This function estimates the DETECT index (Stout, Habing, Douglas & Kim, 1996; Zhang & Stout, 1999a, 1999b) in an exploratory way. Conditional covariances of itempairs are transformed into a distance matrix such that items are clustered by the hierarchical Ward algorithm (Roussos, Stout & Marden, 1998). Note that the function will not provide the same output as the original DETECT software.
expl.detect(data, score, nclusters, N.est=NULL, seed=NULL, bwscale=1.1,
smooth=TRUE, use_sum_score=FALSE, hclust_method="ward.D", estsample=NULL)A list with following entries
Unweighted DETECT statistics
Weighted DETECT statistics. Weighting is done proportionally to sample sizes of item pairs.
Fit of the cluster method
Cluster allocations
use_sum_score
An \(N \times I\) data frame of dichotomous or polytomous responses. Missing responses are allowed.
An ability estimate, e.g. the WLE, sum score or mean score
Maximum number of clusters used in the exploratory analysis
Number of students in a (possible) validation of the DETECT index.
N.est students are drawn at random from data.
Random seed
Bandwidth scale factor
Logical indicating whether smoothing should be applied for conditional covariance estimation
Logical indicating whether sum score should be used. With this option, the bias corrected conditional covariance of Zhang and Stout (1999) is used.
Clustering method used as the argument
method in stats::hclust.
Optional vector of subject indices that defines the estimation sample
Roussos, L. A., Stout, W. F., & Marden, J. I. (1998). Using new proximity measures with hierarchical cluster analysis to detect multidimensionality. Journal of Educational Measurement, 35, 1-30.
Stout, W., Habing, B., Douglas, J., & Kim, H. R. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20, 331-354.
Zhang, J., & Stout, W. (1999a). Conditional covariance structure of generalized compensatory multidimensional items, Psychometrika, 64, 129-152.
Zhang, J., & Stout, W. (1999b). The theoretical DETECT index of dimensionality and its application to approximate simple structure, Psychometrika, 64, 213-249.
For examples see conf.detect.