Sorry if these end up being kind of naive questions, but I'm only starting to get into this type of data analysis technique:
-When I decide to remove a specific variable from my Rotated Component Matrix because of considerable cross-loading (therefore a complex variable), should I run the whole thing (PCA) again taking the said variable out from the start, or should I simply proceed with my original analysis only removing that variable's line from the Rotated Component Matrix?
-I've read that, ideally, the difference between the primary target loading of a variable and other secondary loadings should be greater 0.2 (lets call this the "0,2 rule" for easier understanding). Now my question here is how does this work in cases with positive/negative signs. For example: variable A loads primarily to factor 3 at .530, should the fact it also loads to factor 8 at -.356 concern me somehow? I know that if it were positive (.356) it certainly should. I also already know that any loading above the .3 range should be taken in consideration, so my question here is about the "0.2 rule" specifically.
Hi Leonidas,
First, when you remove a variable from the rotated matrix because you deem it less useful, you will need to conduct the entire PCA again and recheck if you are satisfied with the figures. Regarding the second question, I will recommend you keep it simple: any variable with major of its cross-tabulation factor loadings less than 0.1 should be considered for removal. Likewise, any variable with several loadings above 0.9 should be removed (it implies the variable is already measuring something which is already being measured). In the example attached here, I will consider the variables "material_floor" and "motorbike or bicycle" for removals. Hope this helps? Cheers!
No it should not concern you, you use the .530 and neglect the -.356. Why would you use it if it were positive. You decide to consider those factors above .400. You can restrict the number of factors usually to 4. Sometimes based on Cattel's scree test there is an obvious change between, for example, factor 3 and 4 and then you decide to keep 3 factors instead of 4.
Hello,
what do you mean by PCA (factor analysis) ?
PCA, principal componant analysis deal with numeric variables whereas, correspandance analysis CA is meant to deal with factors. Even if numericaly the analysis close (data matrices in the case of PCA or contengency tables for CA) interpretations are not the same.
That being sayed, PCA and CA are exploratory analysis or hypothesis-free, that is a tool to help researchers to deal with there data set in order to produce hypothesis or create pipologies (clustering). As a consequence there is no things such as rules in those analysis. Just explore you data and be aware of what you are doing.
Best,
Marc
Hi Leonidas,
First, when you remove a variable from the rotated matrix because you deem it less useful, you will need to conduct the entire PCA again and recheck if you are satisfied with the figures. Regarding the second question, I will recommend you keep it simple: any variable with major of its cross-tabulation factor loadings less than 0.1 should be considered for removal. Likewise, any variable with several loadings above 0.9 should be removed (it implies the variable is already measuring something which is already being measured). In the example attached here, I will consider the variables "material_floor" and "motorbike or bicycle" for removals. Hope this helps? Cheers!
Thank you all for your valuable input and sorry on my part if I was somehow unclear with what I was asking (again, I'm still new to this).
Despite already having a better understanding of what to do now based on your answers, I'll add my Rotated Matrix here in order to try to clarify even further (it might not be the cleanest matrix but it accounts for 73% of total variance explained). My objective here was simply to try to verify if some of my 16 variables (that in this case were Likert Scale questions) could be grouped around a smaller number of major aggregating topics.
Now, regarding the "rules" (or maybe "best practices") I'm talking about, I've read about them here:
"Cross-loadings - indicate how strongly each item loads on the other (non-target) factors. There should be a gap of at least ~.2 between the primary target loadings and each of the cross-loadings. Cross-loadings above .3 are worrisome."
Ref.: Exploratory factor analysis - Criteria for selecting itemst: (https://en.wikiversity.org/wiki/Exploratory_factor_analysis)
Hi Leônidas Soares Pereira, with regard to your first question, if a variable is decided to be removed from the analysis because it has an important load then the PCA must be run again to obtain the new factorial loads. Now, charges greater than 0.2, in absolute value, are consigned as charges that are important and must remain in the analysis. Negatives indicate that some variables load factors with an inverse relationship.
Greetings.
Dear all. I tend to concurr with Alejandro Salas-Vargas . Any type of exploratory data analysis is, bydefinition, contingent to the data set. If you remove a variable, then you need to re-run the exploration. But I have a question: why chosing on the basis of a rotation? As far as I understand, rotation (e.g., varimax) is just a presentation trick but I am not sure the loading factor after rotation remains the same as before (truth being, I never use rotation so I never cared). I’d rather look at the PCA results themselves, before rotation.
- Badges
- Science topic
- Similar topics
- Mathematics
- Statistics
- Statistical Software
- R