NPC: Estimation of examinees' attribute profiles using the NPC...

In NPCDTools: The Nonparametric Classification Methods for Cognitive Diagnosis

Estimation of examinees' attribute profiles using the NPC method

Description

The function estimates examinees' attribute profiles using the nonparametric classification (NPC) method (Chiu & Douglas, 2013). An examinee's attribute profile is estimated by minimizing the distance between the observed and ideal item responses.

Usage

NPC(
  Y,
  Q,
  distance = c("hamming", "whamming", "penalized"),
  gate = c("AND", "OR"),
  wg = 1,
  ws = 1
)

Arguments

Y	A N \times J binary data matrix consisting of the responses from N examinees to J items.
Q	A J \times K binary Q-matrix where the entry q_{jk} describes whether the kth attribute is required by the jth item.
distance	The type of distance used to compute the loss function. The possible options include (i) "hamming" representing the plain Hamming distance method, (ii) "whamming" representing the Hamming distance weighted by the inverse of item variance, and (iii) "penalized" representing the Hamming distance weighted by the inverse of item variance and specified penalizing weights for guess and slip.
gate	A character string specifying the type of gate. The possible options include "AND" and "OR" standing for conjunctive and disjunctive gate, respectively.
wg	Additional argument for the "penalized" method. It is a weight assigned to guesses in the DINA or DINO models. A large value of weight results in a stronger impact on the distance (i.e., larger loss function values) caused by guessing.
ws	Additional input for the "penalized" method. It is the weight assigned to slips in the DINA or DINO models. A large value of weight results in a stronger impact on the distance (i.e., larger loss function values) caused by slipping.

Value

The function returns a series of outputs, including:

att.est

A N \times K matrix representing the estimated attribute profiles. 1 = examinee masters the attribute, 0 = examinee does not master the attribute.

est.ideal

A N \times J matrix indicating the estimated ideal response to all items from all examinees. 1 = correct, 0 = incorrect.

est.class

A N-dimensional vector showing the class memberships for all examinees.

n.tie

The number of ties in the Hamming distance among the candidate attribute profiles for each person. When ties occur, one of the tied attribute profiles is randomly chosen.

pattern

All possible attribute profiles in the latent space.

loss.matrix

A 2^K \times N matrix containing the values of the loss function (the distances) between each examinee's observed response vector and the 2^K ideal response vectors.

Details

The nonparametric classification (NPC) method (Chiu & Douglas, 2013) assigns examinees to the proficiency classes they belong to by comparing their observed item response patterns with each of the ideal item response patterns of the 2^K proficiency classes. When there is no data perturbation, an examinee's ideal response pattern corresponding to the examinee's true attribute pattern and his/her observed item response patterns are identical, and thus the distance between them is 0. When data perturbations are small, this ideal response pattern remains the one most similar to the observed response pattern, which is exactly the setup of data conforming to the DINA or DINO model. Hence, based on this rationale, an examinee's attribute profile is obtained by minimizing the distance between the observed and the ideal item response patterns. The nonparametric nature of the NPC method furthermore makes it suitable for data obtained from small-scale settings.

References

Chiu, C. Y., & Douglas, J. A. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30(2), 225-250. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s00357-013-9132-9")}

See Also

GNPC

Examples

## Not run: 
library(GDINA)
N <- 500
Q <- sim30GDINA$simQ
gs <- data.frame(guess = rep(0.2, nrow(Q)), slip = rep(0.2, nrow(Q)))
sim <- simGDINA(N, Q, gs.parm = gs, model = "DINA")
Y <- extract(sim, what = "dat")
alpha <- extract(sim, what = "attribute")

# Estimate attribute profiles using NPC
result <- NPC(Y, Q, distance = "hamming", gate = "AND")
print(result)
result$att.est

# Check attributed agreement rate
PAR(alpha, result$att.est)
AAR(alpha, result$att.est)

## End(Not run)

NPCDTools documentation built on Sept. 1, 2026, 1:08 a.m.