Analysis Of Square Contingency Tables Research Articles

A model of uniform association plus two-diagonalsparameter and its application to occupational mobility table data

For the analysis of square contingency tables with ordered categories, Agresti (1988) introduced a model having the structure of uniform association plus a main-diagonal parameter. This paper extends that model. The extended model has the structure of uniform association plus two-diagonals-parameter, and it is a special case of the quasi-uniform association model introduced by Goodman (1979). The Danish occupational mobility table data are analyzed using the models introduced here.

A Multiplicative Model Imposed More Restrictions on the Quasi‐Symmetry Model for the Analysis of Square Contingency Tables

AbstractFor the analysis of square contingency tables, this note proposes a multiplicative model imposed more restrictions on CAUSSINUS' (1965) quasi‐symmetry (QS) model. The model is not so strict as in the quasi‐double symmetry model considered by TOMIZAWA (1985b). The proposed model has the structure of the QS about the main diagonal plus an extended QS about the reverse diagonal of the square contingency table. The model is applied to the data on unaided vision of students in a university in Japan.

Quasi­Diagonals­Parameter Symmetry Model for Square Contingency Tables with Ordered Categories

For the analysis of square contingency tables with ordered categories, this paper introduces the quasi­diagonals­parameter symmetry (QDPS) model which is an extension of the quasi­symmetry (QS) model. It is shown that the QDPS model is preferable to the QS model for unaided vision data of British women earlier analysed by Stuart (1955). Various extended models of QS are expressed in terms of the local odds ratios and the other odds ratios.

Quasisymmetric Models for the Analysis of Square Contingency Tables

SUMMARY A parametric model is presented for the analysis of square contingency tables where there is a one-to-one correspondence between the categories of the row variable and the categories of the column variable. The model is applicable to cross-classifications where the categories are unordered, partially ordered or completely ordered, but the interpretation of the model and associated parameters is most straightforward when the categories are at least partially ordered. Connections with the mover-stayer model and the usual model of quasisymmetry are described. Two data sets are used to illustrate the utility of the model.

A multiplicative model of marginal homogeneity plus marginal point-symmetry plus independence for square contingency tables

For the analysis of square contingency tables, this note proposes a multiplicative model having the structure of marginal homogeneity plus marginal point-symmetry plus usual independence (or the structure of usual symmetry plus point-symmetry plus independence). An example is given.

Models Having Structure of Various Symmetry Plus Diagonal Exponential Frequencies Applied to Data from Endometrial Cancer Study

AbstractFor the analysis of square contingency tables with ordered categories, this note proposes some models having the structure of symmetry or asymmetry plus the main‐diagonal exponential frequencies. These models are applied to the data from the Los Angeles endometrial cancer study in BRESLOW and DAY (1980, p. 185).

Analysis of Square Contingency Tables with Ordered Categories by a New Method of Applying the 1‐Weight Modified Marginal Homogeneity Models

AbstractFor square contingency tables with ordered categories, this note proposes a new method of applying Tomizawa's (1987) 1‐weight modified marginal homogeneity models and applies to the 4×4 tables on unaided vision analysed by Tomizawa (1987) and by Stuart (1955). A possible explanation which is derived from fitting those models is first obtained using this new method.

Analysis of data in square contingency tables with ordered categories using the conditional symmetry model and its decomposed models.

For the analysis of square contingency tables with ordered categories, three kinds of decompositions for the conditional symmetry model derived by Tomizawa are simply described. Using the conditional symmetry model and its decomposed models, this paper analyzes the data of unaided distance vision of women in Britain first analyzed by Stuart, the data of unaided distance vision of students in a university in Japan, and the data of unaided distance vision of pupils at elementary schools at a city in Tokyo.

Multiplicative models for square contingency tables with ordered categories

SUMMARY For the analysis of square contingency tables having ordered categories, this paper introduces the diagonals-parameter symmetry model and other related multiplicative models. When these models are applied to the 4 x 4 table on unaided vision first analysed by Stuart (1953, 1955), a possible explanation is obtained for (i) the 'strange residual pattern' noted by McCullagh (1978), both in his recent analysis of the data using the palindromic symmetry model and in the analysis of the data using the quasisymmetry model as fitted by Plackett (1974, p. 61) and others; (ii) the observed asymmetry in the table; (iii) the inhomogeneity observed between the row marginal, i.e. right eye vision, and the column marginal, left eye vision; and (iv) the observed association between right eye and left eye vision. The models introduced in this paper are included within the general class of multiplicative models considered by Goodman (1972), but they are different from the specific kinds of models considered in that article.

A Class of Parametric Models for the Analysis of Square Contingency Tables with Ordered Categories

A parametric model is developed for the analysis of square contingency tables with ordered categories. Order among the categories is a built-in feature of the new model and this means that it is unnecessary to assign arbitrary ‘scores’ to the row and column variables. Special cases of the proposed model include conditional symmetry and symmetry. The relationship with marginal homogeneity is also described. The model for quasisymmetry is considered and is shown to be invariant under general permutation transformations of the indices, which makes it suitable for analysing data on a nominal scale. On the other hand, the new model, called p symmetry, is invariant only under the special reverse permutation transformation. This restricted invarianoe property makes the latter model more suitable for analysing data on an ordinal scale

A class of parametric models for the analysis of square contingency tables with ordered categories

SUMMARY A parametric model is developed for the analysis of square contingency tables with ordered categories. Order among the categories is a built-in feature of the new model and this means that it is unnecessary to assign arbitrary 'scores' to the row and column variables. Special cases of the proposed model include conditional symmetry and symmetry. The relationship with marginal homogeneity is also described. The model for quasisymmetry is considered and is shown to be invariant under general permutation transformations of the indices, which makes it suitable for analysing data on a nominal scale. On the other hand, the new model, called p symmetry, is invariant only under the special reverse permutation transformation. This restricted invariance property makes the latter model more suitable for analysing data on an ordinal scale.