cdi: Item, attribute, and test-level discrimination indices

In measr: Bayesian Psychometric Measurement Using 'Stan'

Item, attribute, and test-level discrimination indices

Description

The cognitive diagnostic index (CDI) is a measure of how well an assessment is able to distinguish between attribute profiles. The index was originally proposed by Henson & Douglas (2005) for item- and test-level discrimination, and then expanded by Henson et al. (2008) to include attribute-level discrimination indices.

Usage

cdi(model, weight_prevalence = TRUE)

Arguments

model	The estimated model to be evaluated.
weight_prevalence	Logical indicating whether the discrimination indices should be weighted by the prevalence of the attribute profiles. See details for additional information.

Details

Henson et al. (2008) described two attribute-level discrimination indices, \mathbf{d}_{(A)\mathbf{\cdot}} (Equation 8) and \mathbf{d}_{(B)\mathbf{\cdot}} (Equation 13), which are similar in that both are the sum of item-level discrimination indices. In both cases, item-level discrimination indices are calculated as the average of Kullback-Leibler information for all pairs of attributes profiles for the item. The item-level indices are then summed to achieve the test-level discrimination index for each attribute, or the test overall. However, whereas \mathbf{d}_{(A)\mathbf{\cdot}} is an unweighted average of the Kullback-Leibler information, \mathbf{d}_{(B)\mathbf{\cdot}} is a weighted average, where the weight is defined by the prevalence of each profile (i.e., measr_extract(model, what = "strc_param")).

Value

A list with two elements:

• item_discrimination: A tibble with one row per item containing the CDI for the item and any relevant attributes.

• test_discrimination: A tibble with one row containing the total CDI for the assessment and for each attribute.

References

Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29(4), 262-277. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0146621604272623")}

Henson, R., Roussos, L., Douglas, J., & Xuming, H. (2008). Cognitive diagnostic attribute-level discrimination indices. Applied Psychological Measurement, 32(4), 275-288. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0146621607302478")}

Examples

rstn_ecpe_lcdm <- dcm_estimate(
  dcm_specify(dcmdata::ecpe_qmatrix, identifier = "item_id"),
  data = dcmdata::ecpe_data,
  missing = NA,
  identifier = "resp_id",
  method = "optim",
  seed = 63277,
  backend = "rstan"
)

cdi(rstn_ecpe_lcdm)

measr documentation built on Jan. 14, 2026, 5:08 p.m.