5: Factor Analysis

Question 1

_____ is a statistical technique used in research to identify and interpret underlying patterns or structures in a set of observed variables. It is particularly useful in fields like psychology, sociology, and education to understand the relationships among variables and reduce data complexity.

Answer 1

Exploratory Factor Analysis (EFA)

Question 2

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1. Dimensionality Reduction: EFA helps in identifying the underlying factors or dimensions that explain the observed correlations or covariances among variables.
2. Identifying Latent Constructs: It is used to uncover the latent or unobserved constructs that may be influencing the observed variables.

Answer 2

Purpose

Question 3

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1. Linearity: EFA assumes that the relationships among variables are linear.
2. No Multicollinearity: Variables should not be highly correlated with each other.
3. Sample Size: Adequate sample size is required for reliable results, although specific requirements may vary based on the complexity of the data.

Answer 3

Assumptions

Question 4

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1. Data Collection and Preparation: Gather the relevant dataset and ensure that variables are appropriately coded and scaled.
2. Correlation or Covariance Matrix: Calculate the correlation matrix if variables are on different scales, or the covariance matrix if they are on the same scale.
3. Factor Extraction: This step involves selecting a method for extracting the factors. Common methods include Principal Component Analysis (PCA) and Principal Axis Factoring (PAF).
4. Factor Rotation: After extraction, factors can be rotated to achieve a simpler, more interpretable solution. Common rotation methods include Varimax and Promax.
5. Factor Interpretation: Interpret the rotated factors based on the pattern of loadings (correlations between variables and factors).
6. Factor Naming: Assign meaningful names to the identified factors based on the variables with high loadings.

Answer 4

Steps in EFA

Question 5

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1. Factor Loadings: These indicate the strength and direction of the relationship between each variable and the identified factors. Loadings closer to +1 or -1 indicate a stronger relationship.
2. Eigenvalues: They indicate the amount of variance explained by each factor. Higher eigenvalues suggest more important factors.
3. Scree Plot: A graphical representation of eigenvalues, which helps in determining the number of factors to retain.
4. Communality: It measures the proportion of a variable’s variance that is accounted for by the extracted factors.

Answer 5

Results Interpretation

Question 6

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1. Over-Extraction: Extracting too many factors can lead to overfitting and misinterpretation of results.
2. Ignoring Theory: EFA should be guided by theory. Interpreting factors without theoretical basis can lead to spurious findings.
3. Ignoring Model Fit: Some indices, like the Kaiser-Meyer-Olkin (KMO) measure and Bartlett’s Test of Sphericity, help assess the adequacy of the data for factor analysis.

Answer 6

Common Pitfalls

Question 7

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In research papers, report the factors identified, their loadings, eigenvalues, and any rotated factor solutions. Discuss the interpretability and implications of the factors.

Remember, EFA is an exploratory technique, meaning it is used to generate hypotheses rather than confirm them. Confirmatory Factor Analysis (CFA) is a related technique that tests specific hypotheses about the factor structure based on prior theory.

Answer 7

Reporting