Measure of departure from marginal homogeneity using marginal odds for multi-way tables with ordered categories

A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables

“…and where I(•) is the indicator function, I(•) = 1 if true, 0 if not. Note that the asymptotic variances σ 11 and σ 22 of ϕ (λ) and ψ (λ) , respectively, have been shown by Tomizawa et al (2003) and Iki et al (2012).…”

“…2.3 Index ψ (λ) for Measuring Marginal Inhomogeneity Using Cumulative Probabilities of (2.4) Iki et al (2012) proposed the index ψ (λ) that measures the degree of deviation from marginal homogeneity. The index ψ (λ) does not depend on sample size and dimension R. Assuming that H 1(i) + H 2(i) > 0 for i = 1, .…”

A directional measure for marginal homogeneity in square contingency tables with ordered categories

“…When the MH model does not hold, we are interested in measuring the degree of departure from the MH model. For square contingency tables with ordered categories, Iki et al (2012) proposed the power-divergence measure Ψ (λ) to represent the degree of departure from MH (see Appendix for Ψ (λ) ). They also noted that, assuming {H 1(i) + H 2(i) = 0}, (i) the measure Ψ (λ) lies between 0 and 1, (ii) Ψ (λ) = 0 if and only if the MH model holds, and (iii) Ψ (λ) = 1 if and only if the degree of departure from MH is maximum, that is, H 1(i) = 0 (then…”

Improved Estimator of Measure for Marginal Homogeneity using Marginal Odds in Square Contingency Tables

“…For λ > −1, the measure of departure from the marginal homogeneity model considered by Iki et al (2011), is defined by…”

“…Iki et al (2011) considered the measure Φ (λ) to represent the degree of departure from marginal homogeneity for the ordinal data, which is expressed by using the power-divergence (Read and Cressie, 1988, p. 15) or the Patil and Taillie's (1982) diversity index, and as a function of {H 1(i) } and {H 2(i) }. Assuming that {H 1(i) + H 2(i) > 0}, let…”