Loglinear allows us other models

• We can define several other loglinear models of a 2-way table:
  • Grand mean:
    
    $$F_{ij}=\tau_0$$
    
    

  • Equiprobability on one dimension:
    
    $$F_{ij}=\tau_0\tau_i$$
    
    
    and
    
    $$F_{ij}=\tau_0\tau_j$$
    
    

  • Independence:
    
    $$F_{ij}=\tau_0\tau_i\tau_j$$
    
    

  • Association:
    
    $$F_{ij}=\tau_0\tau_i\tau_j\tau_{ij}$$