# How to interpret factor scores saved using the regression method?

I have 30 attribute variables with response on a 1 to 5 scale (e.g., extremely important, very important, important, not that important, etc.). I ran factor analysis and extracted 6 factors and saved the values using the regression approach. Now I want to understand them. I can make sense of the 6 factors themselves, but not the individual scores.

• What is the intuition behind the factor saved scores for each respondent?
• What is the best way to display them visually?
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Sorry, I find this question confusing. If you understand the meaning of a factor itself, then the individual scores are "how low or high the respondent scores on this factor". I don't see how you can understand the one without the other. Could you please clarify? The way the regression method works is explained in this old post of mine. – RubenGeert Dec 6 '12 at 5:46
Explanation of how factor scores and component scores are obtained: stats.stackexchange.com/q/126885/3277. – ttnphns Jan 4 '15 at 11:11

Intuitively, factors are latent variables that underly the scores in your observed variables. Usually, the interpretation of each of these factors is based on the content of the original variables so that each factor is interpreted as whatever the attributes with high loadings for this particular factor have in common. Ideally, factor scores would therefore represent the score of each person on the underlying latent variable (based on your description, I assumed you had various people rate the importance of these 30 attributes).

By construction, regression factor scores in SPSS are standardized. A score of 0 on a factor therefore means that this person's ratings of the importance of the relevant attributes is close to the average for your sample. Similarly, a negative score means that the person gave lower than average importance ratings and vice versa (all this holds for variables with positive loadings, for negative loadings the relationship is inverted, i.e. positive factor scores would correspond to lower than average ratings).

Obviously, the sample average is not necessarily the middle of your scale. For example, if everybody considers the attributes related to one particular factor as important or very important, a factor score of 0 might correspond to an average rating of 4 on the original attributes.

Note that while this approach has been criticized, in psychology it is still common to compute “scales' scores” by simply adding or averaging the ratings on the original variables. Factor analysis is only used to select and refine the subset of the original variables that constitute each scale. One advantage of this approach is that these scores use the same metric than the original variables, so that a score around 4 or 5 could be interpreted as a high level of importance for the relevant attributes, etc. Perhaps you will find this type of scores easier to interpret.

I don't know if this fully answers your question but you might in any case find more relevant information in the following paper:

DiStefano, C., Zhu, M. & Mîndrilă, D. (2009). Understanding and Using Factor Scores: Considerations for the Applied Researcher. Practical Assesment, Research & Evaluation, 14 (20).

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Tx!! Now suppose I get factor scores for respondents that are about -2. How do I interpret this with respect to the likert scale? If my ranking scale is from 1-5 where 5 is the highest possible ranking, what would a respondent's factor score of -2 on such factor variable mean? – JCV Dec 8 '12 at 20:59
It depends on the original distribution of answers: -2 means about two standard deviation below the mean. If you want scores that are directly interpretable on the original scale and don't want to dig into the niceties of factor score estimation, I recommend you simply look at the loadings for each factor, select the items with the highest loadings and compute their means. – Gala Dec 9 '12 at 20:14
Tx! But I want to use these saved reg factor scores as predictors for a multinomial logit where my dependent variable is a categorical var with a few choices for a good. The issue is that I don't know how to interpret the coefficients of my estimation because the predictors as factor scores and they are not very intuitive. – JCV Dec 9 '12 at 23:51
I guess you could still use these simple sums scores in your multinomial logit model. Alternatively, look at the distributions of answers on (the sums of) the original items, to get a feeling for the meaning of the factor scores. – Gala Dec 10 '12 at 6:32