Abstract
For a square contingency table with ordinal categories, there may be a case that one wants to analyze several collapsed tables obtained by combining some adjacent categories of the original table. This paper proposes some new models which indicate double symmetry, quasi double symmetry and marginal double symmetry for the collapsed square tables. It also gives a decomposition of the double symmetry model for collapsed tables. Two kinds of occupational mobility data are analyzed using new models.
Highlights
Consider square contingency tables having same ordinal row and column classifications, for instance, as Tables 1a and 2a
This paper proposes some new models which indicate double symmetry, quasi double symmetry and marginal double symmetry for the collapsed square tables
It gives a decomposition of the double symmetry model for collapsed tables
Summary
Consider square contingency tables having same ordinal row and column classifications, for instance, as Tables 1a and 2a For these data, a lot of observations tend to fall in (or near) the main diagonal cells. Bowker (1948) proposed the symmetry (S) model, which indicates that the probabilities are symmetric with respect to the main diagonal of the table. Yamamoto, Tahata and Tomizawa (2012) proposed some S models for collapsed square contingency tables, for example, the collapsed quasi-symmetry model. Yamamoto, Murakami and Tomizawa (2013) proposed some PS models for collapsed square contingency tables, for example, the collapsed quasi point-symmetry model.
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