Factor Analysis

Definition

Factor analysis is a statistical method used to identify underlying relationships between variables by grouping them into factors. This technique simplifies data by reducing the number of variables and uncovering the latent structure that explains the correlations among observed variables. It is widely used in multivariate analysis to help researchers understand complex datasets and make informed decisions.

5 Must Know Facts For Your Next Test

1. Factor analysis can be exploratory or confirmatory; exploratory factor analysis (EFA) is used when researchers are unsure about the structure of the data, while confirmatory factor analysis (CFA) tests a hypothesized structure.
2. The number of factors extracted is determined based on criteria like eigenvalues greater than 1, visual inspections of scree plots, or theoretical justification.
3. Communalities indicate how much variance in each variable is explained by the extracted factors, providing insight into how well the model fits the data.
4. Rotation methods, such as Varimax or Promax, are applied to clarify the factor structure and make interpretation easier by maximizing high loadings and minimizing low loadings.
5. Factor analysis assumes linear relationships among variables and requires sufficient sample sizes to produce stable results, typically at least 5-10 observations per variable.

Review Questions

• How does factor analysis assist in simplifying complex datasets, and what role do latent variables play in this process?
  • Factor analysis simplifies complex datasets by identifying groups of related variables, or factors, that explain the underlying patterns within the data. Latent variables represent these underlying factors that are not directly measured but are inferred from observed data. By grouping observed variables into factors based on their correlations, factor analysis helps researchers focus on the most important relationships and reduces dimensionality, making interpretation more manageable.
• What are the differences between exploratory and confirmatory factor analysis, and when would you use each approach?
  • Exploratory factor analysis (EFA) is used when researchers do not have a preconceived notion about how many factors exist within the data, allowing them to uncover potential structures. In contrast, confirmatory factor analysis (CFA) is employed when researchers have specific hypotheses about the number and nature of factors and want to test whether their model fits the observed data. EFA is often used in the initial stages of research, while CFA is more common when validating theoretical constructs.
• Evaluate the impact of rotation methods on factor analysis results and discuss their significance in interpreting the extracted factors.
  • Rotation methods significantly impact the results of factor analysis by clarifying and simplifying the structure of the extracted factors. Techniques like Varimax maximize variance across factors for better separation, while Promax allows for correlations between factors. The choice of rotation can lead to different interpretations of what each factor represents and influence how findings are applied in research. Therefore, understanding rotation methods is crucial for accurately interpreting results and making sound conclusions based on the analysis.

Related terms

Principal Component Analysis:

A technique closely related to factor analysis that transforms correlated variables into a smaller number of uncorrelated variables called principal components.

Latent Variables: Variables that are not directly observed but are inferred from other variables, often representing underlying factors in factor analysis.

Eigenvalues: Values that represent the amount of variance captured by each factor in factor analysis, helping to determine the number of factors to retain.