How to apply published factor analysis loadings to sample data to compute factor scores? I have data on 18 participants responding to a 30-item instrument.
I also have a paper in which the researchers performed a principal axis factor analysis on the same survey where they report the item loadings (4 factors). 
Is it possible  to convert the data that I have, and compute scores for each participant on the four factors based on the published loadings?
 A: Most questionnaires have instructions for how the scale scores are meant to be computed. To foster comparability across studies, it is generally wise to follow those instructions where available.
Unit weighted scale scores


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*The most common approach is to take the rotated factor loadings, and work out which item loads most on which factor. Then the factor score is just the mean or sum for an individual on the items that load most for that factor. There are many good reasons for adopting this approach. The mean creates a scale that matches the original response scale. It is easy to compare means across uses of the test. It is simple to compute. The meaning of the scale can be inferred from the content of the items. And there is a certain robustness in the unit-weighted approach.


Computing scale scores for published factor analyses


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*I don't think you can compute true factor saved scores from factor loadings. As @ttnphns mentions, you would probably need the factor score coefficients (see this example). If you were able to request the raw data from the people who published the previous study then you could then obtain the factor score coefficients. 

*If you could obtain the factor score coefficient matrix then you would still need to be careful. In particular you would need to check that you used the exact same response format. You would also want to be careful that there weren't other subtle differences between your samples.
Using factor loadings to compute factor saved scores


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*If all you have is the factor loading matrix, then you could use them as weights to formed a weighted composite of each factor. If all the items on the same response scale and have roughly the same SD, then you could apply the loadings as they are. Otherwise, you might want to convert the items to z-scores first. Note that this approach is a bit of a hack. It's not giving you true factor saved scores. It's just a composite variable which weights items in a factor score proportion to their loadings.

