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Table 1 Support for model structures. Model A was the best-supported model in italics. Changes in structures from model A are indicated. The differences in WAIC compared to model A were greater than 13 for all models, except model J. Given that model J was more complex, that model A was nested within model J, and that the WAIC difference was small (less than 2), the simpler model A was accepted for parsimony

From: Multiple-true-false questions reveal more thoroughly the complexity of student thinking than multiple-choice questions: a Bayesian item response model comparison

 

Model structures

WAIC

ΔWAIC

WAIC SE

P WAIC

A

Mastery, TTFF partial mastery, informed reasoning based on attractiveness, informed reasoning with double-T endorsement bias, individual student performance

18,520.7

0

200.0

342.1

B

− remove question-level mastery

18,927.0

− 406.3

199.1

288.7

C

− remove TTFF partial mastery

18,566.0

− 45.3

200.2

328.9

D

− remove TTFF partial mastery

+ replace with TTFF-TFTF partial mastery

18,534.3

− 13.6

199.7

341.8

E

− remove TTFF partial mastery

+ replace with TTFF-TFTF-TFFT partial mastery

18,536.5

− 15.8

199.5

333.5

F

− remove informed reasoning based on attractiveness

+ replace with random guessing

19,582.4

− 1061.7

203.4

268.4

G

− remove double-T bias

18,656.1

− 135.4

201.4

330.3

H

− remove double-T bias

+ replace with multi-T bias

18,533.4

− 12.7

200.3

344.6

I

− remove question-level double-T bias

+ replace with global double-T bias for each student

18,539.6

− 18.9

200.0

325.1

J

+ add random guessing for students not in mastery, partial mastery, or informed reasoning

18,519.9

+ 0.8

199.9

356.1

K

− remove individual student performance

19,448.5

− 927.8

196.7

180.2