🚀 go-pugleaf

Tony Downing asks about polychoric correlation...

The polychoric correlation for the dichotomous item score case is a tetrachoric
correlation.  In effect, it is an estimate of what the correlation would be
assuming that the two dichotomously scored items really reflect latent
variables which have a continuous (and normal) distribution of values.  The
tetrachoric is the correlation of the two continuous latent variables.

For a Psychological Context...
On an achievement test, an item may be scored correct or incorrect.  In this
instance, it may be reasonable to assume that responses to items do reflect
some underlying continuous attribute.  Persons of differing level on the
attribute may both answer the item correctly (or incorrectly).  Though the
response is dichotomous, the attribute is likely continuous.  Factoring
of the dichotomously scored items can sometimes give rise to secondary factors
which may be artifacts of the range of item difficulties included in the test.
Some have suggested that conversion of the raw phi (pearson) inter-item
correlations to tetrachoric correlations can eliminate such artifacts.

The PRELIS manual (for the Preprocessor for LISREL) by Scientific Software
discusses the Polychoric (and Polyserial) correlation and provides some
references re: the topic.  Some psychometric texts discuss the tetrachoric
correlation (Nunnally, 1978, _Psychometric Theory_, McGraw-Hill; Hulin, Drasgow
& Parsons, 1983, _Item Response Theory_, Irwin; Allen & Yen, 1979,
_Introduction to Measurement Theory_, Brooks/Cole; ** see in particular Lord &
Novick, 1968, _Statistical Theories of Mental Test Scores_, Addison-Wesley for
the more complete presentation among those I listed **).

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|                                                                       |
|  Gary Lautenschlager                                                  |
|  Psychology                                                           |
|  University of Georgia                                                |
|  Athens, GA    30602-3013   USA                                       |
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