Estimating multiple-strategy cognitive diagnosis models

An (experimental) function for calibrating the multiple-strategy CDMs for dichotomous response data (Ma & Guo, 2019)

GMSCDM(
  dat,
  msQ,
  model = "ACDM",
  s = 1,
  att.prior = NULL,
  delta = NULL,
  control = list()
)

Arguments

dat

A required binary item response matrix

msQ

A multiple-strategy Q-matrix; the first column gives item numbers and the second column gives the strategy number. See examples.

model

CDM used; can be "DINA","DINO","ACDM","LLM", and "RRUM", representing the GMS-DINA, GMS-DINO, GMS-ACDM, GMS-LLM and GMS-RRUM in Ma & Guo (2019), respectively. It can also be "rDINA" and "rDINO", representing restricted GMS-DINA and GMS-DINO models where delta_jm1 are equal for all strategies. Note that only a single model can be used for the whole test.

s

strategy selection parameter. It is equal to 1 by default.

att.prior

mixing proportion parameters.

delta

delta parameters in list format.

control

a list of control arguments

Value

an object of class GMSCDM with the following components:

IRF

A matrix of success probabilities for each latent class on each item (IRF)

delta

A list of delta parameters

attribute

A list of estimated attribute profiles including EAP, MLE and MAP estimates.

testfit

A list of test fit statistics including deviance, number of parameters, AIC and BIC

sIRF

strategy-specific item response function

pjmc

Probability of adopting each strategy on each item for each latent class

sprv

Strategy pravelence

References

Ma, W., & de la Torre, J. (2020). GDINA: An R Package for Cognitive Diagnosis Modeling. Journal of Statistical Software, 93(14), 1-26.

Ma, W., & Guo, W. (2019). Cognitive Diagnosis Models for Multiple Strategies. British Journal of Mathematical and Statistical Psychology.

See also

GDINA for MS-DINA model and single strategy CDMs, and DTM for diagnostic tree model for multiple strategies in polytomous response data

Author

Wenchao Ma, The University of Alabama, wenchao.ma@ua.edu

Examples

if (FALSE) {
##################
#
# data simulation
#
##################
set.seed(123)
msQ <- matrix(
c(1,1,0,1,
1,2,1,0,
2,1,1,0,
3,1,0,1,
4,1,1,1,
5,1,1,1),6,4,byrow = T)
# J x L - 00,10,01,11
LC.prob <- matrix(c(
0.2,0.7727,0.5889,0.8125,
0.1,0.9,0.1,0.9,
0.1,0.1,0.8,0.8,
0.2,0.5,0.4,0.7,
0.2,0.4,0.7,0.9),5,4,byrow=TRUE)
N <- 10000
att <- sample(1:4,N,replace=TRUE)
dat <- 1*(t(LC.prob[,att])>matrix(runif(N*5),N,5))


est <- GMSCDM(dat,msQ)
# item response function
est$IRF
# strategy specific IRF
est$sIRF


################################
#
# Example 14 from GDINA function
#
################################
Q <- matrix(c(1,1,1,1,0,
1,2,0,1,1,
2,1,1,0,0,
3,1,0,1,0,
4,1,0,0,1,
5,1,1,0,0,
5,2,0,0,1),ncol = 5,byrow = TRUE)
d <- list(
  item1=c(0.2,0.7),
  item2=c(0.1,0.6),
  item3=c(0.2,0.6),
  item4=c(0.2,0.7),
  item5=c(0.1,0.8))

  set.seed(123)
sim <- simGDINA(N=1000,Q = Q, delta.parm = d,
               model = c("MSDINA","MSDINA","DINA",
                         "DINA","DINA","MSDINA","MSDINA"))

# simulated data
dat <- extract(sim,what = "dat")
# estimation
# MSDINA need to be specified for each strategy
est <- GDINA(dat,Q,model = c("MSDINA","MSDINA","DINA",
                             "DINA","DINA","MSDINA","MSDINA"),
             control = list(conv.type = "neg2LL",conv.crit = .01))

# Approximate the MS-DINA model using GMS DINA model
est2 <- GMSCDM(dat, Q, model = "rDINA", s = 10,
               control = list(conv.type = "neg2LL",conv.crit = .01))
}