This function estimates the diagnostic tree model (Ma, 2018) for polytomous responses with multiple strategies. It is an experimental function, and will be further optimized.

DTM(dat, Qc, 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. 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. initial item parameters The mapping matrix showing the relation between the OBSERVED responses (rows) and the PSEDUO items (columns); The first column gives the observed responses. The convergence criterion for max absolute change in item parameters. convergence criteria; Can be pr,LL and delta, indicating category response function, log-likelihood and delta parameters,respectively. The maximum iterations allowed.

## References

Ma, W. (2018). A Diagnostic Tree Model for Polytomous Responses with Multiple Strategies. British Journal of Mathematical and Statistical Psychology.

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

## Examples

if (FALSE) {
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)
}