Cell counts {y_ij} in an I × J contingency table have a multinomial (n; {π_ij}) distribution. Show that {P(Y_ij = n_ij), i = 1,..., I, j = 1,..., J} can be expressed as

where α_ij = π_ij π_IJ/π_IJ π_IJ and d is a constant independent of the data. Find an alternative expression using local odds ratios {θ_ij}, by showing that

Transcribed Image Text:

Γ1-1 J-1 d" n!Π Π (n;')' ep| ΣΣnlog(α,) i=1 j=1 -1 I-1 J-1 + Σn4 Ιog( πιμ/ πμ ) + Σn.log( πη/ πμ ) j log( πη/ πιu) i=1 j=1