Hi,
I recently did a survey (116 questions) and received responses from 226 respondents. I conducted the explanatory factor analysis, hoping to discover factors and reduce the number of questions. Seven factors are suggested according to the plot of eigenvalues. I tried both varimax and oblimin methods (loading factor > 0.5). The varimax method drops the question number from 116 to 80 (cumulative variance: 0.65), while the oblimin method drops the question number from 116 to 50 (cumulative variance 0.41).
1. I want to reduce the question number but the varimax method has a higher cumulative variance, I presume varimax method is better in this case?
2. If I decide to go with the varimax method, how do I further reduce the question number? I am thinking that instead of choosing questions with loading >0.5, choose those >0.6. However, two factors do not have questions with loading >0.6. Can I use different loading criteria for different factors? For instance, only select questions with loadings> 0.6 with factor 1, but with factor 7, I select questions with loadings > 0.5. Alternatively, I am thinking to combine some similar questions together in order to reduce the question number, but is there a more objective method of doing so? Or is there any other suggested way to reduce the question number?
Varimax (orthogonal rotation) will lead to uncorrelated factors. Oblique rotation is typically preferred because it allows for correlated factors, which are more realistic for most applications. Oblique rotation also frequently leads to a better simple structure (clearer loading pattern) than orthogonal rotation.
If your goal is to select only the best items, then you may pick the ones that show the best simple structure (high loading only on the intended factor, low or zero secondary loadings on other factors).
For more information, the following paper may be useful to you:
Article Repairing Tom Swift's Electric Factor Analysis Machine
Hao-Yu Shih, I think you might have a fundamental problem in that there are likely to be too few participants given the number of questions/items that you are subjecting to exploratory (note, not explanatory) factor analysis (EFA). There is a range of views about how many participants are needed in EFA, with most methodologists recommending particular ratios of participants to items. A common recommendation - though merely a rule of thumb - is that there be 10 x the number of participants as there are items.
Given that you might have too few participants in your research, I suspect that the results from EFA could be quite "dynamic" - i.e., likely to bounce in any direction.
Therefore, trying to combine items that are similar to each other seems like a good idea. I'm not sure how, at this stage, you could combine items, however. If you wanted to work with your current data, you could obtain interitem correlations and remove one or more items that have very high correlations with other items, retaining only the item among highly correlated items that you think most appropriately captures what you are trying to measure.
Having done that, you could run EFA again, hopefully with a better ratio of participants to items.
Incidentally, although it seems you used a scree plot to identify the number of factors in your data (which I think is advisable), I recommend you use parallel analysis in addition to the scree plot. These days, it's quite easy to conduct parallel analysis. Please feel free to get back to me if you need help with that.
All the best with your research.
The factor loading for every item should exceed 0.5. For established items, the factor loading for every item should be 0.6 or higher.
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