12.4 Q-matrix validation using the PVAF method

Below is the Q-matrix validation procedure (de la Torre & Chiu, 2016):

• Fit the G-DINA model to the data based on a provisional Q-matrix
• Calculate GDI for each item based on each possible q-vector
• Calculate the proportion of variance accounted for (PVAF) by a particular q-vector to the maximum for each item

$$\text{PVAF}_q=\frac{\text{GDI}_q}{\text{GDI}_{\mathbf{1}}}$$ - An appropriate q-vector for item $j$ is the q-vector with PVAF greater than .95 ($\epsilon=.95$) but with fewest 1s

References

de la Torre, J., & Chiu, C.-Y. (2016). A general method of empirical q-matrix validation. Psychometrika, 81(2), 253–273. https://doi.org/10.1007/s11336-015-9467-8