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Item Parameter Recovery With And Without The Use Of Priors, Paulius Satkus, Christine E. Demars
Item Parameter Recovery With And Without The Use Of Priors, Paulius Satkus, Christine E. Demars
Department of Graduate Psychology - Faculty Scholarship
Marginal maximum likelihood (MML), a common estimation method for IRT models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for MML estimation. In this study, using samples sizes of 1000 or smaller, not using priors often led to extreme, implausible parameter estimates. Applying prior distributions to the c-parameters alleviated the estimation problems with samples of 1000; priors on both the a-parameters and c-parameters were needed for the samples of …
Considerations In S-Χ2: Rest Score Or Summed Score, Priors, And Violations Of Normality, Christine E. Demars, Derek Sauder
Considerations In S-Χ2: Rest Score Or Summed Score, Priors, And Violations Of Normality, Christine E. Demars, Derek Sauder
Department of Graduate Psychology - Faculty Scholarship
The S-χ2 item fit index is one of the few item fit indices that appears to maintain accurate Type I error rates. This study explored grouping examinees by the rest score or summed score, prior distributions for the item parameters, and the shape of the ability distribution. Type I error was slightly closer to the nominal level for the total-score S-χ2 for the longest tests, but power was higher for the rest-score S-χ2 in every condition where power was < 1. Prior distributions reduced the proportion of estimates with extreme standard errors but slightly inflated the Type I error rates in some conditions. When the ability distribution was not normally distributed, integrating over an empirically-estimated distribution yielded Type I error rates closer to the nominal value than integrating over a normal distribution.