Separation: Ordinal Variables
At the first stage of calculating R_{t}, we model ordinal T on binary Z for each trial, as in (11.5). Separation can also occur in this circumstance, with the same consequences as in the binary case. Imagine that we collapse the categories of an ordinal variable into a binary variable at each possible threshold. For each collapse in which one or more of the cells in the binary crosstabulation is zero, quasicomplete separation exists (Agresti, 2014).
In Table 11.4, dichotomizing the sevenpoint scale into binary groups at
TABLE 11.3
Quasicomplete separation.
TABLE 11.4
Quasicomplete separation for an ordinal variable. A, A2, B1, C1, D, Ei,
F, and G1 are all greater than zero.
1 
2 
3 
4 
5 
6 
7 
A1 
Bi 
Cl 
Ex 
Fx 
Gx 

a_{2} 
B_{2} = 0 
0 
0 
0 
0 
0 
Treatment 
Placebo 

Surrogate 
Y 
A ^ 0 
В yt 0 
N 
Cyt 0 
0 
any threshold would result in a crosstabulation containing an empty cell, similar to the quasicomplete separation seen in Table 11.3. However, if B_{2} = 0 in Table 11.4, dichotomizing at 1 would give a similar pattern to Table 11.1. In this case, since dichotomization at one or more thresholds gives no separation, there is no quasicomplete separation.
An ordinal variable may also have quasicomplete separation if there “exists a pair of rows for which all observations on one row never fall above any observation in the other row” (Agresti, 2014); see Table 11.5.