Extended marginal homogeneity models based on complementary log-log transform for multi-way contingency tables

For square contingency tables with ordered categories, Saigusa et al. (2018) proposed the marginal cumulative complementary log-log model being an extension of the marginal homogeneity model. The present paper considers the marginal cumulative complementary log-log and conditional marginal cumulative complementary log-log models for multi-way tables. It also gives the decompositions of the marginal homogeneity model into the proposed model and a model of the equality of marginal means for multi-way tables. An example is given.