12.8 Stepwise method

To address the both limitations, Ma & de la Torre (2020) proposed a stepwise procedure, which use the Wald test as the central component for determining the best q-vector for each item.

To show how Wald test can be used for q-vector validation, assume an item measures three attributes. We want to use Wald test to test whether Attribute 1 is required statistically, the null hypothesis (Attribute 1 is not necessary) would be $$\left[\begin{array}{cccccccc}1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& -1& 0& 0& 0\\ 0& 0& 0& 1& 0& -1& 0& 0\\ 0& 0& 0& 0& 0& 0& -1& 1\end{array}\right]\times \left[\begin{array}{c}P\left(000\right)\\ P\left(100\right)\\ P\left(010\right)\\ P\left(001\right)\\ P\left(110\right)\\ P\left(101\right)\\ P\left(011\right)\\ P\left(111\right)\end{array}\right]=0.$$

References

Ma, W., & de la Torre, J. (2020). An empirical q-matrix validation method for the sequential generalized DINA model. The British Journal of Mathematical and Statistical Psychology, 73(1), 142–163. https://doi.org/10.1111/bmsp.12156