In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal factors called ordinal multivariate process. To show the relationship between these factors, an ordinal contingency table is used and modeled with ordinal log-linear model. In this paper, a new control charts based on ordinal-normal statistic is developed to monitor the ord...

Kateri and Papaioannou [1997. Asymmetry models for contingency tables. J. Amer. Statist. Assoc. 92, 1124–1131] proved that, under certain conditions, quasi-symmetry is the closest model to symmetry. A simpler ordinal quasi-symmetry model is the closest to symmetry, under a weaker condition of unequal marginal mean scores. It is a special case of a class of ordinal models based on f-divergence. ...

An alternative approach to classical correspondence analysis was developed in [3] and involves decomposing the matrix of Pearson contingencies of a contingency table using orthogonal polynomials rather than via singular value decomposition. It is especially useful in analysing contingency tables which are of an ordinal nature. This short paper demonstrates that the confidence circles of Lebart,...

Abstract: For square contingency tables with the same row and column ordinal classifications, this paper proposes the quasi-symmetry model based on the marginal ridits. The model indicates that the log-odds that an observation will fall in the (i, j) cell instead of in the (j, i) cell, i < j, is proportional to the difference between the average ridit score of row and column marginal distributi...

For the analysis of square contingency tables with the same row and column ordinal classifications, this article proposes new models which indicate the structures of symmetry with respect to the anti-diagonal of the table. Also, this article gives a simple decomposition in 3 × 3 contingency table using the proposed models. The proposed models are applied to grip strength data.

Pearson’s statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtos...

For square contingency tables with the same row and column ordinal classifications, we propose a model of quasi-symmetry using the row and column marginal ridits scores. Using the proposed model, the model of equality of marginal mean ridits and the model of equality of marginal variance ridits, we give a theorem such that the symmetry model holds if and only if all these models hold. Moreover,...

• A marginal homogeneity model tests whether the row and column distributions of a square contingency table have the same sample margins. However, for variables with ordered categories, the marginal homogeneity model does not take into account the ordering information, leading to significant loss of power. Score-based tests have been proposed for ordinal variables. In this paper, we extend the ...

Exact conditional tests of independence in cross-classification tables are formulated based on the x 2 statistic and statistics with stronger operational interpretations, such as some nominal and ordinal measures of association. Guidelines for the table dimensions and sample sizes for which the tests are economically implemented on a computer are given. Some selected sample sizes and marginal d...

Beef cattle research commonly uses Yield grade (YG) and Quality grade (QG) as outcomes in nutrition and health experiments. These outcomes, as commonly reported and analyzed, are ordinal variables with an assumed rank derived from an underlying latent variable that may or may not be available for analysis. The objective of this study was to employ mixed-effects ordinal regression and approaches...