No non-extreme persons/items: Guttman deterministic patterns and splits

See also Guttman Scalogram and Guttman Coefficient of Reproducibility.

 

Winsteps reports: "No non-extreme persons/items"

 

Guttman pattern: 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.

 

Deterministic (Guttman) data contain only information about the ordering of the persons and items. Guttman data do not contain information about the relative spacing between the items or the persons. We need randomness in the data. Then the closer together the items the more disorder (Guttman reversals) there are in the data. To analyze these data with Rasch, we need to introduce some pseudo-randomness into the data. When reporting, omit dummy persons/items using IDELETE= or PDELETE= from the Specification menu,

 

Here is a Guttman deterministic pattern with dichotomous data:

 

Easy->Hard items (columns)

111111 Most able person (rows)

111110

110000

110000

100000

000000 Least able person

 

1) It is sometimes useful to make this type of data estimable by adding a dummy reversed-Guttman item and person.

 

Easy->Hard items (columns)

1111110 Most able person (rows)

1111000 

1100000

1000000

0000000 Least able person

0000001 < Dummy person record

       ^ Dummy item record

 

or 2) 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

6 0 ; anchor the last (lowest score) person at 0 logits

*

&END

END LABELS

111111 Most able person (rows)

111110 

111100

110000

100000

000000 Least able person

 

or 3) by adding two dummy data records: 0101... and 1010...

 

Easy->Hard items (columns)

111111 Most able person (rows)

111110 

110000

100000

000000 Least able person

101010 Dummy person

010101 Dummy person

 

 

 

Guttman split: a more subtle Guttman effect splits the data into high and low subsets:

 

Easy->Hard items (columns)

1111101 Most able person (rows)

1111010 

1110110

------- Guttman split

0110000

1100000

1000000 Least able person

 

There is no item for which there is success in the lower half, but failure in the upper half of this dataset. The remedies are the same as above.