April 22nd, 2024

Exploratory Factor Analysis

By Alex Kuo · 10 min read

Statistician using Explanatory Factor Analysis to determine underlying constructs for a set of measured variables.

Overview

In the realm of statistical analysis, Exploratory Factor Analysis (EFA) stands out as a powerful technique for simplifying complex data sets. By reducing data to a smaller set of summary variables, EFA helps researchers uncover the underlying theoretical structure of phenomena. It's particularly useful for identifying the structure of relationships between variables and respondents. In this blog, we'll delve into the intricacies of EFA, its methods, and how tools like Julius can assist in this process.

Understanding EFA Methods

EFA can be performed using two primary methods:
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1. R-type Factor Analysis: This method involves calculating factors from the correlation matrix.

2. Q-type Factor Analysis: Here, factors are calculated from individual respondents.

Driving Factor Methods

There are two methods for driving factors:
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- Principle Component Factor Analysis Method: Used when the goal is to derive the minimum number of factors and explain the maximum variance in the original variable.

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- Common Factor Analysis: Applied when the nature of the factor to be extracted is unknown, along with the common error variance.

Selection of Factors

The selection of factors to be extracted is crucial. Theoretical understanding is the first criterion. Many researchers rely on the Eigenvalue criteria, while others use the percentage and variance explained method. The scree test criteria, where Eigenvalue is plotted on a graph, is also a popular choice.

Orthogonal Rotation

Orthogonal rotation maintains axes at 90 degrees, ensuring factors are uncorrelated. It includes three methods based on rotation:

     - QUARTIMAX: Simplifies rows so variables are loaded on a single factor.

     - VARIMAX: Simplifies the factor matrix column for clear association and separation among variables.

     - EQUIMAX: A combination of QUARTIMAX and VARIMAX, simplifying both rows and columns.

Criteria for Factor Loadings

Factor loadings can be classified based on their magnitude:

     - Greater than +0.30: Minimum consideration level
     - +0.40: More important
    - +0.50: Practically significant

Power and Significance Level

Researchers can determine the statistical power and significance level. For instance, to achieve a factor loading of .55 with a power of .80, a sample of 100 is needed.

Assumptions of EFA

- Variables: Should be metric, with dummy variables considered only in special cases.

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- Sample Size: Ideally more than 200, or 5 observations per variable in some cases.

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- Homogeneous Sample: Essential for reducing sample size as the number of variables increases. Reliability analysis checks homogeneity.

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- Multivariate Normality: Not required in EFA.

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- Correlation: At least 0.30 correlation is needed between research variables.

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- Outliers: Data should be free from outliers.

Conclusion

In summary, Exploratory Factor Analysis is a robust statistical tool for simplifying and understanding complex data sets. With the right tools and understanding of its methods and assumptions, EFA can provide insightful and meaningful results in various research fields.

In the complex process of Exploratory Factor Analysis, tools like Julius can be invaluable. Julius is capable of reading and analyzing data from various sources, including Excel and CSV files. It can assist in performing regression analysis, cluster analysis, and visualizing data through graphs and charts. With Julius, researchers can efficiently manage the intricacies of EFA, from factor extraction to rotation and interpretation, streamlining the process and enhancing the accuracy of their findings.

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