A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
A Note on Exploratory Item Factor Analysis by Singular Value Decomposition
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DOI：
10.1007/s11336-020-09704-7
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发表时间：
2019-07
期刊：
影响因子：
3
通讯作者：
Haoran Zhang;Yunxiao Chen;Xiaoou Li
中科院分区：
文献类型：
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作者：
Haoran Zhang;Yunxiao Chen;Xiaoou Li
我们重新审视奇异值分解（SVD）算法在陈等人。（Psychometrika 84：124-146，2019 b）进行探索性项目因素分析（IFA）。该算法通过奇异值分解估计多维IFA模型，并在Chen等人中用于获得联合最大似然估计的起始点。（2019 b年版）。由于SVD的分析和计算特性，该算法保证了唯一的解决方案，并具有计算优势，比其他探索性IFA方法。当被调查者、项目和因子的数量都很大时，它的计算优势变得很明显。该算法可以看作是主成分分析在二进制数据上的推广。在本说明中，我们提供了算法的统计基础。特别是，我们在相同的双渐近设置下，在陈等人的统计一致性。（2019 b年版）。我们还演示了如何该算法提供了一个scree情节调查的因素，并提供其渐近理论。进一步扩展的算法进行了讨论。仿真结果表明，该算法具有良好的有限样本性能.
We revisit a singular value decomposition (SVD) algorithm given in Chen et al. (Psychometrika 84:124–146, 2019b) for exploratory item factor analysis (IFA). This algorithm estimates a multidimensional IFA model by SVD and was used to obtain a starting point for joint maximum likelihood estimation in Chen et al. (2019b). Thanks to the analytic and computational properties of SVD, this algorithm guarantees a unique solution and has computational advantage over other exploratory IFA methods. Its computational advantage becomes significant when the numbers of respondents, items, and factors are all large. This algorithm can be viewed as a generalization of principal component analysis to binary data. In this note, we provide the statistical underpinning of the algorithm. In particular, we show its statistical consistency under the same double asymptotic setting as in Chen et al. (2019b). We also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory. Further extensions of the algorithm are discussed. Finally, simulation studies suggest that the algorithm has good finite sample performance.