## Key Points

- Factor analysis is a family of statistical methods that help you discover the underlying dimensions or factors that give rise to your observed data.
- EFA and CFA are two main types of factor analysis with different goals, assumptions, and procedures.
- EFA allows you to explore the possible structure of your data without prior assumptions, while CFA will enable you to test whether your data fit a predefined or hypothesized structure.
- The choice between EFA and CFA depends on your research question, data, and analysis level.
- EFA and CFA can be applied to various research fields, such as personality, job satisfaction, education, health, etc.

Hello, this is Zubair Goraya, a data analyst and writer for Data Analysis, a website that provides tutorials on statistical data analysis.

In this article, I will explain the difference between confirmatory factor analysis and exploratory factor analysis, two popular methods for studying data structure. I will also provide some examples, tips, and resources for using these techniques in your research.

But first, let me ask you a question:

- Have you ever wondered how to measure something that is not directly observable, such as intelligence, personality, or satisfaction?
- How do you know if the questions or the tests you use are valid and reliable indicators of these latent variables?
- How do you reduce the complexity of your data and identify the most critical factors that explain the variation in your outcomes?

If you have ever faced these questions, you must learn about factor analysis.

# Difference between Exploratory and Confirmatory factor analysis (EFA vs CFA)

Factor Analysis is a family of statistical methods that help you discover the underlying dimensions or factors that give rise to your observed data. Factor analysis can help you with theory development, psychometric instrument development, and data reduction. There are two main types of factor analysis:

- Exploratory factor analysis (EFA)
- Confirmatory factor analysis (CFA).

## What is Exploratory Factor Analysis?

Exploratory factor analysis (EFA) is a method that allows you to explore the possible structure of your data without imposing any prior assumptions or hypotheses. EFA aims to identify the number and nature of the latent factors that account for the correlations among your observed variables.

**For example**, you want to measure the construct of self-esteem using ten items from a questionnaire. You can use EFA to examine how these items are related to each other and how they can be grouped into one or more factors that represent different aspects of self-esteem.

EFA can also tell you how much variance in each item is explained by the common factors and how much is due to unique or error variance.

### EFA is helpful when

- It would help if you had a clear theoretical framework or previous research to guide your expectations about the factor structure of your data.
- You want to explore new concepts or domains that need more well-defined or measured.
- You want to reduce the dimensionality of your data and identify the most critical factors that capture the essence of your construct.
- You want to evaluate the validity and reliability of your measurement instrument and improve its design by eliminating redundant or irrelevant items.

## What is Confirmatory Factor Analysis?

**CFA requires**you to specify in advance: how many factors there are,

- Which variables are indicators of which factors?
- Whether the elements are correlated.
- CFA then compares your model with the observed data
- Provides various goodness-of-fit measures.

**For example**, suppose you have a theory that self-esteem consists of two distinct but related factors:

- Self-competence
- Self-liking.

### CFA is useful when

- You have a clear theoretical framework or previous research that supports a specific factor structure for your data.
- You want to test hypotheses or compare alternative models about the nature and number of factors underlying your construct.
- You want to assess the adequacy of your measurement instrument and its correspondence with your theoretical construct.
- You want to estimate the parameters of your model, such as factor loadings, factor correlations, and error variances.

## How are EFA and CFA Different?

## How to Choose Between EFA and CFA?

The choice between EFA and CFA depends on your research question, data, and analysis level.

Here are some guidelines to help you decide which method to use:

- If you want to explore your data structure without preconceptions, use EFA.
- If you have a clear and well-supported theory about the design of your data, use CFA.
- If you need more clarification about the structure of your data, you can use both EFA and CFA in a sequential manner. First, use EFA to generate a tentative model based on your data. Then, use CFA to test and refine your model using a different or more significant sample of data.
- If you have a large number of variables and a small number of cases, use EFA to reduce the complexity of your data and avoid overfitting.
- If you have a small number of variables and a large number of cases, use CFA to test the adequacy of your measurement instrument and estimate the parameters of your model.

## Examples of EFA and CFA

### Example 1: EFA of Personality Traits

One of the most famous applications of EFA is the development of the **Big Five personality traits model**. The Big Five model proposes that personality can be described by five broad factors:

- Openness
- Conscientiousness
- Extraversion
- Agreeableness
- Neuroticism.

To conduct an EFA of personality traits, collect data from a sample of people who respond to items measuring different personality aspects.

**For example**, you can use the 60-item NEO Five-Factor Inventory (NEO-FFI), which has 12 items for each factor. You can then apply EFA to the correlation matrix of the items using a software program such as SPSS or R.

The output of EFA will show you how many factors can be extracted from your data based on criteria such as eigenvalues, scree plots, or parallel analysis. You can also rotate the elements using methods such as varimax or obliged to make them more interpretable. The output will also show you the factor loadings, which indicate how strongly each item is related to each factor. You can then name the factors based on the content and meaning of the things with high loadings.

