Identifiability Conditions of the DINA Model
Check necessary and sufficient identifiability conditions of the DINA model according Gu and Xu (xxxx) for a given Q-matrix.
din_identifiability(q.matrix) ## S3 method for class 'din_identifiability' summary(object, ...)
q.matrix |
Q-matrix |
object |
Object of class |
... |
Further arguments to be passed |
List with values
dina_identified |
Logical indicating whether the DINA model is identified |
index_single |
Condition 1: vector of logicals indicating whether skills are measured by at least one item with a single loading |
is_three_items |
Condition 2: vector of logicals indicating whether skills are measured by at least three items |
submat_distinct |
Condition 3: logical indicating whether all columns of the submatrix Q^\ast are distinct. |
Gu, Y., & Xu, G. (2018). The sufficient and necessary condition for the identifiability and estimability of the DINA model. Psychometrika, xx(xx), xxx-xxx. https://doi.org/10.1007/s11336-018-9619-8
See din.equivalent.class for equivalent (i.e., non-distinguishable)
skill classes in the DINA model.
############################################################################# # EXAMPLE 1: Some examples of Gu and Xu (2019) ############################################################################# #* Matrix 1 in Equation (5) of Gu & Xu (2019) Q1 <- diag(3) Q2 <- matrix( scan(text="1 1 0 1 0 1 1 1 1 1 1 1"), ncol=3, byrow=TRUE) Q <- rbind(Q1, Q2) res <- CDM::din_identifiability(q.matrix=Q) summary(res) # remove two items res <- CDM::din_identifiability(q.matrix=Q[-c(2,5),]) summary(res) #* Matrix 1 in Equation (6) of Gu & Xu (2019) Q1 <- diag(3) Q2 <- matrix( c(1,1,1), nrow=4, ncol=3, byrow=TRUE) Q <- rbind(Q1, Q2) res <- CDM::din_identifiability(q.matrix=Q) summary(res)
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