How to Conduct Factor Analysis in IBM SPSS

Edited 1 day ago by ExtremeHow Editorial Team

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Factor analysis is a useful statistical technique used to understand the structure of a set of variables. It is typically applied to identify underlying relationships and reduce data into a smaller set of factors. In this guide, we will explore how to perform factor analysis using IBM SPSS Statistics, a popular software for data analysis.

Understanding factor analysis

The purpose of factor analysis is to explain the variation among observed variables and to identify latent (hidden) factors that may influence these variables. The primary goal is to reduce the complexity of a data set by grouping correlated variables together. These groups are called factors, and each factor is represented by one or more variable components that provide meaning to the data.

There are two main types of factor analysis:

• Exploratory factor analysis (EFA): This is used when you have no preconceived theory about the structure or number of factors. You explore the data to find patterns.
• Confirmatory factor analysis (CFA): This is used when you have a certain hypothesis about the alleged factor structure. CFA is not covered by the basic procedures in SPSS, but requires AMOS or other structural equation modeling tools.

Preparing data for factor analysis

Before conducting factor analysis, it is important to make sure that your data is suitable for this technique:

1. Sample size: A larger sample size is better for factor analysis. As a general rule, the sample size should be at least five times the number of variables.

2. Data suitability: Ensure that the data is suitable for factor analysis by conducting Bartlett's test of sphericity and the Kaiser-Meyer-Olkin (KMO) sampling adequacy measure. If Bartlett's test is significant (p < 0.05) and the KMO is above 0.6, your data is considered suitable.

3. Normality and linearity: The variables should be approximately normally distributed and linearly related. This helps to ensure stable and interpretable factors.

Conducting factor analysis in SPSS

Follow the steps given below to perform factor analysis in IBM SPSS Statistics:

Step 1: Open your data file

Start by launching SPSS and opening the data file you want to analyze. Click File > Open > Data and navigate to the location where your data file is located.

Step 2: Access the factor analysis menu

From the main menu, choose Analyze > Dimension Reduction > Factor. This will open the Factor Analysis dialog box, where you will specify your variables and preferences.

Step 3: Choose variables

Move the variables to be included in the analysis from the left window (variable list) to the right window (variable box). These variables are those that you think share some common factor. For example, if you are studying psychological constructs, you may have variables like anxiety, depression, stress, etc.

Step 4: Choose the extraction method

Click the Extraction... button to specify how the factors should be extracted:

• Principal components analysis: This is the most common method when the goal is purely data reduction, and no underlying factor model is assumed.
• Principal axis factoring: This is used when the assumption of underlying factors exists, focusing on shared variance.
• You can choose any other extraction method depending on your purpose and data assumptions.

Choose the number of factors you want to extract, or click Eigenvalues to let SPSS decide based on the variance.

Step 5: Specify the rotation method

Click Rotation... to open the Rotation dialog box. Rotation helps to obtain a simpler and more interpretable factor structure:

• Varimax: An orthogonal rotation method that minimizes the number of high loadings on each factor, thus simplifying interpretation.
• Oblimin: An oblique rotation method that allows factors to be correlated. Use this when you think factors may be related.

Choose a method that is consistent with your hypothesis about inter-factor relationships.

Step 6: Assess the causality of the data

In the Descriptive... option, choose KMO and Bartlett test. These statistics will help assess the factorability of your data. The output will show you whether your data is suitable for factor analysis or not.

Step 7: Run the analysis

After specifying your options, click OK to run the factor analysis. SPSS will process your data and produce an output window containing the results.

Interpreting SPSS factor analysis output

Once the analysis is complete, you will need to interpret several key components of the output generated by SPSS:

1. KMO and Bartlett test

The KMO should be above 0.6 to indicate that your sample size is sufficient for factor analysis. Bartlett's test of sphericity should be significant (p < 0.05), suggesting that the variables are correlated enough to provide a reliable factor structure.

2. Explaining the total variance

This table shows the variance explained by each extracted factor. The number of factors selected should generally account for at least 60% of the cumulative variance. The percentage of variance explained by each factor will help determine how many factors you should retain.

3. Scree plot

The scree plot provides a visual representation of the eigenvalues of each factor. Look for the "elbow," where the eigenvalues begin to flatten out. Retain factors with eigenvalues > 1, or those that are past the point where the curve flattens out.

4. Component matrix

The component matrix shows the loadings of each variable on each factor. Loading values close to 1 or -1 indicate strong relationships, while values close to 0 indicate weak relationships. Look for patterns where some variables load highly on particular factors.

5. Rotating component matrix

Rotation often makes the pattern of loadings clearer and the interpretation simpler. Each variable loads primarily on one factor, giving an idea of what the factor represents.

6. Factor transformation matrix

This matrix is only relevant if you apply oblique rotation, which makes the correlation between the rotated factors explicit. If orthogonal rotation is used, the factors will not be correlated and this matrix may not be necessary.

Detailed example of factor analysis in SPSS

Let us work through an example to illustrate the concept and implementation of factor analysis in SPSS.

Suppose you have collected survey data from 200 participants who answered questions on mental health, lifestyle, and productivity. You have variables such as "happiness," "work motivation," "fitness level," "stress level," "social activity," and so on. You suspect that common underlying factors may explain these variables.

1. Load your dataset into SPSS and select these variables: “happiness,” “work motivation,” “fitness level,” “stress level,” “social activity.”

2. Open the Factor Analysis window via Analysis > Dimension Reduction > Factor.

3. Move the selected variables to the Variables box.

4. Under Extraction, select “Principal Components” and note the eigenvalues above 1 to decide the number of factors.

5. Choose the Varimax rotation method to simplify your factor structure.

6. Run the analysis by clicking OK.

In the output, check for:

• KMO: Make sure it is above 0.6.
• Bartlett test: Verify that it is significant.
• Total variance explained: Make sure the factors explain more than 60% of the variance.
• Scree Plot: Identify where the curve flattens out.
• Rotated component matrix: Check for strong loadings on a single factor for clarity.

Based on the component loadings in the rotated component matrix, you can interpret the factors as follows:

• Factor 1: Related to "social activity" and "happiness".
• Factor 2: This includes “work motivation” and “fitness level.”
• Factor 3: Dominance of “stress level”, which indicates a negative aspect.

These results suggest three underlying factors related to social happiness, productivity-motivation, and stress. These interpretations can guide further exploratory or confirmatory research to strengthen the findings.

Conclusion

Factor analysis within SPSS is a powerful method for uncovering hidden relationships and reducing data dimensionality, helping researchers and analysts interpret complex datasets efficiently. Through proper execution of this technique – data preparation, appropriate method choice, and thorough result interpretation – you can gain meaningful insights that align with your research objectives.

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