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首页> 外文期刊>Advances in data analysis and classification >Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories
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Generalized marginal homogeneity model and its relation to marginal equimoments for square contingency tables with ordered categories

机译：具有排序类别的正方形列联表的广义边际同质化模型及其与边际均衡的关系

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For square contingency tables with ordered categories, Tomizawa(Calcutta Stat Assoc Bull 43:123–125, 1993a; Sankhya Ser B 60:293–300, 1998)gave theorems that the marginal homogeneity (MH) model is equivalent to certain two or three models holding simultaneously. This paper proposes a generalized MH model, which describes a structure of the odds that an observation will fall in row category i or below and column category i +1 or above, instead of in column category i or below and row category i +1 or above. In addition, this paper gives the theorems that the MH model is equivalent to the generalized MH model and some models holding simultaneously whose each indicates: (1) the equality of m-order moment of row and column variables, (2) the equality of skewness of them and (3) the equality of kurtosis of them. When the MH model fits the data poorly, these may be useful for seeing the reason for the poor fit; for instance, the poor fit of theMH model is caused by the poor fit of the equality of row and column means rather than the generalized MH model.Examples are given.
机译：对于有序类别的方形列联表，Tomizawa（Calcutta Stat Assoc Bull 43：123–125，1993a; Sankhya Ser B 60：293–300，1998）得出定理，即边际均一性（MH）模型等于某些两个或三个模特同时举行。本文提出了一种广义的MH模型，该模型描述了观测值落在行类别i或以下和列类别i +1或以上，而不是列类别i或以下和行类别i +1或以下的可能性的结构。以上。此外，本文给出了定理，即MH模型等效于广义MH模型，并且同时持有一些模型，这些模型分别表明：（1）行列变量的m阶矩相等，（2）它们的偏度;（3）它们的峰度相等。当MH模型无法很好地拟合数据时，这些数据可能有助于了解拟合不良的原因;例如，MH模型的拟合不佳是由于行和列均值相等性的拟合不佳而不是广义的MH模型引起的。

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