Linear Diagonals‐Parameter Symmetry and Quasi‐Symmetry Models for Cumulative Probabilities in Square Contingency Tables with Ordered Categories
Linear Diagonals‐Parameter Symmetry and Quasi‐Symmetry Models for Cumulative Probabilities in Square Contingency Tables with Ordered Categories
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有序类别方形列联表中累积概率的线性对角线参数对称性和拟对称模型
DOI：
10.1002/bimj.200410066
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发表时间：
2004
影响因子：
1.7
通讯作者：
S. Tomizawa
中科院分区：
文献类型：
--
作者：
N. Miyamoto;Wataru Ohtsuka;S. Tomizawa
对于具有有序类别的方形列联表的分析，Caussinus（1965）考虑了准对称（QS）模型，Goodman（1979）考虑了对角参数对称（DPS）模型，而Albersti（1983）考虑了线性对角参数对称（LDPS）模型。这些模型显示了细胞概率的对称结构。Tomizawa（1993）提出了另一个DPS模型，该模型具有类似的累积概率乘法形式，即观测值将落入行（列）类别i或以下和列（行）类别j（> i）或以上。本文提出了另一种LDPS和QS模型，具有相应的类似的乘法形式的累积概率，而不是细胞概率。所提出的模型的特殊情况包括对称性。使用这些模型分析了两种独立的远距离视觉数据和子宫内膜癌数据。（© 2004 WILEY ‐ VCH Verlag GmbH & Co. KGaA，魏因海姆）
For the analysis of square contingency tables with ordered categories, Caussinus (1965) considered the quasi‐symmetry (QS) model, Goodman (1979) considered the diagonals‐parameter symmetry (DPS) model, and Agresti (1983) considered the linear diagonals‐parameter symmetry (LDPS) model. These models show the structures of symmetry for cell probabilities. Tomizawa (1993) proposed another DPS model which has a similar multiplicative form for cumulative probabilities that an observation will fall in row (column) category i or below and column (row) category j (>i) or above. This paper proposes another LDPS and QS models that have the corresponding similar multiplicative forms for cumulative probabilities instead of cell probabilities. Special cases of the proposed models include symmetry. Two kinds of unaided distance vision data and endometrial cancer data are analyzed using these models. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)