This study compared four methods of determining
the dimensionality of a set of test items: linear factor
analysis, nonlinear factor analysis, residual analysis,
and a method developed by Bejar (1980). Five artificial
test datasets (for 40 items and 1,500 examinees)
were generated to be consistent with the three-parameter
logistic model and the assumption of either a one- or
a two-dimensional latent space. Two variables were
manipulated: (1) the correlation between the traits
(r = .10 or r = .60) and (2) the percent of test items
measuring each trait (50% measuring each trait, or
75% measuring the first trait and 25% measuring the
While linear factor analysis in all instances overestimated
the number of underlying dimensions in the
data, nonlinear factor analysis with linear and quadratic
terms led to correct determination of the item dimensionality
in the three datasets where it was used.
Both the residual analysis method and Bejar’s method
proved disappointing. These results suggest the need
for extreme caution in using linear factor analysis, residual
analysis, and Bejar’s method until more investigations
of these methods can confirm their adequacy.
Nonlinear factor analysis appears to be the most promising
of the four methods, but more experience in applying
the method seems necessary before wide-scale
use can be recommended.
Hambleton, Ronald K & Rovinelli, Richard J. (1986). Assessing the dimensionality of a set of test items. Applied Psychological Measurement, 10, 287-302. doi:10.1177/014662168601000307
Hambleton, Ronald K.; Rovinelli, Richard J..
Assessing the dimensionality of a set of test items.
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