Evaluation of the Linear Composite Conjecture for Unidimensional IRT Scale for Multidimensional Responses.

IF 1 4区 心理学 Q4 PSYCHOLOGY, MATHEMATICAL
Tyler Strachan, Uk Hyun Cho, Terry Ackerman, Shyh-Huei Chen, Jimmy de la Torre, Edward H Ip
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Abstract

The linear composite direction represents, theoretically, where the unidimensional scale would lie within a multidimensional latent space. Using compensatory multidimensional IRT, the linear composite can be derived from the structure of the items and the latent distribution. The purpose of this study was to evaluate the validity of the linear composite conjecture and examine how well a fitted unidimensional IRT model approximates the linear composite direction in a multidimensional latent space. Simulation experiment results overall show that the fitted unidimensional IRT model sufficiently approximates linear composite direction when correlation between bivariate latent variables is positive. When the correlation between bivariate latent variables is negative, instability occurs when the fitted unidimensional IRT model is used to approximate linear composite direction. A real data experiment was also conducted using 20 items from a multiple-choice mathematics test from American College Testing.

Abstract Image

多维响应下一维IRT尺度线性复合猜想的评价。
线性复合方向在理论上表示一维尺度在多维潜在空间中的位置。利用补偿性多维IRT,可以从项目的结构和潜在分布推导出线性复合。本研究的目的是评估线性复合猜想的有效性,并检查拟合的一维IRT模型在多维潜在空间中近似线性复合方向的程度。仿真实验结果总体上表明,拟合的一维IRT模型在二元潜变量之间为正相关时,能充分逼近线性复合方向。当二元潜变量之间的相关性为负时,用拟合的一维IRT模型近似线性复合方向会产生不稳定性。采用美国大学考试数学多项选择题中的20个题目进行了真实数据实验。
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来源期刊
CiteScore
2.30
自引率
8.30%
发文量
50
期刊介绍: Applied Psychological Measurement publishes empirical research on the application of techniques of psychological measurement to substantive problems in all areas of psychology and related disciplines.
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