Most Commonly used Terms in Factor Analysis
In factor analysis, several terms are commonly used to describe various concepts and components of the analysis. Below is a table listing some of the most commonly used terms in factor analysis:
| Term | Description |
|---|---|
| Factor | Latent variable representing a group of observed variables that are related and tend to co-occur. |
| Factor Loading | Correlation coefficient between the observed variable and the underlying factor. |
| Eigenvalue | A value indicating the amount of variance explained by each factor. |
| Communalities | The proportion of each observed variable’s variance that can be explained by the factors. |
| Extraction Method | The technique used to extract the initial factors from the observed variables (e.g., principal component analysis, maximum likelihood). |
| Rotation | A method used to rotate the factors to achieve simpler and more interpretable factor structure (e.g., Varimax, Promax). |
| Factor Matrix | A matrix showing the loadings of observed variables on extracted factors. |
| Scree Plot | A plot used to determine the number of factors to retain based on the magnitude of eigenvalues. |
| Kaiser-Meyer-Olkin (KMO) Measure | A measure of sampling adequacy, indicating the suitability of data for factor analysis. Values range from 0 to 1, with higher values indicating better suitability. |
| Bartlett’s Test | A statistical test used to determine whether the observed variables are intercorrelated enough for factor analysis. |
| Factor Rotation | The process of rotating the factors to achieve a simpler and more interpretable factor structure. |
| Factor Scores | Scores that represent the value of each factor for each individual observation. |
| Factor Variance | The amount of variance in the observed variables explained by each factor. |
| Loading Plot | A plot used to visualize the factor loadings of observed variables on the extracted factors. |
| Factor Rotation Criterion | A rule or criterion used to determine the appropriate rotation method and angle to achieve a simpler and more interpretable factor structure. |
Let us discuss some of these Factor Analysis terms:
- Factor Loadings:
- Factor loadings represent the correlations between the observed variables and the underlying factors in factor analysis. They indicate the strength and direction of the relationship between each variable and each factor.
- Squaring the standardized factor loading gives the “communality,” which represents the proportion of variance in a variable explained by the factor.
- Factor loadings represent the correlations between the observed variables and the underlying factors in factor analysis. They indicate the strength and direction of the relationship between each variable and each factor.
- Communality:
- Communality is the sum of the squared factor loadings for a given variable across all factors.It measures the proportion of variance in a variable that is explained by all the factors jointly.
- Communality can be interpreted as the reliability of the variable in the context of the factors being considered.
- Communality is the sum of the squared factor loadings for a given variable across all factors.It measures the proportion of variance in a variable that is explained by all the factors jointly.
- Spurious Solutions:
- If the communality of a variable exceeds 1.0, it indicates a spurious solution, which may result from factors such as a small sample size or extracting too many or too few factors.
- Uniqueness of a Variable:
- Uniqueness of a variable represents the variability of the variable minus its communality.It reflects the proportion of variance in a variable that is not accounted for by the factors.
- Eigenvalues/Characteristic Roots:
- Eigenvalues measure the amount of variation in the total sample accounted for by each factor.They indicate the importance of each factor in explaining the variance in the variables.
- A higher eigenvalue suggests a more important factor in explaining the data.
- Eigenvalues measure the amount of variation in the total sample accounted for by each factor.They indicate the importance of each factor in explaining the variance in the variables.
- Extraction Sums of Squared Loadings:
- These are the sums of squared loadings associated with each extracted factor.They provide information on how much variance in the variables is accounted for by each factor.
- Factor Scores:
- Factor scores represent the scores of each case (row) on each factor (column) in the factor analysis.They are computed by multiplying each case’s standardized score on each variable by the corresponding factor loading and summing these products.
Factor Analysis | Data Analysis
Factor analysis is a statistical method used to analyze the relationships among a set of observed variables by explaining the correlations or covariances between them in terms of a smaller number of unobserved variables called factors.
Table of Content
- What is Factor Analysis?
- What does Factor mean in Factor Analysis?
- How to do Factor Analysis (Factor Analysis Steps)?
- Factor Analysis Example (Factor Analyzer):
- Why do we need factor analysis?
- Most Commonly used Terms in Factor Analysis
- Types of Factor Analysis
- Types of Factor Extraction Methods
- Assumptions of Factor Analysis
- FAQs : Factor analysis