The purpose of this investigation was to study the
nature of the item and ability estimates obtained when
the modified three-parameter logistic model is used
with two-dimensional data. To examine the effects of
two-dimensional data on unidimensional parameter estimates,
the relative potency of the two dimensions
was systematically varied by changing the correlations
between the two ability dimensions. Data sets based
on correlations of .0, .3, .6, .9, and .95 were generated
for each of four combinations of sample size and
test length. Also, for each of these four combinations,
five unidimensional data sets were simulated for comparison
purposes. Relative to the nature of the unidimensional
estimates, it was found that the [circumflex a] value
seemed best considered as the average of the true a
values. The [circumflex b] value seemed best thought of as an
overestimate of the true b[subscript 1] values. The [circumflex theta] value seemed
best considered as the average of the true ability parameters.
Although there was a consistent trend for
these relationships to strengthen as the ability dimensions
became more highly correlated, there was always a
substantial disparity between the magnitudes of
these values and of those derived from the unidimensional
data. Sample size and test length had very little
effect on these relationships.
Ansley, Timothy N & Forsyth, Robert A. (1985). An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data. Applied Psychological Measurement, 9, 37-48. doi:10.1177/014662168500900104
Ansley, Timothy N.; Forsyth, Robert A..
An examination of the characteristics of unidimensional IRT parameter estimates derived from two-dimensional data.
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