Qval {GDINA}

Q-matrix validation

Description

Q-matrix validation for the (sequential) G-DINA model based on PVAF (de la Torre & Chiu, 2016; Najera, Sorrel, & Abad, 2019; Najera et al., 2020), stepwise Wald test (Ma & de la Torre, 2020) or mesa plot (de la Torre & Ma, 2016). All these methods are suitable for dichotomous and ordinal response data. If too many modifications are suggested based on the default PVAF method, you are suggested to try the stepwise Wald test method, iterative procedures or predicted cutoffs. You should always check the mesa plots for further examination.

Usage

Qval(
  GDINA.obj,
  method = "PVAF",
  iter = "none",
  eps = 0.95,
  digits = 4,
  wald.args = list(),
  iter.args = list(empty.att = FALSE, max.iter = 150, verbose = FALSE)
)

## S3 method for class 'Qval'
extract(object, what = c("sug.Q", "varsigma", "PVAF", "eps", "Q"), ...)

## S3 method for class 'Qval'
summary(object, ...)

Arguments

GDINA.obj

an estimated model object of class GDINA

method

which Q-matrix validation method is used? Can be either "PVAF" or "wald".

iter

implement the method iteratively? Can be "none" for non-iterative validation (by default), "test", "test.att", or "item" (Najera et al., 2020).

eps

cutoff value for PVAF from 0 to 1. Default = 0.95. Note that it can also be -1, indicating the predicted cutoff based on Najera, Sorrel, and Abad (2019).

digits

how many decimal places in each number? The default is 4.

wald.args

a list of arguments for the stepwise Wald test method.

SE.type

type of covariance matrix for the Wald test

alpha.level

alpha level for the wald test

GDI

it can be 0, 1 or 2; 0 means GDI is not used to choose the attribute - when more than one attributes are significant, the one with the largest p-value will be selected; GDI=1 means the attribute with the largest GDI will be selected; GDI=2 means the q-vector with the largest GDI will be selected.

verbose

print detailed information or not?

stepwise

TRUE for stepwise approach and FALSE for forward approach

iter.args

a list of arguments for the iterative implementation.

empty.att

can a Q-matrix with an empty attribute (i.e., measured by no items) be provided? Default is FALSE

max.iter

maximum number of iterations. Default is 150

verbose

print information after each iteration? Default is FALSE

object

Qval objects for S3 methods

what

argument for S3 method extract indicating what to extract; It can be "sug.Q" for suggested Q-matrix, "Q" for original Q-matrix, "varsigma" for varsigma index, and "PVAF" for PVAF.

...

additional arguments

Value

An object of class Qval. Elements that can be extracted using extract method include:

sug.Q

suggested Q-matrix

Q

original Q-matrix

varsigma

varsigma index

PVAF

PVAF

Methods (by generic)

• extract(Qval): extract various elements from Qval objects

• summary(Qval): print summary information

Author(s)

Wenchao Ma, The University of Alabama, [e-mail],
Miguel A. Sorrel, Universidad Autónoma de Madrid,
Jimmy de la Torre, The University of Hong Kong

References

de la Torre, J. & Chiu, C-Y. (2016). A General Method of Empirical Q-matrix Validation. Psychometrika, 81, 253-273.

de la Torre, J., & Ma, W. (2016, August). Cognitive diagnosis modeling: A general framework approach and its implementation in R. A Short Course at the Fourth Conference on Statistical Methods in Psychometrics, Columbia University, New York.

Ma, W., & de la Torre, J. (2020). An empirical Q-matrix validation method for the sequential G-DINA model. British Journal of Mathematical and Statistical Psychology, 73, 142-163.

Najera, P., Sorrel, M. A., & Abad, F.J. (2019). Reconsidering cutoff points in the general method of empirical Q-matrix validation. Educational and Psychological Measurement, 79, 727-753.

Najera, P., Sorrel, M. A., de la Torre, J., & Abad, F. J. (2020). Improving robustness in Q-matrix validation using an iterative and dynamic procedure. Applied Psychological Measurement.

See Also

GDINA

Examples

## Not run: 
################################
#
# Binary response
#
################################
dat <- sim10GDINA$simdat
Q <- sim10GDINA$simQ
Q[10,] <- c(0,1,0)

# Fit the G-DINA model
mod1 <- GDINA(dat = dat, Q = Q, model = "GDINA")

# Q-validation using de la Torre and Chiu's method
pvaf <- Qval(mod1,method = "PVAF",eps = 0.95)
pvaf
extract(pvaf,what = "PVAF")
#See also:
extract(pvaf,what = "varsigma")
extract(pvaf,what = "sug.Q")

# Draw mesa plots using the function plot

plot(pvaf,item=10)

#The stepwise Wald test
stepwise <- Qval(mod1,method = "wald")
stepwise
extract(stepwise,what = "PVAF")
#See also:
extract(stepwise,what = "varsigma")
extract(stepwise,what = "sug.Q")

#Set eps = -1 to determine the cutoff empirically
pvaf2 <- Qval(mod1,method = "PVAF",eps = -1)
pvaf2

#Iterative procedure (test-attribute level)
pvaf3 <- Qval(mod1, method = "PVAF", eps = -1,
              iter = "test.att", iter.args = list(verbose = 1))
pvaf3

################################
#
# Ordinal response
#
################################
seq.est <- GDINA(sim20seqGDINA$simdat,sim20seqGDINA$simQ, sequential = TRUE)
stepwise <- Qval(seq.est, method = "wald")

## End(Not run)