Gamma parameters use shape and rate. DORO-Unif and the Gamma(1,3) literature default from Paganin et al. (2023) are external references. The hard solution is a sensitivity analysis; the Rasch hard prior is effectively fixed at alpha=2.
| Data | Prior | Gamma (shape, rate) | Prior count [90%] | P(W_SB > .5) | P(W_SB > .9) |
|---|---|---|---|---|---|
| STAR | Vague | (1.00, 1.00) | 4.61 [1.00, 11.00] | 0.591 | 0.303 |
| STAR | DORO-Unif | (2.33, 2.18) | 4.99 [1.00, 10.00] | 0.527 | 0.187 |
| STAR | TSMM | (5.13, 4.94) | 5.00 [2.00, 9.00] | 0.510 | 0.140 |
| STAR | Dual-Anchor | (15.77, 11.11) | 6.24 [3.00, 10.00] | 0.385 | 0.051 |
| STAR | Dual-Anchor (hard) | alpha approximately 2 | 7.93 [4.00, 12.00] | 0.250 | 0.010 |
| Bangert--Drowns | Vague | (1.00, 1.00) | 4.12 [1.00, 10.00] | 0.591 | 0.303 |
| Bangert--Drowns | DORO-Unif | (2.81, 3.19) | 3.99 [1.00, 8.00] | 0.576 | 0.217 |
| Bangert--Drowns | TSMM | (1.15, 1.22) | 4.00 [1.00, 9.00] | 0.597 | 0.297 |
| Bangert--Drowns | Dual-Anchor | (3.78, 2.50) | 5.66 [2.00, 10.00] | 0.395 | 0.084 |
| Bangert--Drowns | Dual-Anchor (hard) | (11.56, 5.44) | 7.15 [3.00, 12.00] | 0.250 | 0.017 |
| Vocabulary checklist | Vague | (1.00, 1.00) | 6.44 [1.00, 17.00] | 0.591 | 0.303 |
| Vocabulary checklist | Literature default | (1.00, 3.00) | 3.03 [1.00, 8.00] | 0.812 | 0.566 |
| Vocabulary checklist | TSMM | (2.11, 3.08) | 5.00 [1.00, 11.00] | 0.652 | 0.308 |
| Vocabulary checklist | Dual-Anchor | (20.30, 14.51) | 8.75 [4.00, 14.00] | 0.388 | 0.050 |
| Vocabulary checklist | Dual-Anchor (hard) | alpha approximately 2 | 11.59 [7.00, 17.00] | 0.250 | 0.010 |