Fellinghauer Carolina, Debelak Rudolf, Strobl Carolin
University of Zurich, Switzerland.
Educ Psychol Meas. 2023 Dec;83(6):1249-1290. doi: 10.1177/00131644221143051. Epub 2023 Jan 13.
This simulation study investigated to what extent departures from construct similarity as well as differences in the difficulty and targeting of scales impact the score transformation when scales are equated by means of concurrent calibration using the partial credit model with a common person design. Practical implications of the simulation results are discussed with a focus on scale equating in health-related research settings. The study simulated data for two scales, varying the number of items and the sample sizes. The factor correlation between scales was used to operationalize construct similarity. Targeting of the scales was operationalized through increasing departure from equal difficulty and by varying the dispersion of the item and person parameters in each scale. The results show that low similarity between scales goes along with lower transformation precision. In cases with equal levels of similarity, precision improves in settings where the range of the item parameters is encompassing the person parameters range. With decreasing similarity, score transformation precision benefits more from good targeting. Difficulty shifts up to two logits somewhat increased the estimation bias but without affecting the transformation precision. The observed robustness against difficulty shifts supports the advantage of applying a true-score equating methods over identity equating, which was used as a naive baseline method for comparison. Finally, larger sample size did not improve the transformation precision in this study, longer scales improved only marginally the quality of the equating. The insights from the simulation study are used in a real-data example.
本模拟研究调查了在使用具有共同人员设计的部分计分模型通过同时校准来对量表进行等值化时，与构念相似性的偏离程度以及量表难度和目标定位的差异对分数转换的影响程度。讨论了模拟结果的实际意义，重点是健康相关研究环境中的量表等值化。该研究模拟了两个量表的数据，改变了项目数量和样本量。量表之间的因子相关性用于衡量构念相似性。通过增加与等难度的偏离程度以及改变每个量表中项目参数和人员参数的离散程度来衡量量表的目标定位。结果表明，量表之间的相似性较低会导致转换精度较低。在相似性水平相同的情况下，当项目参数范围涵盖人员参数范围时，精度会提高。随着相似性的降低，分数转换精度从良好的目标定位中受益更多。难度偏移高达两个对数单位会稍微增加估计偏差，但不会影响转换精度。观察到的对难度偏移的稳健性支持了应用真分数等值化方法优于恒等等值化的优势，恒等等值化被用作天真的基线方法进行比较。最后，在本研究中，较大的样本量并没有提高转换精度，较长的量表仅略微提高了等值化的质量。模拟研究的见解被用于一个实际数据示例中。
