GNPC: Estimation of examinees' attribute profiles using the GNPC...
| GNPC | R Documentation |
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 |
Q |
A |
initial.dis |
The type of distance used in the |
initial.gate |
The type of relation between examinees' attribute profiles
and the items.
Allowable relations are |
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)}
