Log-linear modeling is a popular statistical tool for analysing a contingency table. This presentation focuses on an alternative approach to modeling ordinal categorical data. The technique, based on orthogonal polynomials, provides a much simpler method of model fitting than the conventional approach of maximum likelihood estimation, as it does not require iterative calculations nor the fittin...

For the analysis of an r by c contingency table having ordered row categories and ordered column categories, a bootstrap method is applied for the model-based likelihood ratio test for independence. A model-based likelihood ratio chi-square statistic and the statistic of the maximum eigenvalue of a Wishart matrix are also discussed. A simulation study is performed to compare the proposed method...

For the analysis of square contingency tables with the same row and column ordinal classifications, McCullagh (1978) considered the palindromic symmetry (PS) model, which has a 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. The present paper proposes a modified PS model which indicate...

The correspondence analysis of a two-way contingency table is now accepted as a very versatile tool for helping users to understand the structure of the association in their data. In cases where the variables consist of ordered categories, there are a number of approaches that can be employed and these generally involve an adaptation of singular value decomposition. Over the last few years, an ...

A new procedure for testing quasi-independence in an ordinal triangular contingency table is proposed as a generalization of Pearson's chi square test. The test is asymptotically equivalent in terms of power to the corresponding restricted likelihood ratio test for contiguous alternatives. Numerical results are also included in this study.

We generalize the conditional symmetry model for an I×I×I contingency table with commensurable ordinal classification variables. The new family of models is constructed in such a way so that possesses the usual desirable properties that appear in the similar generalizations of symmetry and marginal homogeneity models, that is connections between the models above obey a coherent structure.

• For the analysis of square contingency tables, Tomizawa, Miyamoto and Ashihara (2003) considered a measure to represent the degree of departure from marginal homogeneity. However, the maximum value of this measure cannot distinguish two kinds of marginal inhomogeneity. This paper proposes a measure which can distinguish two kinds of marginal inhomogeneity for square tables with ordered catego...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompass m...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses...

We propose a comprehensive Bayesian approach for graphical model determination in observational studies that can accommodate binary, ordinal or continuous variables simultaneously. Our new models are called copula Gaussian graphical models (CGGMs) and embed graphical model selection inside a semiparametric Gaussian copula. The domain of applicability of our methods is very broad and encompasses...