Hi all,
I am new here. I would like to apologize beforehand if my post misses some of the forum's norms.
I am using treelet transform (TT) to obtain dietary patterns from register data with almost 100,000 observations, and dietary carbon footprint patterns, for my master's thesis. I am also using PCA to compare components with that of TT. I have two significant issues I needed clarification with.
Background of the issue:
After performing PCA and comparing the principal components (PCs) with treelet components (TCs), while there was strong correlations between the first two components (PC1 and TC1/PC2 andTC2) TC3 had no correlation with PC3 but it had a very strong correlation with PC5, TC4 had also strong correlation with PC3. Based on some related work by Gorst-Rasmussen et al (2011) and Schoenaker et al.(2013), they were able to reproduce rotated PCs which mirror the treelet components (TCs) respectively, for example Rotated PC1, PC2, PC3, PC4 had strong correlation with TC1, TC2, TC3 and TC4 respectively. In my case, though,neither varimax rotation nor promax (oblique Procrustes rotation) could change the outcome (i.e after rotation PC1 was correlated with TC1 PC2 with TC2, PC3 with TC4, PC5 with TC3 and PC6 with TC5). These rotations somehow reduced the strong correlation between the first two components (eg from 0.93 to 0.8) and they resolved some ambiguity (for example before rotation TC4 had a correlation of -0.6 with PC4 and 0.72 with PC3 but after rotation TC4 PC4 (0.17) TC4 PC3(0.77).) I would like to add that the TT had 5 components retained and the PCA had 7 components retained. I cant retain 7 components with TT because only one variable loads on the additional components. By Reducing the number of PCs to 5, I will lose PC6 which has a correlation of 0.936 with TC4 (for women) and I will lose the criteria I used to retain 7 components for PCA.
SO my question is:
1. after rotation of PCs, is the order of the rotated components important? If for example rotated Component 7 correlate with my treelet component 5, but rotated PC6 does not correlate with any of my treelet component, can I just assume correlated PC7 as PC5 ( in short can I reorder the rotated components for my convenience assuming they have equal variance).
2. The references I read mention that they used procrustes rotation to obtain factors. Is that the "promax, rotate" command or the "procrustes (target variables) (Source variables)" command? I assumed the first because the procrustes command does not produce loading of variables on components ( In short, Is the promax oblique rotation a procrustes rotation?)
I had tried to look for every available resource to get explanation but I could not and some of the important references were from 1960s articles which I don't have access with. I hope my questions are clear enough. Thanks for your help
Regards,
wossenseged
I am new here. I would like to apologize beforehand if my post misses some of the forum's norms.
I am using treelet transform (TT) to obtain dietary patterns from register data with almost 100,000 observations, and dietary carbon footprint patterns, for my master's thesis. I am also using PCA to compare components with that of TT. I have two significant issues I needed clarification with.
Background of the issue:
After performing PCA and comparing the principal components (PCs) with treelet components (TCs), while there was strong correlations between the first two components (PC1 and TC1/PC2 andTC2) TC3 had no correlation with PC3 but it had a very strong correlation with PC5, TC4 had also strong correlation with PC3. Based on some related work by Gorst-Rasmussen et al (2011) and Schoenaker et al.(2013), they were able to reproduce rotated PCs which mirror the treelet components (TCs) respectively, for example Rotated PC1, PC2, PC3, PC4 had strong correlation with TC1, TC2, TC3 and TC4 respectively. In my case, though,neither varimax rotation nor promax (oblique Procrustes rotation) could change the outcome (i.e after rotation PC1 was correlated with TC1 PC2 with TC2, PC3 with TC4, PC5 with TC3 and PC6 with TC5). These rotations somehow reduced the strong correlation between the first two components (eg from 0.93 to 0.8) and they resolved some ambiguity (for example before rotation TC4 had a correlation of -0.6 with PC4 and 0.72 with PC3 but after rotation TC4 PC4 (0.17) TC4 PC3(0.77).) I would like to add that the TT had 5 components retained and the PCA had 7 components retained. I cant retain 7 components with TT because only one variable loads on the additional components. By Reducing the number of PCs to 5, I will lose PC6 which has a correlation of 0.936 with TC4 (for women) and I will lose the criteria I used to retain 7 components for PCA.
SO my question is:
1. after rotation of PCs, is the order of the rotated components important? If for example rotated Component 7 correlate with my treelet component 5, but rotated PC6 does not correlate with any of my treelet component, can I just assume correlated PC7 as PC5 ( in short can I reorder the rotated components for my convenience assuming they have equal variance).
2. The references I read mention that they used procrustes rotation to obtain factors. Is that the "promax, rotate" command or the "procrustes (target variables) (Source variables)" command? I assumed the first because the procrustes command does not produce loading of variables on components ( In short, Is the promax oblique rotation a procrustes rotation?)
I had tried to look for every available resource to get explanation but I could not and some of the important references were from 1960s articles which I don't have access with. I hope my questions are clear enough. Thanks for your help
Regards,
wossenseged
