Hello everyone,
I am quite new to statistics and research in general, so please bear with me if some of my explanations don't make sense.
I'm doing my data analysis for my master thesis, and after running factor analysis and having saved the factor scores as variables, I would like to proceed further with hierarchichy regression since I have interaction terms as well. However, I've read that I need to centre the variable first before multiplying them. So after getting the mean value of those factor scores, is way too low to make any difference after subtracting. My question are:
1. Did i get the correct mean value (from Descriptive in SPSS using factor score variables)? or did I make a misake at that point?
2. What are the difference between using factor scores to run further regression and getting the average sum of the items loaded in individual factor to create an index?
Thank you so much!
Best,
1. I think you mistook the point. The centred scores just differ in terms of the mean - which should be zero (or close enough with rounding error depending on software). This means zero on the scale represents the mean of the score and therefore somewhere in the middle of your data. Because the regression estimates are the value of the outcome when all other predictors including intercept are zero this can aid interpretation - especially when you have interactions. This is because most scales are positive and evaluating the predictors for impossible or implausible values of the predictors and intercept (and where there is usually no data) can be confusing. For interactions this matters most because by definition the impact of the predictor changes when at least one other predictor changes.
Overall the model is just fine without centering in the sense that it will generate correct predictions and you can look at the margin effects etc. but interpreting coefficients is very, very confusing.
2. Generally they will be similar but the factor scores weight the impact of each item by its loading so if the loadings are very dissimilar it might matter. There is an argument that the equal weighted loadings of the sum scores are more robust but there is no general agreement that one is preferable to another (but strong feelings in either camp).
In line with Thom Baguley 's answer, factor scores are already centered (mean = 0), so there is no need for further centering before computing the product terms.
Factor scores in SPSS are typically standardized (mean ≈ 0, SD = 1), so centering them won’t change their values. You can create interaction terms directly. Using factor scores (weighted by loadings) is more statistically rigorous than simple averages, but both approaches are valid. If you averaged items instead, you would need to center them first before creating interactions. Always check multicollinearity (VIFs) when including interaction terms in regression. For interpretation, visualize significant interactions using simple slopes at ±1SD
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