I would like to use weighted sum scores (multiplying the score of each item into its factor loading and then summing all of them). If I use this method, there will be 3 questions?
1- Is basically weighted sum scores a correct method?
2- What should I do if a factor loading of an item in a factor is negative (While I am sure that I have already recoded this item and this item’s direction is the same as the whole scale direction not opposite). Should I ignore the negative sign?
3- I am using SPSS. The score I get for each factor in this way have different lower and upper limit. How can I standardize them to be able to use them in an analysis?
If you want to estimate internal consistency reliability of your factor scores (Cronbach's alpha) afterwards, you should use simple (0,1) weighting. That is if an item loads on a factor give it a weight of one, and zero weight if it does not load. You can then simply add up the responses to items that load on a factor to yield a factor score (and perhaps divide by the number of items to yield an average item response for that factor). Cronbach's alpha assumes that all items on a scale are given equal weight in order to estimate reliability. This simple weighting scheme is also more likely to replicate in another sample.
Is it correct to divide the weighted sum scores that I got for each factor by the sum of the item loadings in that factor?
Hi,
The best method to calculate factor score after conducting factor analysis:
http://www.ats.ucla.edu/stat/spss/output/factor1.htm
http://files.eric.ed.gov/fulltext/ED516588.pdf
http://core.ecu.edu/psyc/wuenschk/MV/FA/FA-SPSS.docx
All the responses are satisfactory. It is true that to calculate factor score, original variables are made free of scale for their summation over variables as factor loadings are treated as weights of the dimension for which factor scores are calculated. Generally, Zero Mean and Unit Variance reduction of original variables is preferred, but one can choose a method of making variables scale-free and has to be applied for all variables.
I suggest do not calculate the factor scores. Theay are not unique even the mdel is identified. see attachmen
@Giorgio: I know this problem, but what would you suggest for applied researchers, who are not using SEM?
What would be better, using FSC or simple sum scores?
Christoph
Thank you all for your professional responses.
I am architect and my research is an interdisciplinary research between architecture and psychology. so I appreciate you to know the most simple and correct method for calculating the factor score as not many people in my discipline are expert in sophisticated statistics.
May I ask if it is correct to simply multiply the factor loading of each item into the raw score of that item, and then sum up all these gained values for all items of a factor , and finally divide this sum into the sum of the factor loadings (of all items of that specific scale)?
I have even seen in many papers that researchers simply calculate the average score for each factor...
If you want to estimate internal consistency reliability of your factor scores (Cronbach's alpha) afterwards, you should use simple (0,1) weighting. That is if an item loads on a factor give it a weight of one, and zero weight if it does not load. You can then simply add up the responses to items that load on a factor to yield a factor score (and perhaps divide by the number of items to yield an average item response for that factor). Cronbach's alpha assumes that all items on a scale are given equal weight in order to estimate reliability. This simple weighting scheme is also more likely to replicate in another sample.
when a clear pattern of loading exists in any case, the researcher may take a simpler approach. Factor could be created simply by summing the variables with high loading and creating a summated scale representing that factor. While, not necessary, it is often wise to divide these summated scale by number of items so the scale of the factor is the same as the original items. (Business Research Methods, Zikmund, Babin, Adhikari, Griffin, 8e, Cengage learning, Page No655, 656)
What is the formula to find factor scores after conducting factor analysis on binary data?
I want to know more about Calculate scale scores by using a weighted approach, which includes creating factor scores via confirmatory factor analysis or structural equation models
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