Hello Esther,

With that many variables, it would be ideal to have far more cases in your data set. However, on to your question!

There are many methods from which to choose for trying to develop "good" or "optimal" classification models. Many of these are discussed in texts on data mining (e.g., https://www.amazon.com/Data-Mining-Practical-Techniques-Management/dp/0123748569).

Here's a good link to R examples for a large number of these methods: https://mhahsler.github.io/Introduction_to_Data_Mining_R_Examples/

Good luck with your work.

Hello Esther,

If I understood correctly what you are saying, the 200 samples represent the total number of samples when considering the 3 groups (e.g., some 67 samples per group). If that is the case, then I cannot but agree with David that you ought to have far more cases in your dataset in order to be able to draw a sensible conclusion from your data.

If there is no way you can obtain more cases, I would suggest you reduce the dimensionality of your predictor variables (i.e., the 600 protein measurements), by performing e.g. a PCA and then considering afterwards only the protein measurements that have high loadings. In doing that you should not run 3 PCAs but only one, on the data of all groups confounded.

Let's see what other people think too.

hth

cheers,

Serban

Great advice from David Morse , Serban C. Musca and Dr Sharma ; you should follow it. After obtaining more data I would like to posit one additional caveat.

Principal Component analysis creates composites of the original variables that manifest monotonically decreasing maximum variance, given the condition of orthogonality. So, one may attend to the PCs with maximum variance, perhaps as suggested, excluding variables that are not heavily loaded on the largest "X" components. This will all work fine, but if, and only if, those X components also have maximum, or at least appreciable, covariance with the criterion; this is not necessarily the case. This is the reason that, in consideration of the predictive accuracy of regression on PCs (and other alternatives to OLS regression), Richard Darlington (1978) coined the term "validity concentration" in respect to those PCs. The question therefore in respect to validity concentration is the degree to which large eigenvalues of the PCs align with large component-criterion correlations. If, for instance, substantial correlation with the criterion is "hidden" in PCs with "smaller" eigenvalues (beyond X), it will not be available to this modeling technique.

So, you should consider this issue after the PCs are extracted. There are various paths, with perhaps the most important being "eye-balling" the correlations of all PCs with the criterion. We have also created a metric of validity concentration that you may have some interest in. I have done some simulation work on it, but it has not yet been widely vetted; it may be another lens worth using. The article is here on RG if it is on interest at:

Article Validity concentration formula validation

Darlington, R.B. (1978). Reduced variance regression. Psychological Bulletin, 85, 1238-1255.

My best on your research,

John