You do not need to follow this calculation process. If you are a SPSS user, you can easily create a composite factor score, which is based on weighting each item with standardized factor loading, through the option of factor score saving.

In addition, you can create your own syntax to the same aim (see below).

FACTOR /VARIABLES x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 /SELECT=DATSET (1) /PRINT UNIVARIATE INITIAL EXTRACTION ROTATION /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION PC /CRITERIA ITERATE(25) /ROTATION VARIMAX /SAVE REG(ALL) /METHOD=CORRELATION .

Hi Mahoud;

For item weighting;

"sum of squared factor loading" means that eigenvalue for that factor. And if you use " (factor loading)^2/ (sum of squared factor loading) " for weighting, this means that items with higher factor loading are more weighted. but if the factor loading is negative then weighting the items negatively is correct.

This is because it shows a negative correlation with the common factor. For item weighting, you will get similar results if you weight directly with factor loadings instead of this calculation. However, this method can be used.

The method used to weight factor is expressed as the "explained variance". There is no problem to weight the vectors according to the variance explained, i think.

Better suggestions may come if you explain exactly what your purpose is. For example, if you are interested in the individual's scores after this calculation, the factor scores can give a better result. I suggest you take a look at this article for that.

Best Regards.

Distefano, C., Zhu, M. ve Mîndrilă, D. (2009). Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research & Evaluation, 14(20), 1–11.

Dear Mahmoud,

In SPSS just make sure you are using the appropriate factor analysis method then save the regression scores.

I would also recommend first identifying groups which load together and ensure that the analysis has stabilized then use principal component analysis with that group of variables on its own and save the regression score for that group.

Thanks everyone for your valuable feedback

Actually I am not an expert in Factor analysis neither in SPSS

My research (PhD), is about developing performance measurement model ,

so I gathered items from literature , then conducted focus group to filter the relevant items ,

After that I conducted survey ( likert scale based) asking opinions of experts who were asked to indicate to what extent do they agree that each of the performance measures listed in the questionnaire can be used to measure FM organization performance.

1- Is it ok to run factor analysis based on opinions ?

2-I used Principal Axis factoring (common factor analysis) as an extraction method, my purpose is not to do data reduction , it is for getting structure and underlined dimensions (unobserved variables )

3- My purpose is to get :

a.weighting of each item/variable within the factor/dimension

b. weighting of each factor/dimension with the overall scale/model

I am not familiar with factor scores ... what I know is : factor loading ( in the rotation table , extraction table (eigenvalue ,% of variance ...) , how can I use these in simple way to get the weighting

Thanks a lot ...

Hello Mahmoud

I don't know what do you mean about opinion. but if you have items and you wanna shrink them to some factors, the correct way is using Principal Axis factoring. My thesis is similar to you, not in field but in methodology.

and about weighting... sorry, I cant help.

I would advise you to look at Discovering Statistics Using IBM SPSS Statistics 5th (2017) Edition by Andy Field.

I used factor analysis a long time ago, but not on Time Series data. Although negative weighting is common and useful in psychology but not in development economics. One of the ways to avoiding negative weighting is to substitute (1-variable) for the variable, For example, for quality of life index, number of people per room will have negative value so replace it with number of room pr person..

Dear Mahmoud,

In the presentation on the link below, there are explanations and examples of obtaining both factor analysis and factor scores. I think it will be useful.

Good luck.

http://core.ecu.edu/psyc/wuenschk/MV/FA/FA-SPSS.pptx