conf.detect: Confirmatory DETECT and polyDETECT Analysis

Description

This function computes the DETECT statistics for dichotomous item responses and the polyDETECT statistic for polytomous item responses under a confirmatory specification of item clusters (Stout, Habing, Douglas & Kim, 1996; Zhang & Stout, 1999a, 1999b; Zhang, 2007; Bonifay, Reise, Scheines, & Meijer, 2015).

Item responses in a multi-matrix design are allowed (Zhang, 2013).

An exploratory DETECT analysis can be conducted using the expl.detect function.

Usage

conf.detect(data, score, itemcluster, bwscale=1.1, progress=TRUE,
        thetagrid=seq(-3, 3, len=200), smooth=TRUE, use_sum_score=FALSE, bias_corr=TRUE)
# S3 method for conf.detect
summary(object, digits=3, file=NULL, ...)

Value

A list with following entries:

detect: Data frame with statistics DETECT, ASSI, RATIO, MADCOV100 and MCOV100
ccovtable: Individual contributions to conditional covariance
ccov.matrix: Evaluated conditional covariance

Arguments

data: An \(N \times I\) data frame of dichotomous or polytomous responses. Missing responses are allowed.
score: An ability estimate, e.g. the WLE, sum score or mean score
itemcluster: Item cluster for each item. The order of entries must correspond to the columns in data.
bwscale: Bandwidth factor for calculation of conditional covariance (see ccov.np)
progress: Display progress?
smooth: Logical indicating whether smoothing should be applied for conditional covariance estimation
thetagrid: A vector which contains theta values where conditional covariances are evaluated.
use_sum_score: Logical indicating whether sum score should be used. With this option, the bias corrected conditional covariance of Zhang and Stout (1999) is used.
bias_corr: Logical indicating whether bias correction (Zhang & Stout, 1999) should be utilized if use_sum_score=TRUE.
object: Object of class conf.detect
digits: Number of digits for rounding in summary
file: Optional file name to be sunk for summary
...: Further arguments to be passed

Details

The result of DETECT are the indices DETECT, ASSI and RATIO (see Zhang 2007 for details) calculated for the options unweighted and weighted. The option unweighted means that all conditional covariances of item pairs are equally weighted, weighted means that these covariances are weighted by the sample size of item pairs. In case of multi matrix item designs, both types of indices can differ.

The classification scheme of these indices are as follows (Jang & Roussos, 2007; Zhang, 2007):

Strong multidimensionality	DETECT > 1.00
Moderate multidimensionality	.40 < DETECT < 1.00
Weak multidimensionality	.20 < DETECT < .40
Essential unidimensionality	DETECT < .20

Maximum value under simple structure	ASSI=1	RATIO=1
Essential deviation from unidimensionality	ASSI > .25	RATIO > .36
Essential unidimensionality	ASSI < .25	RATIO < .36

Note that the expected value of a conditional covariance for an item pair is negative when a unidimensional model holds. In consequence, the DETECT index can become negative for unidimensional data (see Example 3). This can be also seen in the statistic MCOV100 in the value detect.

References

Bonifay, W. E., Reise, S. P., Scheines, R., & Meijer, R. R. (2015). When are multidimensional data unidimensional enough for structural equation modeling? An evaluation of the DETECT multidimensionality index. Structural Equation Modeling, 22(4), 504-516. tools:::Rd_expr_doi("10.1080/10705511.2014.938596")

Jang, E. E., & Roussos, L. (2007). An investigation into the dimensionality of TOEFL using conditional covariance-based nonparametric approach. Journal of Educational Measurement, 44(1), 1-21. tools:::Rd_expr_doi("10.1111/j.1745-3984.2007.00024.x")

Stout, W., Habing, B., Douglas, J., & Kim, H. R. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20(4), 331-354. tools:::Rd_expr_doi("10.1177/014662169602000403")

Zhang, J. (2007). Conditional covariance theory and DETECT for polytomous items. Psychometrika, 72(1), 69-91. tools:::Rd_expr_doi("10.1007/s11336-004-1257-7")

Zhang, J. (2013). A procedure for dimensionality analyses of response data from various test designs. Psychometrika, 78(1), 37-58. tools:::Rd_expr_doi("10.1007/s11336-012-9287-z")

Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items. Psychometrika, 64(2), 129-152. tools:::Rd_expr_doi("10.1007/BF02294532")