Factor Analysis: Introduction and Types
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Questions and Answers

The ______ rotation method is used for orthogonal rotation.

Varimax

The ______ rotation allows for factors to be correlated with each other.

Promax

Varimax rotation focuses on maximizing the variance of ______ loadings.

squared

Challenges in factor analysis include ensuring the ______ of the correlation matrix.

<p>sphericity</p> Signup and view all the answers

A principal challenge in factor analysis is accurately interpreting ______ loadings.

<p>factor</p> Signup and view all the answers

Quartimax is another type of ______ rotation used in factor analysis.

<p>orthogonal</p> Signup and view all the answers

The decision to use an orthogonal versus an oblique rotation depends on the expected ______ among the factors.

<p>correlation</p> Signup and view all the answers

In factor analysis, the goal is often to reduce data and identify underlying ______.

<p>factors</p> Signup and view all the answers

For uncorrelated factors, select ______ rotation.

<p>Varimax</p> Signup and view all the answers

For correlated factors, choose ______ rotation.

<p>Promax</p> Signup and view all the answers

The ______ rotation aims to simplify the factors by maximizing the variance of the squared loadings of each factor.

<p>Varimax</p> Signup and view all the answers

The interpretation of factor loadings involves examining values above ______ to assess strong associations.

<p>0.5</p> Signup and view all the answers

A common challenge in factor analysis includes determining the appropriate number of ______ to retain.

<p>factors</p> Signup and view all the answers

Using a ______ plot can help visualize the number of factors to keep based on the data’s variance.

<p>Scree</p> Signup and view all the answers

Choosing to suppress small coefficients in your output can help with the ______ of the results.

<p>interpretation</p> Signup and view all the answers

A KMO value greater than ______ indicates that your data is suitable for factor analysis.

<p>0.6</p> Signup and view all the answers

The ______ method is a type of orthogonal rotation that maximizes the variance of factor loadings.

<p>Varimax</p> Signup and view all the answers

In contrast to Varimax, ______ rotation allows for the factors to be correlated.

<p>Promax</p> Signup and view all the answers

The ______ rotation method allows for a more generalized approach by accommodating both orthogonal and oblique structures.

<p>Quartimax</p> Signup and view all the answers

Factor ______ indicate the strength and direction of the relationship between each variable and the underlying factor.

<p>loadings</p> Signup and view all the answers

One of the challenges in factor analysis is deciding on the number of ______ to retain in the model.

<p>factors</p> Signup and view all the answers

Poorly chosen factors can lead to ______ in factor analysis, which may obscure the real structure of the data.

<p>challenges</p> Signup and view all the answers

Orthogonal rotation methods like Varimax assume that the ______ are uncorrelated.

<p>factors</p> Signup and view all the answers

EFA is particularly useful for identifying the ______ structures that underlie observed variables.

<p>latent</p> Signup and view all the answers

Flashcards

PCA in SPSS

Principal Component Analysis (PCA) in SPSS is a statistical method used to reduce a large set of variables into a smaller set of uncorrelated variables called principal components.

KMO > 0.6

Kaiser-Meyer-Olkin Measure of Sampling Adequacy (KMO) value greater than 0.6 indicates that the variables in the dataset are suitable for factor analysis.

Bartlett's Test

A statistical test to determine if the correlation matrix is significantly different from an identity matrix.

Principal Components

Uncorrelated variables extracted from a larger set of variables using PCA, capturing the significant variance in the data

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Eigenvalues > 1

A method to determine the number of principal components to keep in PCA by retaining components with eigenvalues greater than 1.

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Varimax Rotation

Orthogonal rotation method used in factor analysis that simplifies component interpretation by maximizing the variance in loading values.

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Extraction Method

The method used to determine the factors from the original variables.

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Suppress Small Coefficients

Ignoring factor loadings or correlations below a certain threshold to improve the clarity and interpretation of results

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Exploratory Factor Analysis (EFA)

A statistical method used to identify underlying patterns or factors in a set of observed variables.

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Factor Loading

The correlation between a variable and a factor; a value above 0.5 indicates a strong relationship.

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Principal Axis Factoring

A method for extracting factors in EFA based on correlations among the variables.

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KMO and Bartlett's Test

Tests used to check if the data is suitable for factor analysis: High KMO (>0.6) and significant Bartlett's test (p<0.05) are needed.

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Total Variance Explained

A measure of how much variance in the data is explained by the chosen factors.

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Varimax (orthogonal)

A rotation method used in EFA that results in uncorrelated factors.

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Scree Plot

A graphical method used to determine the optimal number of factors to retain in EFA; look for the 'elbow'.

