A Comparison of Bias Correction Adjustments for the DETECT Procedure
Applied Psychological Measurement Volume 35, Number 2, ISSN 0146-6216
DETECT is a nonparametric methodology to identify the dimensional structure underlying test data. The associated DETECT index, "D[subscript max]," denotes the degree of multidimensionality in data. Conditional covariances (CCOV) are the building blocks of this index. In specifying population CCOVs, the latent test composite [theta][subscript TT] is used as the conditional variable. In estimating the CCOVs, the "total test score" of all items in the test ("T") or the rest score of remaining items ("S") are generally used as estimates of the latent composite [theta][subscript TT]. However, estimated CCOVs are biased when using "T" or "S" as a proxy for [theta][subscript TT]. Some type of correction is needed to adjust this bias. This study was an investigation of different ways to estimate the DETECT index based on the conditional scores "T" and "S", and additional bias adjustments, resulting in six different estimates, "D"[subscript 1] through "D"[subscript 6]. These six indices were investigated in simulated settings, varying the test length, sample size, and the degree of multidimensionality (108 in all). The results showed that indices "D"[subscript 1], "D"[subscript 2], and "D"[subscript 5] are not acceptable as they displayed highly inflated "D"[subscript max] values. No statistically significant differences were found between indices "D"[subscript 3] and "D"[subscript 6]. Overall comparison of indices "D"[subscript 3] with "D"[subscript 4] showed that even though they differed significantly in "D"[subscript max] values, there was no practically meaningful difference between the performance of these two indices. For these reasons, it is recommended that the current index "D"[subscript 3] be retained even though index "D"[subscript 4] displayed slightly better results in the current study. (Contains 10 tables and 2 figures.)
Nandakumar, R., Yu, F. & Zhang, Y. (2011). A Comparison of Bias Correction Adjustments for the DETECT Procedure. Applied Psychological Measurement, 35(2), 127-144.