PCA : how to interpret the weights/loadings and Varimax rotation
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- Опубликовано: 21 авг 2024
- See all my videos at www.tilestats....
In this video, we will try to interpret the weights and see how we can compute the loadings. We will also see how we can increase the interpretation of the weights by Varimax rotation.
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The lecture was very helpful. You took your audience along a gentle learning curve, by putting the important concepts together in a logical order. Thank you!
Thank you!
Dear Tilestats and the Guru behind the scene, thank You for enlightening.
Can You make the videos about Principal axis factoring (as extraction method) + Promax (as rotation method)? I often see the 2 commonly used combinations: PCA + Varimax, and PAF + Promax. And i often click and run those combinations on softwares without really knowing what happens in the blackbox.
Can You help enlighten me and the others through this.. Thank You Guru.
Amazingly clear 👏🏻👏🏻👏🏻👏🏻 THANK YOU
Very clear explanation and helpful! Thank you!
Thank you!
VERY GOOD EXPLANATION
Thank you!
bro your work is amazing ! if you have time can you please do one video for canonical correlation analysis as well?
Thank you! I had actually planned for such video.
After we do PCA on SPSS we may got many PCs based on eigen value > 1. As in your case we have 2 PCs, the question is how we can merge these PCs to create weighted index ?
Sir, if you have any video on multidimensional scaling, please provide the link.
At 6:15 you say"increase the interpretation pf our weights or loadings". You mean that it help interpeting both or that weights are also called loadings? I have this doubt because you said that an eigenvector is the vector of weights, while in statquest videos the speaker says that eigen vector is the vector of poadings. Moreover, you expressed loadings as the product of weights and squared root of eigenvalues. These differences between your video and statquest ones confised me a bit. Thanks if you are willing to help😊
I would say that a loading is a weight that represents the correlation coefficient between the given variable and a certain PC, like I explain around 4:00.
really good video
Thank you!
Hello, the explanation is very good, I still have a doubt, how the rotation matrix is calculated, it is known that the spss I calculate it, I am interested in calculating it manually, please, if you have a calculation example, I would be grateful. Clarify that I speak Spanish, I hope I have written well.
Hi
In my second video about PCA, I show how to rotate the data by simple linear algebra. However, Varimax rotation is an iterative method. It means that the data is rotated step-wise to find the best rotation according to some minimization (or maximization) problem (see Wikipedia). In SPSS you can, for example, specify the maximum number of steps the algorithm should take for convergence. Hope this helps.
@@tilestats Hello.
I want to do the rotation manually, doing calculations, I don't understand with what data the diagonal matrix is taken, it is taken with the extracted factors, the eigenvectors are taken from these, etc. I have those doubts. Please, if you had a calculation at least two factor manual; you can share me. It would be very nice if you make a third video with a rotation. With manual calculations.
@@tilestats In your second video how to get the rotation matrix
@@tilestats Please can you share the calculations you made to obtain the rotation matrix, my email is: educoedwin@gmail.com
@@edwinchavarria9943 I took the rotation matrix from, e.g. SPSS. If you like to know the details of how to compute Varimax rotation I would recommend the following page.
www.real-statistics.com/linear-algebra-matrix-topics/varimax/
11:21 What would be the command to multiply the scores with the rotation matrix in R?
Just multiply the two matrices by using %*%, for example:
M1%*%M2
Hello,
How do one compute the final weights for a variable or indicator if two or more PC are retained and what could be the statistical tests to use to check the robustness of those final weights to be able to select the appropriate PCA model that best represent the data?
Please advice.
I'm not sure what you mean with "final weights". If you watch my video "PCA 3 : standardization and how to extract components", you see that the weights do not change when we extract components. This video also shows how many PCs you should extract. The values of the weights only change if you change the constraint (but that is optional). You get other types of weights if you rotate by Varimax rotation. You can use some kind of bootstrapping method to check the robustness of your PCA model.
@@tilestats I am getting what you are saying, but if we have chosen to use two PCs, the variable or indicator Xi will have the weights for PC1 and also the weights on PC2 and now to compute the overall weight of Xi to the Index is my challenge.
If you can also provide some references for the bootstrapping method to check the robustness I will appreciate.
@@tilestats I will also watch your PCA 3 video, thanks for your assistance and your willingness to assist us.
@@mangalanimakananisa6800 Have a look at this paper:
link.springer.com/article/10.1007/s13253-019-00355-5#Sec10
@@tilestats thank you, I will have a look
First at 3:16 a_1^2 + a_2^2 + a_3^2 + a_4^2 = 1, and then at 3:54 it equals var(PC_i). What am I missing? shouldn't you use different letters?
I see what you mean, it would be clearer to use different letters. Anyway, alpha is the general notation for the weights. This is why I kept the notation although I re-scale the weights.
it's not clear at min 7:47 why the loadings, and not the scores , represent the coordinates of the data points in the PC1-PC2 plane
am trying PCA in EXCEL...Got my results except for the weights in PCA....i tried with my centred data, standardized data....But did't get the right ouput.
Please help me out!!!!!........
FORMULA I TRIED FOR WEIGHTS IN EXCEL: (10 variables)
RAW DATA : =MM(Centered data(1st row of my 10 variables ,PC1)
STANDARDIZED DATA : =MM(STANDARDISED 1st row,PC1)
I have never done a PCA in Excel, but this might help you:
www.real-statistics.com/multivariate-statistics/factor-analysis/principal-component-analysis/
I recommend to use R or Python to perform PCA.
Hi I am working in Matlab and I am wondering what name one uses for the coefficient table that shows principal components (columns) and variables (rows)? Thank you!
Usually factor loading table.
So we now know the correlation between the PCs and the original variables, what are the biological interpretation of these numbers? How can we describe this group of people using these numbers?
That is explained in the video after this one:
ruclips.net/video/BiuwDI_BbWw/видео.html
And at the end of the first video about PCA
ruclips.net/video/dz8imS1vwIM/видео.html
good，good，good
Thank you!
Is this factor analysis?
No, this is PCA, which is similar to FA.
@pca898