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Can IRT Solve the Missing Data Problem in Test Equating?

ABSTRACT: In this paper test equating is considered as a missing data problem. The unobserved responses of the reference population to the new test must be imputed to specify a new cutscore. The proportion of students from the reference population that would have failed the new exam and those having failed the reference exam are made approximately the same. We investigate whether item response theory (IRT) makes it possible to identify the distribution of these missing responses and the distribution of test scores from the observed data without parametric assumptions for the ability distribution. We show that while the score distribution is not fully identifiable, the uncertainty about the score distribution on the new test due to non-identifiability is very small. Moreover, ignoring the non-identifiability issue and assuming a normal distribution for ability may lead to bias in test equating, which we illustrate in simulated and empirical data examples.

SUBMITTER: Bolsinova M

PROVIDER: S-EPMC4700285 | biostudies-literature | 2015

REPOSITORIES: biostudies-literature

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Can IRT Solve the Missing Data Problem in Test Equating?

Bolsinova Maria M Maris Gunter G

Frontiers in psychology 20160105

In this paper test equating is considered as a missing data problem. The unobserved responses of the reference population to the new test must be imputed to specify a new cutscore. The proportion of students from the reference population that would have failed the new exam and those having failed the reference exam are made approximately the same. We investigate whether item response theory (IRT) makes it possible to identify the distribution of these missing responses and the distribution of te ...[more]

PMID: 26779074

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Project description:Marker-based human motion analysis is an important tool in clinical research and in many practical applications. Missing marker information caused by occlusions or a marker falling off is a common problem impairing data quality. The current paper proposes a conceptually new gap filling algorithm and presents results from a proof-of-principle analysis. The underlying idea of the proposed algorithm was that a multitude of internal and external constraints govern human motion and lead to a highly subject-specific movement pattern in which all motion variables are intercorrelated in a specific way. Two principal component analyses were used to determine how the coordinates of a marker with gaps correlated with the coordinates of the other, gap-free markers. Missing marker data could then be reconstructed through a series of coordinate transformations. The proposed algorithm was tested by reconstructing artificially created gaps in a 20-step walking trial and in an 18-s one-leg balance trial. The measurement accuracy's dependence on the marker position, the length of the gap, and other parameters were evaluated. Even if only 2 steps of walking or 1.8 s of postural sway (10% of the whole marker data) were provided as input in the current study, the reconstructed marker trajectory differed on average no more than 11 mm from the originally measured trajectory. The reconstructed result improved further, on average, to distances below 5 mm if the marker trajectory was available more than 50% of the trial. The results of this proof-of-principle analysis supported the assumption that missing marker information can be reconstructed from the intercorrelations between marker coordinates, provided that sufficient data with complete marker information is available. Estimating missing information cannot be avoided entirely in many situations in human motion analysis. For some of these situations, the proposed reconstruction method may provide a better solution than what is currently available.

Dataset Information

Can IRT Solve the Missing Data Problem in Test Equating?

Publications

Can IRT Solve the Missing Data Problem in Test Equating?

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