The difference between exploratory and confirmatory factor analysis

Sample Solution

Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) are both statistical techniques used to understand the underlying structure of a set of observed variables by identifying latent factors that explain the patterns of correlations among them. However, they differ significantly in their purpose, approach, and the level of prior knowledge required.  

Exploratory Factor Analysis (EFA)

• Purpose: EFA is primarily used to explore the underlying factor structure of a set of variables when the researcher has little or no prior knowledge or hypotheses about the number of factors or which variables might load onto which factors. It is a data-driven approach aimed at discovering the latent constructs that might be driving the observed relationships. EFA is often employed in the early stages of scale development or theory building.  
• Approach: In EFA, all measured variables are typically allowed to load on any of the extracted factors. The analysis aims to determine:
  • The number of factors that best explain the variance in the data.
  • Which variables are most strongly associated with each factor (factor loadings).
  • The overall structure and interpretability of these factors.
• Prior Knowledge: EFA requires minimal prior theoretical assumptions about the factor structure. The researcher lets the data reveal the underlying relationships.

Full Answer Section

• Output: The main outputs of EFA include:
  • A correlation matrix of the observed variables.
  • Eigenvalues and scree plots to help determine the number of factors.
  • A factor loading matrix indicating the strength and direction of the relationship between each variable and each factor.
  • Communalities, representing the proportion of variance in each variable accounted for by the extracted factors.
  • Rotated factor loadings (using methods like Varimax or Oblimin) to improve interpretability.
• Goal: The goal of EFA is to identify and define the underlying constructs and to generate hypotheses about the relationships between observed variables and these constructs.  

Confirmatory Factor Analysis (CFA)

• Purpose: CFA is used to test a pre-specified hypothesis about the factor structure of a set of variables. The researcher has a clear theoretical framework or prior empirical evidence suggesting a particular number of factors and which variables should load onto which factors. CFA aims to determine how well the hypothesized model fits the observed data. It is often used to validate the factor structure of existing scales or to test specific theoretical models of latent constructs.  
• Approach: In CFA, the researcher explicitly specifies the factor structure, including:
  • The number of factors.
  • Which observed variables are indicators of which latent factors (factor loadings are constrained to be zero for variables not expected to load on a particular factor).
  • Whether the factors are correlated or uncorrelated.
• Prior Knowledge: CFA requires a strong theoretical or empirical basis for the hypothesized factor structure. The researcher has a clear model in mind before analyzing the data.  
• Output: The main outputs of CFA include:
  • Model fit indices (e.g., Chi-square, RMSEA, CFI, TLI) that indicate how well the hypothesized model reproduces the observed covariance matrix.  
  • Factor loadings, indicating the strength and significance of the relationships between the observed variables and their hypothesized latent factors.  
  • Covariances or correlations between the latent factors.
  • Modification indices, which suggest potential ways to improve model fit by freeing constrained parameters.
• Goal: The goal of CFA is to evaluate the goodness of fit of a theoretically derived measurement model to the observed data. It aims to confirm whether the data supports the hypothesized relationships between observed variables and latent constructs.  

Key Differences Summarized:

In essence, EFA is used when you don't know the factor structure and want to find out, while CFA is used when you have a good idea of the factor structure and want to test if your data supports it. It's not uncommon for researchers to use EFA on one dataset to develop a model and then use CFA on a new dataset to confirm that model.