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Rotated Factor Matrix

A table showing the factor loadings after rotation, helps to interpret factors based on the variables with high loadings.

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PCA's Role in Data Preprocessing

PCA reduces noise and multicollinearity in data, preparing it for analyses like clustering or regression.

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PCA Components

Linear combinations of original variables used to represent the data's variance.

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PCA's Goal

Reduce dataset dimensions while preserving most variance (information).

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EFA's Purpose

Finds underlying structure in a dataset, assuming latent constructs explain correlations among variables.

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EFA's Exploratory Nature

Used when the researcher lacks a specific hypothesis on the underlying factor structure.

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Correlation Matrix (EFA)

Used in EFA to find highly correlated variables, grouping them together.

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Factor Extraction (EFA)

Identifies factors explaining correlations amongst the variables using methods like Principal Axis Factoring or Maximum Likelihood.

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Study Notes

Factor Analysis: Introduction and Types

  • Factor analysis is a statistical method used to reduce a large number of observed variables into a smaller set of underlying factors.
  • It identifies patterns and relationships among variables, revealing latent constructs.
  • Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA) are two main types.
  • PCA aims to maximize variance in data. It doesn't assume latent variables.
  • EFA aims to unveil underlying latent constructs and their relationships. It assumes unobserved factors affect the observed variables.

Principal Component Analysis (PCA)

  • PCA standardizes variables (if necessary) to work with data measured on different scales.
  • It calculates the covariance matrix of the standardized variables.
  • It extracts eigenvalues and eigenvectors to determine the principal components.
  • Eigenvalues represent the amount of variance explained by each component.
  • Components are ranked by how much variance they explain. The first explains the maximum, then the second and so on.
  • Variables with eigenvalues greater than 1 (or visual inspection of scree plot) are retained for dimension reduction. Reducing the number of variables simplifies data.
  • PCA is used for dimensionality reduction and visualization of high-dimensional data. It's also used as a preprocessing step in other analyses.

Exploratory Factor Analysis (EFA)

  • EFA begins by calculating a correlation matrix to identify groups of highly correlated variables.
  • Several extraction methods exist; Principal Axis Factoring and Maximum Likelihood are common choices.
  • Rotations (orthogonal or oblique) simplify factor structure for easier interpretation (e.g. Varimax or Promax).
  • Factor loadings represent the strength of relationship between variables and factors.
  • Decisions about the number of factors are made based on statistical criteria (e.g., eigenvalues > 1) or scree plots. Statistical criteria & scree plots are helpful for determining relevant variables to keep for the analysis.
  • EFA is used for scale development, identifying latent constructs, and simplifying data.

Differences Between PCA and EFA

  • PCA focuses on maximizing variance, while EFA aims to uncover latent constructs.
  • PCA does not assume underlying factors, EFA assumes they exist.
  • PCA is appropriate for dimension reduction, EFA is used when uncovering constructs is the goal.

Performing Factor Analysis in SPSS

  • Preliminary Steps: Ensure variables are continuous, check correlations (0.3-0.8), and have a sufficient sample size (e.g., 5-10 cases per variable).
  • PCA (in SPSS): Open data, select 'Analyze' -> 'Dimension Reduction' -> 'Factor', enter variables, select extraction method, choose rotation method (Varimax or Promax), check 'options' to generate output (sorted loadings, suppressing small coefficients) & run.
  • EFA (in SPSS): Similar steps to PCA , but specify either 'Principal Axis Factoring' or 'Maximum Likelihood' as the extraction method in the 'Extraction' tab.

Interpreting Factor Analysis Output

  • KMO and Bartlett's Test: Evaluate the suitability of data for factor analysis. A high KMO value (e.g., > 0.6) and significant Bartlett's test suggests appropriate data.
  • Total Variance Explained: Shows how much variance each extracted component explains, ideally ≥60% for satisfactory results.
  • Component Matrix: Displays the correlations between variables and extracted components.
  • Rotated Component Matrix: After rotation, displays factor loadings (correlations between variables and factors) clarifying factor structure. Visualization via a scree plot.

Parsimonious Factors

  • Parsimony in factor analysis emphasizes using the fewest factors possible to explain observed variables effectively.
  • Criteria for factor retention include eigenvalues (Kaiser's rule), scree plots, and parallel analysis.
  • High factor loadings improve parsimonious factors (factors representing distinctive underlying themes), while low or cross-loadings indicate redundant/unclear factors.
  • Rotation methods and selection of appropriate factors improve efficiency and clarity of interpretations.

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Related Documents

Factor Analysis PDF

Description

Explore the fundamentals of factor analysis, including its purpose in reducing observed variables to underlying factors. Learn about the main types, Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA), and their distinct approaches to understanding data patterns.

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