din_identifiability {CDM} R Documentation

## Identifiability Conditions of the DINA Model

### Description

Check necessary and sufficient identifiability conditions of the DINA model according Gu and Xu (xxxx) for a given Q-matrix.

### Usage

```din_identifiability(q.matrix)

## S3 method for class 'din_identifiability'
summary(object, ...)
```

### Arguments

 `q.matrix` Q-matrix `object` Object of class `din_identifiability` `...` Further arguments to be passed

### Value

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.

### References

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.

### Examples

```#############################################################################
# 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)
```

[Package CDM version 7.5-15 Index]