Table 8.
The Proportion of Overall Item Usage.
| PWKL |
MPWKL |
GDI |
|||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Number of required attributes |
|||||||||||||||||
| True Model | Item quality | J | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
| DINA | HD-HV | 10 | 0.25 | 0.45 | 0.23 | 0.06 | 0.01 | 0.38 | 0.27 | 0.31 | 0.02 | 0.01 | 0.34 | 0.34 | 0.28 | 0.03 | 0.01 |
| 20 | 0.25 | 0.48 | 0.22 | 0.04 | 0.01 | 0.27 | 0.39 | 0.30 | 0.03 | 0.01 | 0.27 | 0.37 | 0.29 | 0.05 | 0.02 | ||
| 40 | 0.28 | 0.49 | 0.18 | 0.04 | 0.01 | 0.24 | 0.44 | 0.27 | 0.05 | 0.01 | 0.24 | 0.39 | 0.30 | 0.05 | 0.01 | ||
| LD-LV | 10 | 0.26 | 0.30 | 0.34 | 0.08 | 0.02 | 0.50 | 0.30 | 0.16 | 0.03 | 0.01 | 0.52 | 0.29 | 0.15 | 0.03 | 0.01 | |
| 20 | 0.29 | 0.34 | 0.28 | 0.07 | 0.02 | 0.37 | 0.35 | 0.23 | 0.04 | 0.01 | 0.38 | 0.34 | 0.22 | 0.05 | 0.01 | ||
| 40 | 0.25 | 0.34 | 0.31 | 0.08 | 0.02 | 0.27 | 0.35 | 0.30 | 0.07 | 0.02 | 0.28 | 0.35 | 0.29 | 0.07 | 0.02 | ||
| DINO | HD-HV | 10 | 0.26 | 0.44 | 0.23 | 0.07 | 0.01 | 0.30 | 0.38 | 0.27 | 0.04 | 0.01 | 0.36 | 0.28 | 0.30 | 0.05 | 0.01 |
| 20 | 0.25 | 0.44 | 0.24 | 0.06 | 0.01 | 0.28 | 0.40 | 0.26 | 0.06 | 0.01 | 0.23 | 0.41 | 0.26 | 0.08 | 0.02 | ||
| 40 | 0.24 | 0.46 | 0.24 | 0.05 | 0.01 | 0.21 | 0.49 | 0.23 | 0.06 | 0.01 | 0.22 | 0.41 | 0.29 | 0.07 | 0.01 | ||
| LD-LV | 10 | 0.23 | 0.32 | 0.32 | 0.11 | 0.02 | 0.46 | 0.32 | 0.17 | 0.04 | 0.01 | 0.49 | 0.30 | 0.16 | 0.04 | 0.01 | |
| 20 | 0.27 | 0.33 | 0.29 | 0.09 | 0.02 | 0.35 | 0.36 | 0.22 | 0.05 | 0.01 | 0.37 | 0.34 | 0.22 | 0.05 | 0.01 | ||
| 40 | 0.22 | 0.36 | 0.30 | 0.10 | 0.02 | 0.26 | 0.37 | 0.27 | 0.08 | 0.02 | 0.26 | 0.37 | 0.27 | 0.08 | 0.02 | ||
| A-CDM | HD-HV | 10 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 |
| 20 | 0.95 | 0.02 | 0.02 | 0.01 | 0.00 | 0.96 | 0.02 | 0.02 | 0.01 | 0.00 | 0.96 | 0.02 | 0.02 | 0.01 | 0.00 | ||
| 40 | 0.93 | 0.06 | 0.01 | 0.00 | 0.00 | 0.96 | 0.03 | 0.01 | 0.00 | 0.00 | 0.98 | 0.01 | 0.01 | 0.00 | 0.00 | ||
| LD-LV | 10 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 | 0.92 | 0.03 | 0.03 | 0.02 | 0.00 | |
| 20 | 0.96 | 0.02 | 0.02 | 0.01 | 0.00 | 0.96 | 0.02 | 0.02 | 0.01 | 0.00 | 0.96 | 0.02 | 0.02 | 0.01 | 0.00 | ||
| 40 | 0.98 | 0.01 | 0.01 | 0.00 | 0.00 | 0.98 | 0.01 | 0.01 | 0.00 | 0.00 | 0.98 | 0.01 | 0.01 | 0.00 | 0.00 | ||
Note. PWKL = posterior-weighted Kullback–Leibler index; MPWKL = modified posterior-weighted Kullback–Leibler index; GDI = G-DINA model discrimination index; G-DINA = generalized DINA; DINA = deterministic inputs, noisy “and” gate; DINO = deterministic input, noisy “or” gate; A-CDM = additive CDM; CDM = cognitive diagnosis model; HD-LV = high discrimination–low variance; HD-HV = high discrimination–high variance; LD-LV = low discrimination–low variance; LD-HV = low discrimination–high variance.