python因子分析
Factor Analysis (FA) is an exploratory data analysis method used to search influential underlying factors or latent variables from a set of observed variables. It helps in data interpretations by reducing the number of variables. It extracts maximum common variance from all variables and puts them into a common score.
因子分析(FA)是一种探索性数据分析方法，用于从一组观察到的变量中搜索有影响力的潜在因子或潜在变量。 通过减少变量数量，它有助于数据解释。 它从所有变量中提取最大共同方差，并将它们放入一个共同得分。
Factor analysis is widely utilised in market research, advertising, psychology, finance, and operation research. Market researchers use factor analysis to identify price-sensitive customers, identify brand features that influence consumer choice, and helps in understanding channel selection criteria for the distribution channel.
因子分析广泛应用于市场研究，广告，心理学，金融和运营研究。 市场研究人员使用因素分析来识别价格敏感的客户，识别影响消费者选择的品牌特征，并帮助理解分销渠道的渠道选择标准。
In this tutorial, you are going to cover the following topics:
在本教程中，您将涵盖以下主题：
- Factor Analysis 因子分析
- Types of Factor Analysis 因子分析的类型
- Determine Number of Factors 确定因素数
- Factor Analysis Vs. Principle Component Analysis 因子分析与 主成分分析
- Factor Analysis in Python Python中的因素分析
- Adequacy Test 充足性测试
- Interpreting the results 解释结果
- Pros and Cons of Factor Analysis 因素分析的利弊
- Conclusion 结论
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因子分析 (Factor Analysis)
Factor analysis is a linear statistical model. It is used to explain the variance among the observed variable and condense a set of the observed variable into the unobserved variable called factors. Observed variables are modeled as a linear combination of factors and error terms (Source). Factor or latent variable is associated with multiple observed variables, who have common patterns of responses. Each factor explains a particular amount of variance in the observed variables. It helps in data interpretations by reducing the number of variables.
因子分析是线性统计模型。 它用于解释观察变量之间的方差，并将一组观察变量浓缩为称为因子的未观察变量。 观察变量被建模为因子和误差项的线性组合( Source )。 因子或潜在变量与具有共同响应模式的多个观察变量相关。 每个因素都说明了观察变量中的特定方差量。 通过减少变量数量，它有助于数据解释。
Factor analysis is a method for investigating whether a number of variables of interest X1, X2,……., Xl, are linearly related to a smaller number of unobservable factors F1, F2,..……, Fk.
因子分析是一种研究感兴趣的变量X1，X2，……，X1是否与较少数量的不可观察因子F1，F2，……，Fk线性相关的方法。
Source: This image is recreated from an image that I found in factor analysis notes. The image gives a full view of factor analysis.
来源：此图像是根据我在因子分析说明中找到的图像重新创建的。 该图提供了因素分析的完整视图。
Assumptions:
假设：
- There are no outliers in data. 数据中没有异常值。
- The sample size should be greater than the factor. 样本数量应大于因子。
- There should not be perfect multicollinearity. 不应有完美的多重共线性。
- There should not be homoscedasticity between the variables. 变量之间不应有同调性。
因子分析的类型 (Types of Factor Analysis)
- Exploratory Factor Analysis: It is the most popular factor analysis approach among social and management researchers. Its basic assumption is that any observed variable is directly associated with any factor. 探索性因素分析：它是社会和管理研究人员中最流行的因素分析方法。 它的基本假设是，任何观察到的变量都与任何因素直接相关。
- Confirmatory Factor Analysis (CFA): Its basic assumption is that each factor is associated with a particular set of observed variables. CFA confirms what is expected on the basis. 验证性因素分析(CFA)：其基本假设是每个因素都与一组特定的观察变量相关联。 CFA确认在此基础上的期望。