### Example 2: CFA of Job Satisfaction

**job satisfaction**. Job satisfaction is a complex construct that can be influenced by various aspects of work, such as:

- Pay
- Promotion
- Supervision
- Co-workers
- Work

*scale such as the Job Satisfaction Survey (JSS)*, which has 36 items that assess nine facets of job satisfaction:

- Pay
- Promotion
- Supervision
- Fringe benefits
- Contingent rewards
- Operating procedures
- Co-workers
- Nature of work
- Communication.

To conduct a CFA of job satisfaction, you must collect data from a sample of employees who respond to the JSS items using a six-point Likert scale. You can then apply CFA to the covariance matrix of the items using a software program such as AMOS or Mplus.

The output of CFA will show you how well your data fit the hypothesized model of job satisfaction. You can specify different models based on your theory or previous research.

**For example**, you can test whether job satisfaction is *a one-factor model, a nine-factor model, or a second-order model with one general factor and nine sub-factors*. The output will also show you the parameter estimates of your model, such as **factor loadings, error variances, factor correlations, and model fit indices**.

## Tips and Resources for EFA and CFA

If you want to learn more about EFA and CFA and how to apply them in your research, here are some tips and resources that you may find helpful:

- Before conducting EFA or CFA, ensure that your data meet the assumptions and requirements of these methods, such as normality, linearity, multicollinearity, sample size, etc.
- Choose an appropriate extraction method for EFA based on the type and distribution of your data. For example, principal component analysis (PCA) suits continuous and normally distributed data, while central axis factoring (PAF) is ideal for ordinal or skewed data.
- Choose an appropriate rotation method for EFA based on whether you expect your factors to be orthogonal (uncorrelated) or oblique (correlated). For example, varimax is an orthogonal rotation method, while oblivion is a diagonal rotation method.
- Choose an appropriate number of factors for EFA based on multiple criteria, such as eigenvalues more significant than one, scree plot elbow point, parallel analysis, minimum average partial correlation (MAP), etc.
- Choose an appropriate estimation method for CFA based on the type and distribution of your data. For example, maximum likelihood (ML) is suitable for continuous and normally distributed data, while weighted least squares (WLS) is suitable for ordinal or skewed data.
- Choose an appropriate model fit index for CFA based on the complexity and parsimony of your model. For example, the chi-square test is sensitive to sample size and model complexity, while the comparative fit index (CFI) and root mean square error of approximation (RMSEA) are more robust and economical.
- Compare alternative models for CFA using nested model comparison tests or information criteria. For example, the likelihood ratio test (LRT) is a nested model comparison test that compares two models that differ by one or more parameters. Akaike information criterion (AIC) and Bayesian information criterion (BIC) are information criteria that compare models based on their fit and complexity.

Interpret your results from EFA or CFA in light of your research question, theory, and previous research. Consider both the statistical significance and practical significance of your findings.

Here are some books and articles that provide more details and examples of EFA and CFA:

Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). New York: Guilford Press.

Fabrigar, L. R., & Wegener, D. T. (2012). Exploratory factor analysis. New York: Oxford University Press.

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Upper Saddle River, NJ: Prentice Hall.

Kline, R. B. (2016). Principles and practice of structural equation modelling (4th ed.). New York: Guilford Press.

Schumacker, R. E., & Lomax, R. G. (2016). A beginner's guide to structural equation modelling (4th ed.). New York: Routledge.

## Conclusion

Factor analysis is a powerful and versatile tool for studying data structure and measuring latent variables. EFA and CFA are two main types of factor analysis with different goals, assumptions, and procedures. EFA allows you to explore the possible structure of your data without prior assumptions, while CFA will enable you to test whether your data fit a predefined or hypothesized structure.

The choice between EFA and CFA depends on your research question, data, and analysis level.

I hope this article has helped you understand the difference between confirmatory factor analysis and exploratory factor analysis and how to use them in your research.

If you have any questions or comments, please contact me at info@rstudiodatalab.com or visit our discussion forum. To hire us for your data analysis needs at https://www.rstudiodatalab.com/p/order-now.html.

## FAQs

**What is the difference between EFA and CFA?**

EFA is a method that allows you to explore the possible structure of your data without prior assumptions, while CFA is a method that will enable you to test whether your data fit a predefined or hypothesized structure.

**When should I use EFA or CFA?**

It would help if you used EFA when you have no clear theoretical framework or previous research to guide your expectations about the factor structure of your data or when you want to reduce the dimensionality of your data and identify the essential factors that capture the essence of your construct. It would help if you used CFA when you have a clear theoretical framework or previous research that supports a specific factor structure for your data or when you want to test hypotheses or compare alternative models about the nature and number of factors underlying your construct.

**How do I conduct EFA or CFA?**

To conduct EFA or CFA, you need to collect data from a sample of people who respond to a set of items that measure different aspects of your construct. You can then apply EFA or CFA to the items' correlation or covariance matrix using a software program such as SPSS, R, AMOS, or Mplus.

**How do I interpret the results from EFA or CFA?**

To interpret the results from EFA or CFA, you need to consider your findings' statistical and practical significance. Following your field and journal guidelines, you must report your results using tables, figures, and text. You must also compare your results with your research question, theory, and previous research.