A Comparison of Two Procedures for Computing IRT Equating Coefficients

Baker, Frank B.; Al-Karni, Ali

doi:10.1111/j.1745-3984.1991.tb00350.x

Cited by 76 publications

(59 citation statements)

References 11 publications

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“…Again, item difficulty parameters tend to yield more stable estimates than item discrimination parameters (the mean/sigma method uses only item difficulty parameters), but sample means tend to yield more stable estimates than sample standard deviations (Baker & Al-Karni, 1991).…”

Section: Mean/sigma Methodsmentioning

confidence: 98%

“…An advantage of the mean/mean method (over the mean/sigma method) is that the sample mean tends to yield more stable estimates of the respective population value than the sample standard deviation (Baker & Al-Karni, 1991). However, item difficulty parameters tend to yield more stable estimates than item discrimination parameters (Kolen & Brennan, 2004).…”

Section: Mean/mean Methodsmentioning

confidence: 99%

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Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

Brossman

Lee

2013

Applied Psychological Measurement

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The purpose of this research was to develop observed score and true score equating procedures to be used in conjunction with the Multidimensional Item Response Theory (MIRT) framework. Currently, MIRT scale linking procedures exist to place item parameter estimates and ability estimates on the same scale after separate calibrations are conducted. These procedures account for indeterminacies in (1) translation, (2) dilation, (3) rotation, and (4) correlation. However, no procedures currently exist to equate number correct scores after parameter estimates are placed on the same scale. This research sought to fill this void in the current psychometric literature.Three equating procedures-two observed score procedures and one true score procedure-were created and described in detail. One observed score procedure was presented as a direct extension of unidimensional IRT observed score equating, and is referred to as the "Full MIRT Observed Score Equating Procedure." The true score procedure and the second observed score procedure incorporated the statistical definition of the "direction of best measurement" in an attempt to equate exams using unidimensional IRT (UIRT) equating principles. These procedures are referred to as the "Unidimensional Approximation of MIRT True Score Equating Procedure" and the "Unidimensional Approximation of MIRT Observed Score Equating Procedure," respectively. Three exams within the Iowa Test of Educational Development (ITED) Form A andForm B batteries were used to conduct UIRT observed score and true score equating, MIRT observed score and true score equating, and equipercentile equating. The equipercentile equating procedure was conducted for the purpose of comparison since this procedure does not explicitly violate the IRT assumption of unidimensionality.Results indicated that the MIRT equating procedures performed more similarly to the equipercentile equating procedure than the UIRT equating procedures, presumably due to the violation of the unidimensionality assumption under the UIRT equating procedures. Future 2 studies are expected to address how the MIRT procedures perform under varying levels of multidimensionality (weak, moderate, strong), varying frameworks of dimensionality (simple structure vs. complex structure), and number of dimensions, among other conditions. Abstract Approved:

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Section: Mean/sigma Methodsmentioning

confidence: 98%

Section: Mean/mean Methodsmentioning

confidence: 99%

Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

Brossman

Lee

2013

Applied Psychological Measurement

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“…Another approach for calculating the linking coefficients are characteristic curve methods. These methods are based on minimizing a loss function that depends on the metric of test calibration (Baker & Al-Karni, 1991). Characteristic curve methods consider all parameters simultaneously to find linking coefficients that minimize differences in the characteristic curve between tests.…”

Section: Irt Test Equatingmentioning

confidence: 99%

“…It is known that characteristic curve scale linking methods produce more accurate results than the moment methods (Baker & Al-Karni, 1991;Hanson & Beguin, 2002;Kim & Cohen, 1992;Kim & Kolen, 2006;Kim & Lee, 2004;Ogasawara, 2001). Could we generalize this evident to mixed-format test equating?…”

Section: The Purpose and Significance Of The Studymentioning

confidence: 99%

The Impact of Test Dimensionality, Common-Item Set Format, and Scale Linking Methods on Mixed-Format Test Equating

2016

EDUC SCI-THEOR PRACT

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The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design. The equity property was evaluated based on firstorder equity (FOE) and second-order equity (SOE) properties. A simulation study was conducted based on actual item parameter estimates obtained from the TIMSS 2011 8th grade mathematics assessment.The results showed that: (i) The FOE and SOE properties were best preserved under the unidimensional condition, were poorly preserved when the degree of multidimensionality was severe. (ii) The TSE and OSE results, which were provided by using a mixed-format common-item set, preserved FOE better compared to equating results, which provided only a multiple-choice common item set. (iii) Under the unidimensional and multidimensional test structure, characteristic curve methods performed significantly better than moment scale linking methods in terms of preserving FOE and SOE properties.

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“…Mean-mean and mean-sigma methods are based on the transformation of item and ability parameters using common items, whereas characteristic curve methods are based on reducing the gap between the item or test characteristic curves of common items. Research has revealed that characteristic curve methods are better than meanmean and mean-sigma methods and tend to produce more stable results (Baker & Al-Karni, 1991;Gök, 2012;Stocking & Lord, 1983).…”

Section: Separate Calibration Irm-scmentioning

confidence: 99%

Effect of Differential Item Functioning on Test Equating

2015

EDUC SCI-THEOR PRACT

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This study examines the effect of differential item functioning (DIF) items on test equating through multilevel item response models (MIRMs) and traditional IRMs. The performances of three different equating models were investigated under 24 different simulation conditions, and the variables whose effects were examined included sample size, test length, DIF magnitude, and the test type. The MIRMs, in which the DIF factors were added as parameters, were compared with the Stocking-Lord (SL) method (one of the IRM-based calibration methods) and concurrent calibration method. According to the results, differences were found in the performances of the methods under the analyzed conditions. More specifically, the MIRMs were able to identify the DIF items, carry out the equating processes, and eliminate the biases caused by DIF in only one analysis. However, this does not indicate that using MIRMs is the best approach since the increase in sample size and test length generally had a positive effect on IRM-based equating, whereas MIRMs were less affected by these two conditions. Considering the IRM-based methods, it was found that separate calibration methods were more affected by the presence of DIF items compared to concurrent calibration. Moreover, this effect becomes most significant when DIF items are in common test and the magnitude of DIF is C.

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A Comparison of Two Procedures for Computing IRT Equating Coefficients

Cited by 76 publications

References 11 publications

Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

Observed Score and True Score Equating Procedures for Multidimensional Item Response Theory

The Impact of Test Dimensionality, Common-Item Set Format, and Scale Linking Methods on Mixed-Format Test Equating

Effect of Differential Item Functioning on Test Equating

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