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Tests
We verified the functions in lsasim package (version 1.0.1) and took into considertayion the following factors: sample size, test length, number of booklets, item parameters, and population distributions.
Three open-source R software package TAM (version 2.4-9), mirt (version 1.25), and ltm version (1.0-0) were chosen for IRT calibration. Default settings such as the estimation method, which is marginal maximum likelihood was used in TAM and ltm, and unconditional maximum likelihood factor analysis model in ltm, via the Expectation-Maximization (EM) algorithm approach, were used.
We tested the following conditions:
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Item parameter recovery: unrotated booklet design
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Item parameter recovery: rotated booklet design
- Multiple booklets, single format: 1PL items
- Multiple booklets, single format: 2PL items
- Multiple booklets, single format: 3PL items
- Multiple booklets, single format: PC items
- Multiple booklets, single format: GPC items
- Multiple booklets, mixed formats: 1PL and PC items
- Multiple booklets, mixed formats: 2PL and GPC items
- PISA 2012 mathematics items
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Latent trait recovery: group differences
- Unrotated booklet design, Rasch model with latent regressors
- Rotated booklet design, Rasch model with latent regressors
- PISA 2012 design, background questions (ST88) as latent regressors
- PISA 2012 design, background questions (ST89) as latent regressors
- Two groups’ distributions recovery
- Nine groups’ distributions recovery
The current development version of lsasim (> 2.0.0) is currently going through a testing phase regarding the calculation of sampling weights. A tutorial for helping with the testing is available in the link below; all contributions are welcome.