Abstract
This study proposes a new marginal asymmetry model which can infer the relation between marginal ridits of row and column variables for ordinal square contingency tables. When the marginal homogeneity model does not hold, we will apply marginal asymmetry models (e.g., the marginal cumulative logistic and extended marginal homogeneity models). On the other hand, we may measure the degree of departure from the marginal homogeneity model. To measure the degree of that, multiple indexes were proposed. Some of them correspond to the marginal cumulative logistic and extended marginal homogeneity models. The proposed model corresponds to the index, which represents the degree of departure from the MH model, using marginal ridits. We compare the proposed model with the existing marginal asymmetry models and show that the proposed model provides better fit performance than them for real data.
Highlights
This study focuses on comparing marginal distributions for matched pair of ordered categorical data with same classifications
We introduce first the marginal asymmetry models, second the relation between the marginal asymmetry models and indexes to measure the degree of departure from the marginal homogeneity (MH) model
This study proposes a new marginal asymmetry model using marginal ridits that corresponds to the index of Tahata et al (2006)
Summary
This study focuses on comparing marginal distributions for matched pair of ordered categorical data with same classifications. The index of Tomizawa et al. Asymmetry Model Using Marginal Ridits (2003) corresponds to the MH(m) model because it is expressed as the function of m−1 k=0 ψkik under the MH(m) model. The index of Iki et al (2012) corresponds to the MCL(m) model because it is expressed as the function of m−1 k=0 ψkik under the MCL(m) model. This study proposes a new marginal asymmetry model using marginal ridits that corresponds to the index of Tahata et al (2006). Under the proposed model, the index of Tahata et al (2006) is expressed as the function of asymmetry parameters. We are interested in what a structure is necessary to obtain the MH model in addition to the proposed model, in the similar to Tahata and Tomizawa (2008) and Kurakami et al (2013).
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