Symmetrical and Non-symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables

被引：10

作者：

Lombardo, Rosaria ^{[1
]}

Beh, Eric J. ^{[2
,3
]}

Kroonenberg, Pieter M. ^{[4
]}

机构：

[1] Univ Campania L Vanvitelli, Econ Dept, Stat, Via Gran Priorato di Malta, Capua, CE, Italy

[2] Univ Newcastle, Sch Math & Phys Sci, Stat, Callaghan, NSW 2308, Australia

[3] Univ Newcastle, Sch Math & Phys Sci, Stat Discipline, Callaghan, NSW 2308, Australia

[4] Leiden Univ, Three Mode Co, Multivariate Data Anal, Wasstr 11, NL-2313 JG Leiden, Netherlands

来源：

STATISTICAL SCIENCE | 2021年 / 36卷 / 04期

关键词：

Symmetrical and non-symmetrical three-way correspondence analysis; ordinal categorical variables; orthogonal polynomials; trivariate moment decomposition; CONTINGENCY-TABLES; CROSS-CLASSIFICATIONS; ASSOCIATION; RANKING; BIPLOTS; MODELS;

D O I：

10.1214/20-STS814

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the framework of multi-way data analysis, this paper presents symmetrical and non-symmetrical variants of three-way correspondence analysis that are suitable when a three-way contingency table is constructed from ordinal variables. In particular, such variables may be modelled using general recurrence formulae to generate orthogonal polynomial vectors instead of singular vectors coming from one of the possible three-way extensions of the singular value decomposition. As we shall see, these polynomials, that until now have been used to decompose two-way contingency tables with ordered variables, also constitute an alternative orthogonal basis for modelling symmetrical, non-symmetrical associations and predictabilities in three-way contingency tables. Consequences with respect to modelling and graphing will be highlighted.

引用

页码：542 / 561

页数：20

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