In this lesson, we applied the log-linear model to ordinal data and showed how it can be used to describe a linear relationship between two ordinal variables. For a given set of numeric scores representing the ordinal categories, we introduced a regression-like slope parameter to describe the linear relationship, replacing the ANOVA-like interaction terms previously used when variables were nominal. The advantage of this was to reduce the number of parameters involved to a single slope and increase the power for testing its significance.
We also showed how agreement between two categorical variables can be measured and tested. This is a question of interest when variables are matched within-subjects, such as in repeated measures over time. In such cases, some association is usually taken for granted, and the focus is then on the specific type of association, such as symmetry or marginal homogeneity.
In the next lesson, we extend this idea of dependent or matched-pairs data to cases involving three or more measurements. This would be the three-way (or higher) table extension to the examples considered so far.