Q-matrix validation for the (sequential) G-DINA model based on PVAF (de la Torre & Chiu, 2016; Najera, Sorrel, & Abad, 2019), stepwise Wald test (Ma & de la Torre, 2019) 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 or predicted cutoffs. You should always check the mesa plots for further examination.

Qval(GDINA.obj, method = "PVAF", eps = 0.95, digits = 4,
wald.args = list())

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

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

## Arguments

GDINA.obj An estimated model object of class GDINA which Q-matrix validation method is used? Can be either "PVAF" or "wald". 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, P., Sorrel, M., and Abad, P. (2019). How many decimal places in each number? The default is 4. a list of arguments for the stepwise Wald test method. SE.typeType of covariance matrix for the Wald test alpha.levelalpha level for the wald test GDIIt 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. verbosePrint detailed information or not? stepwiseTRUE for stepwise approach and FALSE for forward approach Qval objects for S3 methods 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: extract various elements from Qval objects

• summary: print summary information

## 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. (2019). An Empirical Q-Matrix Validation Method for the Sequential G-DINA Model. British Journal of Mathematical and Statistical Psychology

Najera, P., Sorrel, M., & Abad, P. (2019). Reconsidering Cutoff Points in the General Method of Empirical Q-Matrix Validation. Educational and Psychological Measurement.

GDINA

## Examples

if (FALSE) {
################################
#
# 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")
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")
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
################################
#
# Ordinal response
#
################################
seq.est <- GDINA(sim20seqGDINA$simdat,sim20seqGDINA$simQ,sequential = TRUE)
stepwise <- Qval(seq.est, method = "wald", eps = -1)
}