I was checking a Principal Components Analysis that a colleague performed on a bio-separation process and I found two abnormalities.
First, despite PC1 explained more than of 80% of variance, samples were distributed along PC2 in score plot.
Second, in loadings plot there was one variablle had more than 100 explained variance, it was beyond the outsider line of Hotelling's Ellipse.
I told her to make PCA rotation.
Dear Roberto Eloy Hernández Regalado
This type of error usually happen when the data has not been standardized before carrying out the PCA algorithm. Please confirm with your friend is she/he standardized the data before processing with PCA?
Standardize the data means to mean centering and scaling the data. By doing this, each X-variable got the same variance and could not dominate over another and thus influence the model.
You could scaling the data by multiplying each X-variable with the inverse of the standard deviation of the corresponding variable (1/SD),
Wish you all the best
First, If there is a high amount of variance (variation away from zero) explained by PC1 but little variation (variation away from mean) explained, then you need to centre your data (usually mean centering).
Second: A loading dependent on a single variable may have two explanations. It may be that the one variable is uncorrelated with any others and attempting a data reduction including it is not useful (exclude the variable then combine after PCA). Such a situation is not the most likely however, rather it may also be a sign, as Edenio suggests, that the data needs appropriately scaled to ensure the variation of each is on an equivalent dynamic range.
Thank you both.
An useful information that I didn't mention was that PCA was runned on The Unscramble x 10.4.
The first trouble was solved changing the scale of the second component. Because it was on 10^(-1) units of first component. When the change was made to equal units data was dispersed along PC1.
In the data there was negative values. Thus transformations made were center by minimum, which was a recommendation of the program. Besides data was scaled by range so all points had positive values.
She is aware of your recommendations so instead another scale transformation will be apply.
If the problem with the loading persists, should I remove this variable from PCA?
We tried all the centering-scaling combinations in The Unscramble x 10.4. The problematic point remains very close to the external ellipse, but it is still there.
Dear Roberto Eloy Hernández Regalado
I also use The Unscrambler to process my data. Check the user manual and their PCA chapter, you can find very important information and an example on it ( https://www.camo.com/downloads/user-manuals.html ).
Please, could you upload some picture of how do you scale the data in the software (PrintScreen) and also the result page?
All the best,
Edenio Olivares Diaz here is the picture of the PCA Overview, please look closely at Correlation Loadings plot.
All the best
Dear Roberto Eloy Hernández Regalado
Thank you very much for showing the result.
I think this is a 2 PC model, and as you can see the two first components explain 90% of the total variance.
Related to your question, there are two loadings near to the external extreme of the ellipse. Which there are ruling the model (the most important), but as I told you in my previous comment, I would like to see the capture picture of how do you scale the data in the unscrambler. For doing this, you need to process the data once more, but it is very simple.
If you scaling is find, it could be cause by outliers, for that reason I would like to check first the scaling process. Remember, in every single model, pre-processing is one of the most important process to obtain robust model.
Another advice, please down load the unscrambler user manual from CAMO and read the chapter related to PCA. This will help you enormously.
Your PC1 scores are all positive, suggesting you have not mean-centred your data, but it looks like mean centering would help.
Before running the input data, you need to normalize and then run the PCA. Normalization helps in casting your data set in a specified numerical range (-1,+1) or (0, 1), this will help to eliminate the influence of one variable over another. You can generally standardize your data in a multivariate statistical analysis when you want all the selected variables to be in comparable units.
Like Lourdes Zumalacárregui said we tried all centering-scallings combinations and still the variable was still out of external ellipse. Do you have any explanation?
Dear Roberto Eloy Hernández Regalado
Like I said, I would like to see how did you carry out the centering-scaling process, I am asking because in the Unscrambler it is very easy to make a mistake in this step. And as you can see in the James Renwick Beattie comments some variables looks like they are not scaled,
All the best
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