3.3 Attribute Profiles

When $K=3$, the total number of latent classes is $2^K=8$

A1	A2	A3
0	0	0
1	0	0
0	1	0
0	0	1
1	1	0
1	0	1
0	1	1
1	1	1

If item j measures attributes 2 and 3 but not attribute 1, mastering attribute 1 or not will have no impact on the success probability

Using notations from (de la Torre, 2011), Let $K$ be the number of attributes in the test and $K_j^*$ the number of attributes involved in item $j$

Assume $K=3$ and $K_j^*=2$, we have $2^3$ latent classes can be collapsed into $2^{K_j^*}=4$ latent groups:

References

de la Torre, J. (2011). The Generalized DINA Model Framework. Psychometrika, 76(2), 179–199. https://doi.org/10.1007/s11336-011-9207-7