Association

• Association in a two-way table is represented by the $\tau_{ij}$ term which implies that for every combination of the row and column categories there is a different, additional, effect over and above the row and column specific effects.
• This reproduces the observed data exactly and is called the saturated model.
• It has no degrees of freedom because the number of parameters to be estimated is equal to the number of cells.
• Because it exactly reproduces the observations it has no explanatory power.
• It is therefore usually uninteresting but sometimes it can be useful to look at its parameter estimates.
• Later in the course we will look at ways of constraining the $\tau_{ij}$ term to fit restricted forms of association that retain some degrees of freedom, and explanatory power.