Factor analysis is a statistical method that can be used to reduce many variables into a smaller number of factors that explain the underlying structure of the data. Principal components analysis (PCA) is a type of factor analysis that is commonly used in practice.
PCA works by transforming the original variables into a new set of variables called principal components. The principal components are ordered by their eigenvalues, with the first principal component explaining the most variance in the data, followed by the second principal component, and so on.
PCA can be used for a variety of purposes, such as:
- Reducing the dimensionality of data, making it easier to visualize and interpret.
- Identifying underlying constructs that are measured by multiple variables.
- Developing scales and questionnaires
- Testing theoretical models of how variables relate to each other.
Benefits of using PCA for factor analysis in SPSS
SPSS is a popular statistical software package that includes a factor analysis procedure. In this blog post, we will provide a step-by-step guide on how to perform factor analysis using PCA in SPSS.
There are several benefits to using PCA for factor analysis in SPSS:
- PCA is a relatively easy method to understand and implement.
- PCA is relatively robust to violations of the assumptions of factor analysis.
- PCA can be used to reduce the dimensionality of data without losing too much information.
- PCA can be used to identify underlying constructs that are measured by multiple variables.
Steps involved in performing factor analysis using PCA in SPSS
To perform factor analysis using PCA in SPSS, follow these steps:
- Import your data into SPSS.
- Go to Analyze > Dimension Reduction > Factor.
- In the Factor dialog box, select the variables that you want to include in the analysis and move them to the Variables box.
- Under Extraction, select Principal components and make sure that Analyze correlation matrix is checked.
- Under Rotation, you can select a rotation method to improve the interpretability of the factor solution.
- Click OK to run the analysis.
For this blog post, I have used Divorce prediction data from Kaggle.
SPSS will output a number of tables and figures, including the factor loadings, screen plot, and communalities. You can use these results to interpret the factor solution and identify the underlying constructs that are measured by the variables. In my case, this output was generated.
The first table in output is the KMO Test, which tells if the data is adequate for factor analysis. Any value above 0.6 is good. In our case, the value is 0.964.
The next output table is ‘Communalities’. This table tells the amount of information explained by the extracted variable. Extraction value should be more than 0.5, and, in our case, it is more than 0.5.
The next output table is ‘Total Variance Explained. Here the total number of components is same as the total number of variables we selected (54). The sum of total initial eigenvalues would also be 54 and the total extraction is 100%, which means there is no loss of data.
However, we asked the application to only consider extracted components where the eigenvalue is more than 1. So, we have reduced 54 variables into 4 extracted variables (components). These 4 components explains 83.24% of variance. So, we can say that we have lost 27% of information by reducing the variables from 54 to 4.
The next output table is ‘Component Matrix’, which gives the correlation between the variables and new components. These variables were loaded on multiple components. Hence, we did geometric manipulation (rotation and sorting) for ease of interpretation to find the underlying dimension. After this, the eigen values are spread and without losing any additional information.
Note: I have suppressed correlation less than 0.6 to get a clean table for interpretation.
Now, using the Rotated Component Matrix, we can group the variables to form new derived variables. We can save these variables and then use them for our analysis. These factors are standardized (mean = 0 and variance = 1).
Alternatively, you can also compute the variable by taking the average as per the grouping provided by ‘Rotated Component Matrix’. This way the units will be preserved (same scale). This can be done from SPSS > Transform > Compute Variable. Provide the name of the target variable and then enter the expression to calculate the average.
Takeaway
PCA is a powerful tool for reducing the dimensionality of data and identifying underlying constructs. SPSS provides a straightforward way to perform factor analysis using PCA. By following the steps outlined in this blog post, you can easily perform factor analysis in SPSS and gain insights into your data.
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