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首页> 外文期刊>Journal of applied statistics >CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods
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CATANOVA for ordinal variables using orthogonal polynomials with different scoring methods

机译：使用具有不同评分方法的正交多项式对有序变量进行CATANOVA

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In the context of categorical data analysis, the CATegorical ANalysis Of Variance (CATANOVA) has been proposed to analyse the scheme variable-factor, both for nominal and ordinal variables. This method is based on the C statistic and allows to test the statistical significance of the tau index using its relationship with the C statistic. Through Emerson orthogonal polynomials (EOP) a useful decomposition of C statistic into bivariate moments (location, dispersion and higher order components) has been developed. In the construction of EOP the categories are replaced by scores, typically natural scores. In the paper, we provide an overview of the main scoring schemes focusing on the advantages and the statistical properties; we pay special attention to the impact of the chosen scores on the C statistic of CATANOVA and the graphical representations of doubly ordered non-symmetrical correspondence analysis. Through a real data example, we show the impact of the scoring schemes and we consider the RV and multidimensional scaling as tools to measure similarity among the results achieved with each method.
机译：在分类数据分析的背景下，提出了CATegorical方差分析（CATANOVA）来分析方案变量因子，包括名义变量和有序变量。此方法基于C统计量，并允许使用其与C统计量的关系来检验tau指数的统计显着性。通过艾默生正交多项式（EOP），已开发出将C统计量分解为双变量矩（位置，色散和高阶分量）的有用方法。在构建EOP时，类别将替换为分数，通常是自然分数。在本文中，我们概述了主要评分方案，重点是优势和统计属性；我们特别注意所选分数对CATANOVA的C统计量的影响以及双阶非对称对应分析的图形表示。通过一个真实的数据示例，我们展示了评分方案的影响，并且我们将RV和多维标度视为测量每种方法所获得结果之间相似性的工具。

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