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首页> 外文学位 >Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.
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Factor analysis: The effects of distribution type, number of factors, factor loadings, number of variables per factor and sample size on the rules used to determine the number of factors to retain.

机译：因子分析：分布类型，因子数量，因子负载，每个因子的变量数量和样本大小对用于确定要保留的因子数量的规则的影响。

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摘要

The primary goal of factor analysis (FA) is to understand the underlying structure or covariation in a set of distinct items. There are several steps involved in performing FA. Here we focus on the most important step, determining the appropriate number of factors to retain.;Based on the FA population model, we used Monte Carlo simulation to estimate the accuracy of twelve popular rules. Six component analysis (CA)-based rules were also tested including lambda ≥ 1, minimum average partial method, Bartlett's chi2 test, Horn's Parallel Analysis (PA), 80% explained variance and Image lambda ≥ 1. Six factor analysis (FA)-based rules were tested including Kaiser-Guttman's eigenvalue (% variance explained) lambda ≥ 0 and lambda ≥ 1, Cureton and D'Agostino's lambda ≥ (n0.6)/15 (where n = the number of variables), lambda ≥ mean squared multiple correlation (SMC), 100% explained variance and a maximum likelihood based chi2 test. Five conditions of simulation were investigated: distribution of the items (normal, ordinal, binomial), the true number of factors (2 to 10 by 2), strengths of the factor loadings (0.3 to 0.9 by 0.1), the number of variables loading on each factor (3, 4, 5, 6, 9, 12) and the number of observations per variable (5, 10, 20, 30).;The results indicated that among the CA-based rules, PA produced the highest accuracy (more than 87% of the time the true number of factors was retained) and among the FA-based rules, the lambda ≥ (n0.6)/15 rule produced the highest accuracy (>77%) over all conditions of simulation. The default rules in popular statistical computing packages (e.g., SAS, S-Plus) are not the most accurate. The lambda ≥ 1 CA-based rule and the 100% variance FA-based rule were <57% and <48% accurate, respectively, over all conditions of simulation. The distribution of the items had minimal effect on rules' performance. The magnitude of the factor loadings generally had the most impact on the accuracy of the rules. The remaining conditions of simulation have less clear effects on rules' performance. Optimal results are achieved with PA, assuming adequate computer resources, and as an alternative the lambda ≥ (n0.6)/15 is recommended. Best results are achieved with factor loadings of 0.5 or greater and at least ten observations per variable.
机译：因子分析（FA）的主要目标是了解一组不同项目中的基础结构或协变。执行FA涉及几个步骤。在这里，我们着重于最重要的步骤，确定要保留的适当因素数量。；基于FA总体模型，我们使用了蒙特卡洛模拟法来评估十二种流行规则的准确性。还测试了六种基于成分分析（CA）的规则，包括lambda≥1，最小平均部分法，Bartlett's chi2检验，Horn平行分析（PA），80％解释方差和图像lambda≥1。六因素分析（FA）-测试了基于规则的规则，包括Kaiser-Guttman的特征值（解释了方差百分比）lambda≥0和lambda≥1，Cureton和D'Agostino的lambda≥（n0.6）/ 15（其中n =变量数），lambda≥均方多重相关（SMC），100％解释方差和基于最大似然的chi2检验。研究了五个模拟条件：项目的分布（正态，有序，二项式），因子的真实数量（2到10乘2），因子加载的强度（0.3到0.9乘0.1），变量加载的数量每个因子（3、4、5、6、9、12）和每个变量的观察次数（5、10、20、30）。结果表明，在基于CA的规则中，PA产生的准确性最高（超过87％的时间保留了真实的因子数量），并且在基于FA的规则中，lambda≥（n0.6）/ 15规则在所有模拟条件下均产生了最高的准确性（> 77％）。流行的统计计算程序包（例如SAS，S-Plus）中的默认规则不是最准确的。在所有模拟条件下，基于lambda≥1 CA的规则和基于100％方差FA的规则的准确度分别为<57％和<48％。项目的分布对规则的执行影响最小。因子加载的大小通常对规则的准确性影响最大。其余模拟条件对规则性能的影响不太明显。假设有足够的计算机资源，使用PA可获得最佳结果，或者建议使用lambda≥（n0.6）/ 15。因子负载等于或大于0.5且每个变量至少观察10次可获得最佳结果。

著录项

  • 作者

    Dukes, Kimberly Ann.;

  • 作者单位

    Boston University.;

  • 授予单位 Boston University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2002
  • 页码 1035 p.
  • 总页数 1035
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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