Bachelorarbeit
1.0.0
Draxler & Zessin (2015) have proposed a class of pseudo-exact or conditional tests for power calculations of Rasch model assumptions. Sampling algorithms are required to simulate the data required for the power calculation. Verhelst (2008) designed a relatively fast algorithm called the Rasch Sampler that approximates the true distribution using Markov Chain Monte Carlo procedures. Miller & Harrison (2013) have developed an algorithm called the Exact Sampler that can count and extract the exact distribution. The accuracy of the two samplers is compared by examining potential influences of sample size, DIF parameters and item difficulty on the accuracy of the power calculation. In addition, the burn-in phase and the step parameter are checked as influencing factors on the Rasch sampler. The accuracy of the samplers does not differ significantly. As the sample size increases, the power increases. Even with larger model deviations, both positive and negative, higher power can be observed. With moderate item difficulty, the power is almost the same for positive and negative DIF parameters. If there is a model deviation of a slight item, the power is greater for positive deviation than for negative deviation. With a difficult item, an opposite trend can be observed, with the difference that the scatter is significantly higher. Neither the burn-in phase nor the step parameter has an influence on the accuracy of the Rasch sampler. Due to more efficient calculations, the Rasch Sampler should always be used. The results regarding the behavior of the power when varying various parameters correspond to the observations of Draxler & Zessin (2015).
Draxler & Zessin (2015) have proposed a class of pseudo-exact or conditional tests for power calculation of assumptions of the Rasch model. Sampling algorithms are required to simulate the data required for power calculation. Verhelst (2008) has designed a relatively fast algorithm called the Rasch Sampler, which approximates the true distribution using Markov Chain Monte Carlo procedures. Miller & Harrison (2013) have developed an algorithm called the Exact Sampler, which can count the exact distribution and draw from it. The accuracy of the two samplers is compared by examining potential influences of sample size, DIF-parameters and item difficulty on the accuracy of the power calculation. Furthermore, the burn-in phase and the step parameters are checked as influencing factors on the Rasch Sampler. The accuracy of the samplers does not differ meaningfully. The power increases with higher sample size. Also the power increases with larger positive and negative model deviations. With moderate item difficulty, the power for positive and negative DIF parameters is almost equal. If an easy item deviates from the model, the power is greater if the deviation is positive than if the item is negative. With a difficult item, a contrasting trend can be observed with the difference that the range of the power values is relevantly higher. Neither the burn-in phase nor the step parameter has any influence on the accuracy of the Rasch Sampler. Due to more efficient calculation the Rasch Sampler should be used in any case. The results concerning the behavior of the power under variation of different parameters correspond to the observations of Draxler & Zessin (2015).
Keywords: Rasch model, Power, Pseudo-exact tests, Conditional tests, Rasch Sampler, Exact Sampler
