I have 7 factors in my model and each factor contain many items. Is it possible to compare the difference of the reduced factors between groups, or do I have to perform the test for each item individually ?
Have you considered with Multiple Analysis of Variance (MANOVA) or Structural Equation Modeling (SEM)?
David L Morgan Structural Equation Modeling.
I have been looking for an answer and the one that I have got right now is that I can perform Oneway Anova on the reduced factors. Do you concur ?
Can you give more information about your model? Do you want to compare the means of the groups for each factor individually or do you assume any paths also between the factors in your model?
If the former one, maybe a multilevel model may be appropriate, where you would use all information, i.e. all items from all individuals, and account for this by incorporating random effects for the participants and the items.
Rainer Duesing Thank you for response. Initially, I have 7 latent variables that I want to measure via 39 items. After performing, reduction of dimensions of factors, can I perform ANOVA on the reduced dimensions or only on the items ? according to David L Morgan I cant. But I am reading an article where the author seems to do so.
The basis for my sander was that you seem to have seven dependent variables, i.e., one for each factor.
For me and maybe David L Morgan it is nor clear, what you actually mean with "reduction of dimensions of factors" Please clarify. How would you do it?
On the other hand, why would you want to lose the information? The advantage of SEM is that it can account for (un-)reliability and may provide better estimates. But please elaborate what you mean with reduction.
I would like to apologize for my weak ability to put my question correctly. I talked with some lab colleagues and according to them The ANOVA test can be performed on the factors extracted from the principal component analysis (PCA). (which is basically what I meant by reduced dimensions factors. Do you concur ? David L Morgan Rainer Duesing Thank you very much for your help.
You can do ANOVA on each of the factors extracted through PCA, but you would need to do those analyses one-at-a-time (i.e., one ANOVA for each such factor as a dependent variable).
Hello Reda Tamanine. If you really are interested in latent variables (as you said in an earlier post), then you should be using some form of factor analysis, not principal components analysis. See Preacher & MacCallum (2003) for some relevant discussion.
https://kuscholarworks.ku.edu/bitstream/handle/1808/1492/preacher_maccallum_2003.pdf?sequence=1
If you decide you really do want to use principal components (for data reduction), then I suggest you also look at this article by Hadi & Ling (1998):
Hadi, A. S., & Ling, R. F. (1998). Some cautionary notes on the use of principal components regression. The American Statistician, 52(1), 15-19. https://www.tandfonline.com/doi/pdf/10.1080/00031305.1998.10480530?casa_token=H9yBDiUNIQ0AAAAA:CSzXJeIC0DVrNP8jgvbi2oqf_e4l2S-2HYSK22UePlCtNKrDxphpe7iEpK-5fg6NUFAsNmjOniHd
HTH.
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