Skip to main content

Table 1 Examples of association parameters and distinguishability patterns between adjacent categories from NUA models in a 5 × 5 contingency table

From: Power estimation of tests in log-linear non-uniform association models for ordinal agreement

Hypothesis

Association parameters

Distinguishability patterns

H 0

All association parameters are equal

 
 

β 1,2 = β 2,3 = β 3,4 = β 4,5 = log(3)

1 ---- 2 ---- 3 ---- 4 ---- 5

1 association parameter is different

 

β 1,2β 2,3 = β 3,4 = β 4,5 = log(3)

1 - 2 ---- 3 ---- 4 ---- 5

1-------- 2 - 3 - 4 ---- 5

β 2,3β 1,2 = β 3,4 = β 4,5 = log(3)

1 ---- 2 - 3 ---- 4 ---- 5

1 -- 2-------- 3 - 4 -- 5

Β 3,4β 1,2 = β 2,3 = β 4,5 = log(3)

1------ 2 -- 3 - 4 -- 5

1 -- 2 - 3 ------ 4 - 5

Β 4,5β 1,2 = β 2,3 = β 3,4 = log(3)

1 ---- 2 ---- 3 ---- 4 - 5

1 - 2 -- 3 - 4 ---------- 5

2 association parameters are different

 

β 1,2 = β 2,3β 3,4 = β 4,5 = log(3)

1-2 - 3------4------5

1------2------ 3-4-5

β 1,2 = β 4,3β 2,3 = β 3,4 = log(3)

1--2---- 3---- 4--5

1 ---- 2 - 3 - 4 ---- 5

 

All association parameters are different

 

β 1,2β 2,3β 3,4β 4,5

1 - 2 ---- 3 -- 4 ------ 5

  1. *Distinguishabilities values between two categories are proportionnal to number of dashed-lines between these two categories
  2. Symmetric hypotheses in association parameters: and , and