Confirmatory Factor Analysis

Definition

Confirmatory factor analysis (CFA) is a statistical technique used to test whether a set of observed variables can be explained by a smaller number of underlying latent factors. This method is particularly important in validating the factor structure that was hypothesized based on theory or previous research, allowing researchers to confirm or reject their assumptions about the relationships between variables.

5 Must Know Facts For Your Next Test

1. CFA requires a clear hypothesis about the structure of relationships among observed variables and latent factors before the analysis begins.
2. In CFA, researchers specify which observed variables are expected to load onto which latent factors, allowing for testing of the proposed model.
3. Model fit indices, such as Chi-square, RMSEA, and CFI, are critical in CFA to determine how well the model explains the data.
4. CFA can be used to assess measurement invariance across groups, helping researchers understand if different populations respond similarly to measured constructs.
5. It is essential to have a sufficiently large sample size in CFA to ensure reliable and valid results, typically recommended to be at least 5 to 10 times the number of parameters being estimated.

Review Questions

• How does confirmatory factor analysis differ from exploratory factor analysis in terms of hypothesis testing?
  • Confirmatory factor analysis (CFA) differs from exploratory factor analysis (EFA) primarily in its approach to hypothesis testing. While EFA is used to uncover potential relationships and structures without pre-existing assumptions, CFA requires researchers to specify a clear hypothesis about how observed variables relate to latent factors. This means that CFA tests a predetermined model, whereas EFA is more about discovery and exploration of possible factors.
• What are some key goodness-of-fit indices used in confirmatory factor analysis, and why are they important?
  • Goodness-of-fit indices such as Chi-square, RMSEA (Root Mean Square Error of Approximation), and CFI (Comparative Fit Index) are crucial in confirmatory factor analysis because they provide quantitative measures of how well the proposed model fits the observed data. A good fit suggests that the hypothesized relationships align closely with the actual data patterns, validating the model. Understanding these indices helps researchers evaluate their models' effectiveness and make necessary adjustments.
• Critically analyze the implications of measurement invariance tested through confirmatory factor analysis on cross-cultural research.
  • Testing for measurement invariance through confirmatory factor analysis is vital in cross-cultural research as it ensures that constructs measured are understood similarly across different cultural groups. If measurement invariance holds, it implies that comparisons made across groups are valid and meaningful. Conversely, if invariance is not established, it suggests that differences observed might stem from varying interpretations of the constructs rather than true differences in the phenomena being studied. Thus, establishing measurement invariance enhances the reliability and validity of cross-cultural findings.

Related terms

Latent Variables: Variables that are not directly observed but are inferred from other variables that are measured.

Exploratory Factor Analysis:

A statistical method used to identify the underlying relationships between measured variables without a predefined structure.

Goodness-of-Fit:

A measure used in statistics to assess how well a model fits the observed data, often used in the context of confirmatory factor analysis.