This approach effectively solves the problem of selection bias and significantly reduces computation time. The computational savings make it feasible to build tree-structured models that are hitherto impractical to construct. A second objective is to use the methods to model unreplicated and fractionally replicated data from designed experiments. The hierarchical structure of tree-structured models and their variable selection ability make them attractive alternatives to traditional methods. A third objective is extension of the investigator's LOTUS algorithm to fit logistic regression trees to data with multinomial response variables. Statistical models constructed from high-dimensional data are often difficult or unintuitive to interpret. This applies even to the simplest model, the multiple linear regression model, where interpretation of the parameter estimates is fraught with difficulties caused by nonlinearity, multicollinearity, and interactions in the data. Graphical visualization is perhaps the most effective way to interpret a model. But such techniques are inapplicable to more than two or three dimensions. The proposed research enables the application of visualization techniques to high-dimensional data by using a tree-structured method to partition the data space such that at most one, two, or three predictor variables are needed to model the data in each partition. The result is a graphical model whose broad features are representable by a tree structure and whose finer features are visualizable by two and three-dimensional graphical displays.