get.priority: Priority of Attribute

In Qval: The Q-Matrix Validation Methods Framework

Priority of Attribute

Description

This function will provide the priorities of attributes for all items.

Usage

get.priority(Y = NULL, Q = NULL, CDM.obj = NULL, model = "GDINA")

Arguments

Y	A required N × I matrix or data.frame consisting of the responses of N individuals to N × I items. Missing values need to be coded as NA.
Q	A required binary I × K matrix containing the attributes not required or required master the items. The ith row of the matrix is a binary indicator vector indicating which attributes are not required (coded by 0) and which attributes are required (coded by 1) to master item i.
CDM.obj	An object of class CDM.obj. When it is not NULL, it enables rapid validation of the Q-matrix without the need for parameter estimation. @seealso CDM.
model	Type of model to fit; can be "GDINA", "LCDM", "DINA", "DINO" , "ACDM", "LLM", or "rRUM". Default = "GDINA". @seealso CDM.

Details

The calculation of priorities is straightforward (Qin & Guo, 2025): the priority of an attribute is the regression coefficient obtained from a LASSO multinomial logistic regression, with the attribute as the independent variable and the response data from the examinees as the dependent variable. The formula (Tu et al., 2022) is as follows:

\log[\frac{P(X_{pi} = 1 | \boldsymbol{\Lambda}_{p})}{P(X_{pi} = 0 | \boldsymbol{\Lambda}_{p})}] = logit[P(X_{pi} = 1 | \boldsymbol{\Lambda}_{p})] = \beta_{i0} + \beta_{i1} \Lambda_{p1} + \ldots + \beta_{ik} \Lambda_{pk} + \ldots + \beta_{iK} \Lambda_{pK}

Where X_{pi} represents the response of examinee p on item i, \boldsymbol{\Lambda}_{p} denotes the marginal mastery probabilities of examinee p (which can be obtained from the return value alpha.P of the CDM function), \beta_{i0} is the intercept term, and \beta_{ik} represents the regression coefficient.

The LASSO loss function can be expressed as:

l_{lasso}(\boldsymbol{X}_i | \boldsymbol{\Lambda}) = l(\boldsymbol{X}_i | \boldsymbol{\Lambda}) - \lambda |\boldsymbol{\beta}_i|

Where l_{lasso}(\boldsymbol{X}_i | \boldsymbol{\Lambda}) is the penalized likelihood, l(\boldsymbol{X}_i | \boldsymbol{\Lambda}) is the original likelihood, and \lambda is the tuning parameter for penalization (a larger value imposes a stronger penalty on \boldsymbol{\beta}_i = [\beta_{i1}, \ldots, \beta_{ik}, \ldots, \beta_{iK}]). The priority for attribute i is defined as: \boldsymbol{priority}_i = \boldsymbol{\beta}_i = [\beta_{i1}, \ldots, \beta_{ik}, \ldots, \beta_{iK}]

Value

A matrix containing all attribute priorities.

References

Qin, H., & Guo, L. (2025). Priority attribute algorithm for Q-matrix validation: A didactic. Behavior Research Methods, 57(1), 31. DOI: 10.3758/s13428-024-02547-5.

Tu, D., Chiu, J., Ma, W., Wang, D., Cai, Y., & Ouyang, X. (2022). A multiple logistic regression-based (MLR-B) Q-matrix validation method for cognitive diagnosis models: A confirmatory approach. Behavior Research Methods. DOI: 10.3758/s13428-022-01880-x.

Examples

set.seed(123)
library(Qval)

## generate Q-matrix and data
K <- 5
I <- 20
IQ <- list(
  P0 = runif(I, 0.1, 0.3),
  P1 = runif(I, 0.7, 0.9)
)


Q <- sim.Q(K, I)
data <- sim.data(Q = Q, N = 500, IQ = IQ, model = "GDINA", distribute = "horder")
MQ <- sim.MQ(Q, 0.1)

CDM.obj <- CDM(data$dat, MQ)

priority <- get.priority(data$dat, Q, CDM.obj)
head(priority)

Qval documentation built on April 3, 2025, 6:20 p.m.