is_q_strict: Is the Q Matrix Strictly Identifiable?
In tmsalab/edmcore: Algorithms used across Exploratory Diagnostic Modeling

Description Usage Arguments Details Value Author(s) See Also Examples

Checks if the Q matrix is strictly identified.

1	is_q_strict(x)

`x`	A `q_matrix()` or `base::matrix()` to test.

If \mathbf{Q} is in the strictly identifiable set \mathcal{Q}_s, then it must satisfy the following conditions:

(S1) The rows of \boldsymbol{Q} can be permuted to the form, \boldsymbol{Q}^\top=≤ft[{\boldsymbol{I_K},\boldsymbol{I_K}, (\boldsymbol{Q}^\ast)^\top}\right]^\top where \boldsymbol{I_K} is a K-dimensional identity matrix and \boldsymbol{Q}^\ast is a (J-2K)\times K matrix.
(S2) For any two latent classes c and c', there exists at least one item in \boldsymbol{Q}^\ast, in which \boldsymbol{θ}_{jc}\neq \boldsymbol{θ}_{jc'}.

In a more practical light, this means (S1) requires \boldsymbol{Q} to include two simple structure items for each attribute and (S2) states there must be at least one item not specified for (S1) that distinguishes between all pairs of classes.

A logical value.

James Joseph Balamuta and Steven Andrew Culpepper

is_q_generic()

## Check if Q Matrix is Strictly Identified ---
# Create a strict Q matrix
q2_strict = matrix(
  c(0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0),
  ncol = 2
)

# Check if Q matrix is strict
is_q_strict(q2_strict)

# (Extra) Check if Q matrix is generic
is_q_generic(q2_strict)