2018
DOI: 10.3102/1076998618808576
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Estimating Linking Functions for Response Model Parameters

Abstract: Parameter linking in item response theory is generally necessary to adjust for differences between the true values for the same item and ability parameters due to the use of different identifiability restrictions in different calibrations. The research reported in this article explores a precision-weighted (PW) approach to the problem of estimating the linking functions for the common dichotomous logistic response models. Asymptotic standard errors (ASEs) of linking for the new approach are derived and compare… Show more

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Cited by 7 publications
(16 citation statements)
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“…It is clear from the results that the number of required linking items decreases with higher bounds on linking error. Consistent with results in Barrett and van der Linden (), decrease in linking error is steepest with addition of the first 10 or so items, with little decrease associated with additional linking items beyond that point. Note that if the bounds on σu and σv had been allowed to increase considerably further, a design with just one linking item would have been selected as it is theoretically and mathematically possible to link with one item, albeit with substantial linking error.…”
Section: Resultssupporting
confidence: 87%
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“…It is clear from the results that the number of required linking items decreases with higher bounds on linking error. Consistent with results in Barrett and van der Linden (), decrease in linking error is steepest with addition of the first 10 or so items, with little decrease associated with additional linking items beyond that point. Note that if the bounds on σu and σv had been allowed to increase considerably further, a design with just one linking item would have been selected as it is theoretically and mathematically possible to link with one item, albeit with substantial linking error.…”
Section: Resultssupporting
confidence: 87%
“…This article found that optimal linking design for common‐item linking becomes possible and quite practical when using the precision‐weighted estimate of the linking parameters proposed by Barrett and van der Linden (). As illustrated through five instances of implementation with empirical data and real‐world test constraints, the MIP models in the approach are straightforward to build and do have an impact on expected random linking error.…”
Section: Discussionmentioning
confidence: 99%
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“…It should be emphasized that we did not investigate the computation of standard errors in our linking approach. There is ample literature that derives standard error formulas for linking due to sampling of persons (e.g., [44,50,[63][64][65][66][67]) Alternatively, variability in estimated group means due to the selection of items has been studied as linking errors in the literature [47,[68][69][70][71][72]. In future research, it would be interesting to accompany robust Haebara linking with error components that reflect these sources of uncertainty [24,64,73].…”
Section: Discussionmentioning
confidence: 99%