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

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

Checks if the Q matrix is generically identified.

1	is_q_generic(x)

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

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

(G1) The true \boldsymbol{Q} matrix takes the form of \boldsymbol{Q}^\top=≤ft[{\boldsymbol{Q}_1,\boldsymbol{Q}_2, (\boldsymbol{Q}^\ast)^\top}\right]^\top after row swapping, where \boldsymbol{Q}^\ast is a (J-2K)\times K binary matrix and \boldsymbol{Q}_1,\boldsymbol{Q}_2 \in \mathcal{Q}_g with

{\mathbb {Q}}_g =≤ft\{ \boldsymbol{Q} \in \{0,1\}^{J\times K}: \boldsymbol{Q} = \begin{bmatrix} * &{} 1 &{} *&{} … &{} *&{}… &{} *\\ * &{}*&{} 1 &{} … &{} *&{}… &{} *\\ \vdots &{} \vdots &{} &{} \ddots &{} &{} &{} \vdots \\ * &{} * &{} *&{} … &{} 1&{}… &{} *\\ \end{bmatrix}\right\}

where * can be either 0 or 1.
(G2) For any k = 1, 2, …, K, there exists a j_k > 2K, such that q_{j_k, k} = 1.

A logical vector

James Joseph Balamuta and Steven Andrew Culpepper

Gu, Yuqi, and Gongjun Xu. "Sufficient and Necessary Conditions for the Identifiability of the Q-matrix." arXiv preprint arXiv:1810.03819 (2018).

The function implemented is a translation of the publicly available MATLAB code from https://github.com/yuqigu/Identify_Q into C++.

is_q_strict()

## Check if Q Matrix is Generically Identified ---
# Create a generically identified Q matrix
q3_generic = rbind(diag(3),
                   c(1, 1, 0),
                   c(1, 0, 1),
                   c(0, 1, 1),
                   c(1, 1, 1))

# Check if Q matrix is generic
is_q_generic(q3_generic)

# (Extra) Check if Q matrix is strict
is_q_strict(q3_generic)