A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis
A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis
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DOI：
10.1007/s11336-021-09755-4
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发表时间：
2020-08
期刊：
影响因子：
3
通讯作者：
Yinqiu He;Zi Wang;Gongjun Xu
中科院分区：
文献类型：
--
作者：
Yinqiu He;Zi Wang;Gongjun Xu
似然比检验广泛用于探索性因子分析，以评估模型拟合和确定潜在因子的数量。尽管它的流行和明确的统计原理，研究人员发现，当响应数据的维度与样本量相比很大时，经典的卡方近似似然比检验统计量往往会失败。理论上，随着数据维数的增加，这种现象的发生一直是一个悬而未决的问题;实践中，探索性因素分析对高维因素的影响研究较少，传统卡方近似的有效性缺乏明确的统计指导。针对这一问题，本文研究了高维探索性因子分析中似然比检验的卡方近似的失效问题，并推导出了保证卡方近似有效性的必要条件。结果产生简单的定量指导方针，以检查在实践中，也将提供有用的统计见解探索性因素分析的实践。
The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size, the classical Chi-square approximation of the likelihood ratio test statistic often fails. Theoretically, it has been an open problem when such a phenomenon happens as the dimension of data increases; practically, the effect of high dimensionality is less examined in exploratory factor analysis, and there lacks a clear statistical guideline on the validity of the conventional Chi-square approximation. To address this problem, we investigate the failure of the Chi-square approximation of the likelihood ratio test in high-dimensional exploratory factor analysis and derive thenecessary and sufficientcondition to ensure the validity of the Chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis.