Diagnostic multiple-strategy CDMs

This function estimates the diagnostic tree model (Ma, 2018) for polytomous responses with multiple strategies. It can also handle various polytomous models discussed in Gao, et al. (2021).

DTM(
  dat,
  Qc,
  type = "tree",
  linkfunc = "logit",
  eq.const = FALSE,
  delta = NULL,
  Tmatrix = NULL,
  conv.crit = 0.001,
  conv.type = "pr",
  maxitr = 1000
)

Arguments

dat

A required \(N \times J\) data matrix of N examinees to J items. Missing values are currently not allowed.

Qc

A required \(J \times K+2\) category and attribute association matrix, where J represents the number of items or nonzero categories and K represents the number of attributes. Entry 1 indicates that the attribute is measured by the item, and 0 otherwise. The first column gives the item number, which must be numeric and match the number of column in the data. The second column indicates the category number.

type

what type of model is to be fit; can be 'tree','sequential',or 'adjacent'.

linkfunc

link function used; 'logit' is the default.

eq.const

whether effects are constrained to be equal across categories; FALSE is the default.

delta

initial item parameters

Tmatrix

The mapping matrix showing the relation between the OBSERVED responses (rows) and the PSEDUO items (columns); The first column gives the observed responses.

conv.crit

The convergence criterion for max absolute change in item parameters.

conv.type

convergence criteria; Can be pr,LL and delta, indicating category response function, log-likelihood and delta parameters,respectively.

maxitr

The maximum iterations allowed.

References

Gao, X., Ma, W., Wang, D., Cai, Y., & Tu, D. (2021). A class of cognitive diagnosis models for polytomous data. Journal of Educational and Behavioral Statistics, 46, 297-322. Ma, W. (2018). A Diagnostic Tree Model for Polytomous Responses with Multiple Strategies. British Journal of Mathematical and Statistical Psychology.

See also

GDINA for MS-DINA model and single strategy CDMs, and GMSCDM for generalized multiple strategies CDMs for dichotomous response data

Author

Wenchao Ma, The University of Minnesota, wma@umn.edu

Examples

if (FALSE) { # \dontrun{

####################################
#        Example 1.                #
#     sequential G-DINA model.     #
#                                  #
####################################

dat <- sim20seqGDINA$simdat
Qc <- sim20seqGDINA$simQ
fit=DTM(sim20seqGDINA$simdat,Qc,type="sequential")
fit
fit$testfit$AIC

####################################
#        Example 2.                #
#        Tree model                #
#                                  #
####################################
K=5
g=0.2
item.no <- rep(1:6,each=4)
# the first node has three response categories: 0, 1 and 2
node.no <- rep(c(1,1,2,3),6)
Q1 <- matrix(0,length(item.no),K)
Q2 <- cbind(7:(7+K-1),rep(1,K),diag(K))
for(j in 1:length(item.no)) {
  Q1[j,sample(1:K,sample(3,1))] <- 1
}
Qc <- rbind(cbind(item.no,node.no,Q1),Q2)
Tmatrix.set <- list(cbind(c(0,1,2,3,3),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)),
cbind(c(0,1,2,3,4),c(0,1,2,1,2),c(NA,0,NA,1,NA),c(NA,NA,0,NA,1)),
cbind(c(0,1),c(0,1)))
Tmatrix <- Tmatrix.set[c(1,1,1,1,1,1,rep(3,K))]
sim <- simDTM(N=2000,Qc=Qc,gs.parm=matrix(0.2,nrow(Qc),2),Tmatrix=Tmatrix)
est <- DTM(dat=sim$dat,Qc=Qc,Tmatrix = Tmatrix)
} # }