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However, fixing items parameters to known values coming from previous validation studies that integrated IRT models might be interesting because it allows the comparison of patients coming from different studies that made use of the same instrument.
This situation corresponds to the most favourable one regarding power; however it has to be stressed that assuming both person and items parameters to be known implies that the patient population in the trial is similar to the one used for validating the instrument, which can be restrictive.
When person parameters were assumed to be unknown and items parameters to be either known or not, the power achieved using IRT or CTT were similar and always lower than the expected power using the well-known sample size formula for normally distributed endpoints.
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Even when the item parameters are unknown and must also be estimated, there are well-known estimation methods (e.g, Bayesian MCMC, Patz and Junker [1999]) to appropriately fix the scale of θ and the item parameters to ensure that the model is identified.4.4
Specifically, Oliveri and von Davier ([2011], [2014]) have provided empirical evidence that allowing a subset of item parameters to be uniquely estimated offers one way to improve model-to-data fit and reduces problems with comparability across heterogeneous populations and associated parameter estimate bias.
For the unadjusted model involving only equation (7), we used flat N 0,10000) priors on each β coefficient, and a Unif 0,1000) prior on σ 2. Bayesian estimates with these priors are extremely similar to OLS estimates.11 For the full MESE model, we used the same priors on the β's and σ 2 in (7), and we fixed the item parameters to their NCES-estimated values in (8).
We then recalibrated the item parameters to achieve a "general population" mean of 50 and an SD of 10.
Instead of scaling the cognitive impairment scores post-estimation, we performed an equivalent linearly scaling of the ADAS-Cog item parameters to enforce these measurement scales for estimation of memory, language, and praxis impairment.
We used Parscale to estimate item parameters and to obtain option characteristic curves (OCCs) for each item.
Firstly, the item parameters have to be identified in relation to the latent trait.
Note that the item parameters applied to responses before the switching point contain no group index g, so that we assume them to be invariant across groups, although this assumption can be relaxed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com