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Mazenby
Level I

Crossover design and PCA

Hi,

Is it acceptable to apply PCA as a variable reduction method to data collected from a crossover design where each participant was subjected to two levels of the same factor? Each observation consists of 1060 variables.

Thank you

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P_Bartell
Level VI

Re: Crossover design and PCA

OK...I think I understand what you are trying to do...since the FTIR values are responses and it sounds like you are going to use the PCA output for some other purpose I guess I don't see any issue with act of using these values for creating eigenvalues, etc. You may want to see if there are appreciable differences between the PCA results by treatment. It might be inciteful to use a modeling technique such as partial least squares to see what you can learn there even though you don't appear to be in the modeling space with this particular data set. Your problem sounds not too dissmilar from the Baltic.jmp data table...albeit that's a much smaller table.

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P_Bartell
Level VI

Re: Crossover design and PCA

When you wrote '...variable reduction...' are you seeking to identify a smaller set of influential variables within a modeling context to explain or predict a system's behavior? If so, then a 'variable identification' technique is recommended. Generally speaking PCA is used as a dimensionality reduction technique...not a variable identification technique. There are several modeling methods in JMP and even more in JMP Pro along with companion/supporting platforms like the Model Comparision, Make Validation Column, and Formula Depot (all JMP Pro only) that can be used for variable identification. Which method works best is a matter of context, your data, and the practical problem at hand.

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Mazenby
Level I

Re: Crossover design and PCA

Thank you for your reply. I might not have expressed myself well. I want to obtain the scores from my crossover design data and use those scores as input variables for something else. Would that be valid approach?

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P_Bartell
Level VI

Re: Crossover design and PCA

I'm still not 100% sure of the structure of your experimental design. Are there N subjects, and each subject was given Treatment A and Treatment B? And where does the '1060' variables come into play? Are these '1060' variables attributes of each subject? Perhaps you can share the JMP data table?

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Mazenby
Level I

Re: Crossover design and PCA

Yes, I have N cows (subjects) and each cow was given treatment A and treatment B. A milk sample was taken from each cow (subject) and FTIR (Fourier Transform Infrared) spectrum was recorded for that milk sample. The FTIR spectrum contains 1060 spectral variables, or wavenumbers as we say. I am wondering whether the paired observations would be an issue for calculating PCA scores. Does this calculation requires independance of observations? If yes, am I violating this assumption in this case?

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P_Bartell
Level VI

Re: Crossover design and PCA

Are you treating the FTIR values as predictors or responses?

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Mazenby
Level I

Re: Crossover design and PCA

Responses

Highlighted
P_Bartell
Level VI

Re: Crossover design and PCA

OK...I think I understand what you are trying to do...since the FTIR values are responses and it sounds like you are going to use the PCA output for some other purpose I guess I don't see any issue with act of using these values for creating eigenvalues, etc. You may want to see if there are appreciable differences between the PCA results by treatment. It might be inciteful to use a modeling technique such as partial least squares to see what you can learn there even though you don't appear to be in the modeling space with this particular data set. Your problem sounds not too dissmilar from the Baltic.jmp data table...albeit that's a much smaller table.

View solution in original post

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Mazenby
Level I

Re: Crossover design and PCA

@P_BartellThank you for your answer and your time, I really appreciate it.

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