Independence in loglinear terms

• Independence is equivalent to the following loglinear model:
  
  $$F_{ij} = \tau_0 \tau_i^A \tau_j^B$$
  
  

• That is, the fitted or expected value in the $ij$th cell is calculated by multiplying a `grand mean' effect, an effect for row $i$, and an effect for column $j$. Compare with the formula we already used to calculate expected values under independence:
  
  $$E_{ij}=\frac{n_{i+}n_{+j}}{n_{++}}$$