11.3 - Inference for Log-linear Models - Dependent Samples

After the previous discussion on matched and dependent data for square tables, we now consider similar questions with the log-linear model. For the movie ratings example, we concluded that the model of independence is not good (as expected) and that there is only a moderate agreement between Siskel and Ebert (estimate \(\kappa = 0.39\).



con mixed pro total
con 24 8 13 45
mixed 8 13 11 32
pro 10 9 64 83
total 42 30 88 160

 How can we use this approach to test for various degrees of agreement between two variables?

Log-linear Models for Square Tables Section

We can always fit the log-linear models we are already familiar with (e.g., the independence model), but given the nature of matched pairs or repeated measures data, we expect dependence. Thus, there are additional models, specific to these kinds of data that we'd like to consider. Some of those are

  • Symmetry
  • Quasi-symmetry
  • Marginal homogeneity

Fitting of these models typically requires the creation of additional variables, either indicators or other types of numerical variables to be included in the models that we are already familiar with such as an independence model.