Factor Analysis in 2023: What’s New and Why You Should Care

7 min readSep 22, 2023

Factor analysis is a statistical technique that can help you explore the underlying structure of your data. It can also help you to reduce the number of variables and identify latent factors. And test hypotheses about the relationships between observed and unobserved variables.

In this article, you will learn everything you need to know about factor analysis:

What is factor analysis, and why is it useful?
What are the types of factor analysis, and how to choose the right one?
How to perform factor analysis using RStudio?
How to interpret and report the results of factor analysis?

By the end of this article, you will be able to perform factor analysis on your own data sets and use it for data analysis and exploratory research. You will also learn tips and tricks to improve your factor analysis skills and avoid common pitfalls. So, let’s get started!

What is Factor Analysis, and Why is it Useful?

Factor analysis is a statistical method that explains the variation and correlation among a large set of observed variables in terms of a smaller number of unobserved variables called factors. Factors are latent variables that show the underlying dimensions or constructs that influence the observed variables. For example, you measure student’s academic performance in different subjects. In that case, some common factors such as intelligence, motivation, or interest might affect their scores.

Factor analysis can help you with several purposes, such as:

Data reduction: You can reduce the number of variables in your data set by grouping them into smaller factors that capture the most information. It can make your data easier to manage and analyze.
Data exploration: You can discover your data’s hidden structure and patterns by identifying the factors influencing your variables. It can help you generate new hypotheses and insights about your data.
Data validation: You can test whether your variables measure what they are supposed to measure by examining how well they load onto the expected factors. It can help you assess the validity and reliability of your measurements.

Factor analysis is commonly used in various fields, such as psychology, education, marketing, sociology, and economics. It can help you answer questions like:

What are the main factors that affect customer satisfaction?
How many dimensions of personality are there, and what are they?
What are the key skills and competencies that employees need for their jobs?
How do different countries compare on cultural values and attitudes?

What are the Types of Factor Analysis and How to Choose the Right One?

There are two main types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). The difference between them lies in the degree of prior knowledge and assumptions that you have about the factor structure of your data.

Exploratory Factor Analysis (EFA)

Exploratory factor analysis (EFA) is used when you need more prior knowledge about the number and nature of the factors in your data. EFA aims to discover the underlying factors by exploring the patterns of correlations among the observed variables. EFA does not restrict how many factors or how they are related.

EFA involves two main steps:

Factor extraction
Factor rotation

Factor extraction estimates how many factors and how much variance they explain. Factor rotation is the process of adjusting the orientation of the factors to make them easier to interpret.

There are different methods for factor extraction, such as

Principal component analysis (PCA)
Principal axis factoring (PAF)
Maximum likelihood (ML) and others.

Each method has its assumptions and advantages. For example, PCA assumes that all the variance in the observed variables is due to common factors, while PAF assumes that some variance is due to unique factors or errors. PCA tends to extract more factors than PAF, but PAF produces more realistic estimates of factor loadings.

There are also different methods for factor rotation, such as varimax, quartimax, oblimin, promax, and others. Each method has its criteria for optimizing the factor solution. For example, varimax tries to maximize the variance of each factor across the variables, while Oblimin tries to minimize it. Varimax produces orthogonal factors (uncorrelated), while oblimin produces oblique factors (correlated).

The choice of factor extraction and rotation methods depends on several factors, such as:

The type and level of measurement of your variables
The distribution and normality of your data
The size and adequacy of your sample
The purpose and research question of your analysis
The theoretical and empirical support for your factor model

Confirmatory Factor Analysis (CFA)

Confirmatory factor analysis (CFA) is used when you have some prior knowledge or hypothesis about the number and nature of the factors in your data. CFA aims to test whether your data fit your proposed factor model by comparing the observed correlations with the expected correlations based on the model. CFA imposes some restrictions on how many factors there are and how they are related.

CFA involves specifying and estimating your factor model using a structural equation modelling (SEM) framework. SEM is a general technique that can handle complex models with multiple factors, multiple indicators, and multiple relationships. SEM allows you to estimate the factor loadings, factor correlations, factor variances, error variances, and other parameters of your model.

There are different methods for estimating your factor models, such as

Maximum likelihood (ML)
Generalized least squares (GLS)
Weighted least squares (WLS), and others.

Each method has its assumptions and limitations. For example, ML assumes that your data are multivariate normal, while WLS does not. ML tends to produce more accurate estimates than WLS, but WLS produces more robust estimates when the data are abnormal.

There are also different methods for evaluating the fit of your factor model, such as the chi-square test, comparative fit index (CFI), root mean square error of approximation (RMSEA), and others. Each method has its criteria for judging the goodness of fit. For example, the chi-square test compares the observed and expected covariance matrices, while CFI compares the fit of your model with the fit of a null model. The chi-square test tends to be sensitive to sample size and model complexity, while CFI tends insensitive.

The choice of estimation and evaluation methods depends on several factors, such as:

The type and level of measurement of your variables
The distribution and normality of your data
The size and adequacy of your sample
The complexity and parsimony of your model
The reliability and validity of your indicators

Tips and Tricks to Improve Your Factor Analysis Skills

Factor analysis is a powerful and versatile technique that can factor with various data analysis and research purposes. However, it is also a complex and challenging technique that requires careful attention and practice. Here are some tips and tricks to improve your factor analysis skills and avoid common pitfalls:

Always check the assumptions and conditions for factor analysis before performing it. Ensure that your data are measured appropriately, have enough variation and correlation, are normally distributed, and have a sufficient sample size. If your data do not meet these assumptions, you may need to transform or modify them or use a different technique.
Always choose the right type and factor analysis method for your data and research question. Decide whether you want to perform EFA or CFA depending on your prior knowledge and hypothesis. Choose the best extraction, rotation, estimation, and evaluation method depending on your data characteristics and model specifications. Compare different methods and models to find the optimal solution.
Always interpret and report the results of factor analysis clearly and concisely. Explain the meaning and significance of the factors, their indicators, their relationships, and their fit to the data. Use tables, graphs, equations, and text to present the results logically and coherently. Provide evidence and support for your conclusions and implications.
Always use reliable and valid sources of information and guidance for factor analysis. Consult textbooks, journals, websites, blogs, podcasts, videos, courses, workshops, experts, and peers that can help you learn and apply factor analysis correctly and effectively. Avoid sources that are outdated, inaccurate, biased, or misleading.
Always practice and improve your factor analysis skills using real or simulated data sets. Try to perform factor analysis on different types of data sets with different purposes and questions. Compare your results with those of others or with the expected results. Identify your strengths and weaknesses in factor analysis and work on them.

Conclusion

Factor analysis is a statistical technique that can help you explore the underlying structure of your data. It can help you reduce the number of variables, identify latent factors, and test hypotheses about the relationships between observed and unobserved variables.

There are two main types of factor analysis: exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). EFA is used when you know more about the number and nature of the factors in your data. CFA is used when you have some prior knowledge or hypothesis about the number and nature of the factors in your data.

To improve your factor analysis skills, you need to check the assumptions and conditions for factor analysis before performing it, choose the right type and method of factor analysis for your data and research question, interpret and report the results of factor analysis clearly and concisely, use reliable and valid sources of information and guidance for factor analysis, practice and improve your factor analysis skills using actual or simulated data sets.

We hope this article has helped you understand what factor analysis is, how to use RStudio, and how to improve your skills. If you have any questions or comments about this article or factor analysis in general, please get in touch with us at info@data03.online or visit our website at [data03.online]. You can also hire us to perform factor analysis at order now.

Originally published at https://www.data03.online.