# How to calculate composite factor scores post factor analysis for a questionnaire?

I have a question with regard to calculating composite factor scores after running a factor analysis in SPSS. My research is on work related stress and I collected my data through a perceived stress questionnaire. I check for reliability for all sub scales and ran a factor analysis and obtained a clean factor solution extracting four factors. Each factor consists of 5-6 items.

• How do I calculate the totals for each factor?
• Should I calculate the scores before or after centering the data?

Typically, questionnaires where all items are on the same response scale are coded differently to composite variables where you have variables on different metrics (e.g., a set of ability tests).

Sums and means: For questionnaires like yours, you would commonly just take the mean or the sum of items that belong to a given subscale (note that you may need to first reverse code some of the items). I have a few notes here about doing this in SPSS and R. I generally prefer this method: (a) it's simpler; (b) it's easy to compare scores across studies; (c) it doesn't force orthogonality or require choices about degree of correlation between factors, rather it is determined by item content; (d) by using the mean, you get values that are on the same scale as the original response scale.

Test manual: More generally, assuming the test has been used before, you should examine the test manual or other published studies to see how the test is intended to be scored. By following these instructions, you will make your results more comparable to other studies that have used the test.

Factor saved scores: There is also an argument for using factor saved scores. If you do that, there are various methods for deriving scores from a factor analysis. Your software will often provide various means for extracting factor saved scores with various properties. You can also save the coefficients from the factor coefficients table. You can then compute your own factor saved scores by multiplying the coefficients for a given factor by the scores for a particular individual.

Centering: All the above methods (sum, mean, factor saved scores) are examples of weighted composites (i.e., $y_i = \beta_1 x_{i1} + \beta_2 x_{i2} + ... + \beta_p x_{ip}$ for participant $i$ where there are $p$ items, $x$ is the response, and $\beta$ is the weight and where $y$ is one subscale score; you could add another index for multiple subscales). Centering only changes the mean of such a subscale. If you were to create two scales scores, one with centered variables, and one without, the two scale scores would be perfectly correlated. Note that rescaling (e.g., creating z-scores) does make a difference, and is often appropriate where items are on different metrics.

I agree with @Damien's answer that the DiStefano (2009) reference is a good place to get an overview of the issues.

### References

• DiStefano, C., Zhu, M., & Mindrila, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation, 14(20), 1-11. PDF

In addition to the ressources that @Damien has provided I would like to give you a very brief "tutorial":

Factor scores for a subject are defined as the sum of the scores of that subject on the items that belong to a factor, multiplied by their respective factor loadings. It doesn't really matter if you go with the standardized or with the unstandardized loadings. But very often the standardized values are easier to interpret, as they range from $-1$ to $1$.

A good guide how to go about this analysis using the software tools you have described has been written by our very own Jeromy Anglim! "Calculating Composite Scores of Ability and Other Tests in SPSS".

Another article with some details is "Understanding and Using Factor Scores: Considerations for the Applied Researcher" (DiStefano et al. 2009). Their abstract is:

Following an exploratory factor analysis, factor scores may be computed and used in subsequent analyses. Factor scores are composite variables which provide information about an individual’s placement on the factor(s). This article discusses popular methods to create factor scores under two different classes: refined and non-refined. Strengths and considerations of the various methods, and for using factor scores in general, are discussed.

I hope this helps