Logit and Multinomial Response Models

However, before we go any further, let us consider the general 2×J table below.

For the data in the table above, the saturated log-linear model is given by:

with i=1, 2, j=1, 2, 3, …, J, and with the usual constraints. However, since variable A is the dependent variable and is dichotomous (or binary),

we can use logits that are given by:

In particular,

and similarly,

Thus, the logits are the functions of the same λ parameters that appear in the general log-linear model.