# Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA)

## Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA)

Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) are indispensable tools in the realm of statistical analysis, particularly when delving into the internal reliability of a measurement instrument. While both methods share some commonalities, they differ significantly in their approach, assumptions, and applications. This primer aims to elucidate the distinctions and shed light on the primary functions of EFA.

Similarities between EFA and CFA:

1. Examination of Theoretical Constructs:
• Both EFA and CFA are employed to scrutinize the theoretical constructs, or factors, that underlie a set of observed items or variables.
2. Assumption of Uncorrelated Factors:
• Either method can assume that the factors are uncorrelated or orthogonal, simplifying the analysis by considering each factor in isolation.
3. Quality Assessment of Items:
• Both analyses are geared towards evaluating the quality of individual items within a dataset.
4. Applicability for Exploratory and Confirmatory Purposes:
• EFA and CFA can be utilized for both exploratory and confirmatory purposes, adapting to the researcher’s specific goals.

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Differences between EFA and CFA:

1. Number of Factors Determination:
• In EFA, the number of factors is usually determined by examining output from a principal components analysis, utilizing criteria such as eigenvalues. In contrast, CFA requires researchers to specify the number of factors a priori.
2. Factor Structure Specification:
• CFA demands that researchers specify a particular factor structure, indicating which items load on which factor. EFA allows all items to load on all factors without predefining the structure.
3. Model Fit Assessment:
• CFA provides a fit of the hypothesized factor structure to the observed data, enabling a more rigid evaluation of model fit.
4. Estimation Methods:
• While both methods use maximum likelihood to estimate factor loadings, it is crucial to note that maximum likelihood is just one of several estimators used in EFA.
• CFA allows researchers to specify correlated measurement errors, constrain loadings or factor correlations, compare alternative models, test second-order factor models, and statistically compare factor structures across different groups.

Purpose of Exploratory Factor Analysis:

EFA primarily serves the purpose of unraveling the factor structure of a measure and assessing its internal reliability. It becomes particularly valuable when researchers lack hypotheses about the underlying structure of the measure, allowing for an unbiased exploration of the data.

Deciding the Number of Factors in EFA:

The determination of the number of factors in EFA involves crucial decision points. Researchers often generate a scree plot, a graphical representation of eigenvalues against factors, to identify the point where the eigenvalues plateau, indicating the optimal number of factors. Alternatively, the Kaiser-Guttman rule suggests selecting factors with eigenvalues greater than 1.0.

Factor Extraction and Rotation:

Once the number of factors is decided, researchers proceed with factor extraction, utilizing methods such as Principal Axis Factoring. This step yields factor loadings for each item on every extracted factor. Subsequently, researchers may opt for rotation, which aims to simplify the structure by maximizing high loadings and minimizing low ones. Orthogonal and oblique rotations offer different perspectives, with the latter recognizing and incorporating potential correlations between factors.

Conclusion:

In summary, Exploratory Factor Analysis serves as a fundamental tool for researchers seeking to uncover latent structures within their data. While sharing common ground with Confirmatory Factor Analysis, EFA distinguishes itself through its flexibility, lack of a priori factor structure specification, and emphasis on exploration. Understanding the nuances between EFA and CFA is essential for researchers to choose the most suitable approach based on their objectives and the nature of their data.

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