Exploratory factor analysis

Exploratory factor analysis attempts to identify underlying variables, or factors, that explain the pattern of correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a small number of factors that explain most of the variance that is observed in a much larger number of manifest variables. Factor analysis can also be used to generate hypotheses regarding causal mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to performing a linear regression analysis).

The Exploratory Factor Analysis procedure offers a high degree of flexibility:

  • Seven methods of factor extraction are available.
  • Five methods of rotation are available, including direct oblimin and promax for nonorthogonal rotations.
  • Three methods of computing factor scores are available, and scores can be saved as variables for further analysis.
Example
What underlying attitudes lead people to respond to the questions on a political survey as they do? Examining the correlations among the survey items reveals that there is significant overlap among various subgroups of items (questions about taxes tend to correlate with each other, questions about military issues correlate with each other, and so on). With factor analysis, you can investigate the number of underlying factors and, in many cases, identify what the factors represent conceptually. Additionally, you can compute factor scores for each respondent, which can then be used in subsequent analyses. For example, you might build a logistic regression model to predict voting behavior based on factor scores.
Statistics
For each variable: number of valid cases, mean, and standard deviation. For each factor analysis: correlation matrix of variables, including significance levels, determinant, and inverse; reproduced correlation matrix, including anti-image; initial solution (communalities, eigenvalues, and percentage of variance explained); Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett's test of sphericity; unrotated solution, including factor loadings, communalities, and eigenvalues; and rotated solution, including rotated pattern matrix and transformation matrix. For oblique rotations: rotated pattern and structure matrices; factor score coefficient matrix and factor covariance matrix. Plots: scree plot of eigenvalues and loading plot of first two or three factors.

Data considerations

Data
The variables should be quantitative at the interval or ratio level. Categorical data (such as religion or country of origin) are not suitable for factor analysis. Data for which Pearson correlation coefficients can sensibly be calculated should be suitable for factor analysis.
Assumptions
The data should have a bivariate normal distribution for each pair of variables, and observations should be independent. The factor analysis model specifies that variables are determined by common factors (the factors estimated by the model) and unique factors (which do not overlap between observed variables); the computed estimates are based on the assumption that all unique factors are uncorrelated with each other and with the common factors.

Obtaining an Exploratory factor analysis

This feature requires Statistics Base Edition.

  1. From the menus choose:

    Analyze > Dimension reduction > Exploratory factor analysis

  2. Click Select variables under the Variables section and select at least two variables for which you want to identify factors. Click OK after selecting the variables.
  3. Optionally, click Select variable under the Case selection variable section and select a variable that limits the analysis to a subset of cases that have a particular values for the selected variable. Click OK after selecting the variable.

    Click the Define selection rule* link next to the case selection variable and specify an integer as the selection rule value. Cases defined by the selection rule are included in model estimation. Click OK after specifying a value.

  4. Optionally, you can select the following options from the Additional settings menu:
    • Click Statistics to select which statistics to include in the procedure.
    • Click Extraction to specify the method of factor extraction.
    • Click Rotation to select the method of factor rotation.
    • Click Scores to display factor score coefficients information.
    • Click Plots to specify charting options for factor eigenvalues and factor loadings.
    • Click Options to specify display format and missing values settings.
    • Click Save to dataset to create new variables for each factor in the final solution.

This procedure pastes FACTOR command syntax.