论文标题
高维探索性因素分析中有关可能性比测试的注释
A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis
论文作者
论文摘要
似然比测试广泛用于探索性因素分析中，以评估模型拟合并确定潜在因素的数量。尽管其流行和明确的统计理由，但研究人员发现，与样本量相比，响应数据的维度很大时，可能性比率测试统计量的经典卡方近似通常会失败。从理论上讲，当这种现象发生时，随着数据的增加而发生这种现象时，这是一个空旷的问题。实际上，在探索性因素分析中对高维度的影响较少，并且缺乏关于常规卡方近似有效性的明确统计指南。为了解决这个问题，我们研究了高维探索因子分析中类似比测试的卡方近似的失败，并得出了必要和足够的条件以确保卡方近似的有效性。结果产生了简单的定量指南，以检查实践，还将为探索性因素分析实践提供有用的统计见解。
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 the necessary and sufficient condition 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.
