Separation: Ordinal Variables

At the first stage of calculating Rt, 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, quasi-complete separation exists (Agresti, 2014).

In Table 11.4, dichotomizing the seven-point scale into binary groups at

TABLE 11.3

Quasi-complete separation.

TABLE 11.4

Quasi-complete 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

a2

B2 = 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 cross-tabulation containing an empty cell, similar to the quasi-complete separation seen in Table 11.3. However, if B2 = 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 quasi-complete separation.

An ordinal variable may also have quasi-complete 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.

 
Source
< Prev   CONTENTS   Source   Next >