Guttman patterns and Guttman splits

See also Guttman Scalogram and Guttman Coefficient of Reproducibility.

 

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. Here is a Guttman pattern with dichotomous data:

 

Easy->Hard items (columns)

1111111 Most able person (rows)

1111110 

1111100

1111100

1100000

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

11111000

11000000

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

*

&END

END LABELS

1111111 Most able person (rows)

1111110 

1111100

1111100

1100000

1100000

1000000

0000000 Least able 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

 

Notice that there is no item for which there is success in the lower half, but failure in the upper half of this dataset.


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Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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