Guttman patterns

Psychometrician Louis Guttman (1916-1987) perceived the ideal test to be one in which a person succeeds on all the items up to a certain difficulty, and then fails on all the items above that difficulty. When persons and items are ordered by raw score, this produces a data set with a "Guttman pattern". This is data is not analyzable in the usual way by Rasch analysis, because each person or item in turn becomes an extreme score. Here is a Guttman pattern with dichotomous data:

Easy->Hard items (columns)

1111111 Most able person (rows)

1111110

1111100

1100000

1000000

0000000 Least able person

It is sometimes useful to make this type of data estimable by adding a dummy reversed-Guttman record:

Easy->Hard items (columns)

11111110 Most able person (rows)

11111100

11111000

11000000

10000000

00000000 Least able person

00000001 < Dummy person record

^ Dummy item record

or by anchoring the most extreme items (or persons) a conveniently long distance apart, e.g., 10 logits:

PAFILE=*

1 10 ; anchor the first (highest score) person at 10 logits

8 0 ; anchor the last (lowest score) person at 0 logits