The crucial distinction is that in the former case interest centers on estimating proficiency distributions at the group-level or population-level.
This means that any adult with an estimated proficiency of 275 would have a 67% chance of responding correctly to all items at 275 on that scale.
For each of the 49 countries that participated, it provided estimated proficiency (achievement) scores in mathematics and science on the TIMSS scores scale, with an average score set to 500 and a standard deviation to 100, and extensive data on contextual variables social as well as educational.
The problem is that because each individual is exposed to a set of items that constitute a small fraction of the full item pool, the corresponding estimate of proficiency would be associated with a large error variance.
First, we present the bias for the three estimates' mean proficiency difference, β1 and β2.
As a consequence, the estimates of proficiency scores and the inferences based on them (e.g., group differences) are likely to be biased (Eklöf 2010; Wise and DeMars 2005; Wise and Kong 2005).
Adjusting the scale for guessing, and then estimating person proficiencies based on all responses of each student, provides a stronger linearisation of the total scores than an original analysis.
As each plausible value provides an estimate of numeracy proficiency, we can use one plausible value of numeracy proficiency as an instrument for another plausible value of numeracy proficiency to correct for measurement error bias.
A limitation of both SMI and MMI methods is the use of the WLE as a rough proficiency estimate for the unobserved person parameter θ n in the imputation model.
To estimate the classification proficiency, we performed internal cross-validation, using out-of-bag (OOB) samples, and external validation, using an independent test set.
