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

In NPCDTools: The Nonparametric Classification Methods for Cognitive Diagnosis

Estimation of examinees' attribute profiles using the GNPC method

Description

Function GNPC is used to estimate examinees' attribute profiles using the general nonparametric classification (GNPC) method (Chiu, Sun, & Bian, 2018; Chiu & Koehn, 2019). It can be used with data conforming to any CDMs.

Usage

GNPC(
  Y,
  Q,
  initial.dis = c("hamming", "whamming"),
  initial.gate = c("AND", "OR", "Mix")
)

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} describing whether the kth attribute is required by the jth item.
initial.dis	The type of distance used in the AlphaNP to carry out the initial attribute profiles for the GNPC method. Allowable options are "hamming" and "whamming" representing the Hamming and the weighted Hamming distances, respectively.
initial.gate	The type of relation between examinees' attribute profiles and the items. Allowable relations are "AND", "OR", and "Mix", representing the conjunctive, disjunctive, and mixed relations, respectively

Value

The function returns a series of outputs, including

att.est

The estimates of examinees' attribute profiles

class

The estimates of examinees' class memberships

weighted.ideal

The weighted ideal responses

weight

The weights used to compute the weighted ideal responses

GNPC algorithm

A weighted ideal response \eta^{(w)}, defined as the convex combination of \eta^(c) and \eta^(d), is proposed. Suppose item j requires K_{j}^* \leq {K} attributes that, without loss of generality, have been permuted to the first K_{j}^* positions of the item attribute vector \boldsymbol{q_j}. For each item j and \mathcal{C}_{l}, the weighted ideal response \eta_{ij}^{(w)} is defined as the convex combination \eta_{ij}^{(w)} = w _{lj} \eta_{lj}^{(c)}+(1-w_{lj})\eta_{lj}^{(d)} where 0\leq w_{lj}\leq 1. The distance between the observed responses to item j and the weighted ideal responses w_{lj}^{(w)} of examinees in \mathcal{C}_{l} is defined as the sum of squared deviations: d_{lj} = \sum_{i \in \mathcal {C}_{l}} (y_{ij} - \eta_{lj}^{(w)})^2=\sum_{i \in \mathcal {C}_{l}}(y_{ij}-w_{lj}\eta_{lj}^{(c)}-(1-w_{lj})\eta_{lj}^{(d)}) Thus, \widehat{w_{lj}} can be minimizing d_{lj}: \widehat{w_{lj}}=\frac{\sum_{i \in \mathcal {C}_{l}}(y_{ij}-\eta_{lj}^{(d)})}{\left \| \mathcal{C}_{l} \right \|(\eta_{lj}^{(c)}-\eta_{lj}^{(d)})}

As a viable alternative to \boldsymbol{\eta^{(c)}} for obtaining initial estimates of the proficiency classes, Chiu et al. (2018) suggested to use an ideal response with fixed weights defined as \eta_{lj}^{(fw)}=\frac{\sum_{k=1}^{K}\alpha_{k}q_{jk}}{K}\eta_{lj}^{(c)}+(1-\frac{\sum_{k=1}^{K}\alpha_{k}q_{jk}}{K})\eta_{lj}^{(d)}

NPCDTools documentation built on Sept. 23, 2024, 5:10 p.m.