You may use some combination of collinear data. You can use also VIF to check if there is a collinearity between variables. Here are some usefull links:

http://www.statcan.gc.ca/pub/12-001-x/2012001/article/11685-eng.pdf

http://online.stat.psu.edu/online/development/stat501/12multicollinearity/05multico_vif.html

http://econ.ucsd.edu/~rramanat/MoreonMC.pdf

http://www.stat.sc.edu/~hansont/stat704/vif_704.pdf

Thank you very much for the links to a comprehensive literature on the topic. I read it through cautiously, and could come to the conclusion that dropping colinear variables, identified using R² or VIF or PCA (those in the same PC with high loading beeing colinear), seems the best method. However, dropped variables must be accounted for in renaming the variables with which they were colinear, respectively.

This poses certains questions with respect to analysis in proteomis. Indeed, dropping a variable because it correlates with another means that both variables are associated in the tested conditions. This might provide an additional degree of information on the dataset. This an open remark and I would be grateful if you could give your opinion on it.

Regards

I would suggest using PCA to reduce a large number of colinear predictors to a smaller number of uncorelated components (varimax rotation). Component is described by a pattern of loadings that reflect relations between predictor variable and factor or component (same thing, depending on if you perform FA factor analisys or PCA principle component analysis). That way you can name your components (using marker variable with highest saturation or complex pattern of saturations on numerous variables) and enter components (factor scores) as predictors in your analysis. There will be no more problem of colinearyty (components are uncorelated - ortogonal) dough you my encounter problems with interpretation of components (naming them or labeling them). Number of components that you can extract is equal to the number of variables dough it is pointless extracting components with eigen value les than 1 so you usually end up with smaller number of components. Hope this makes sens and helps you. All best. Darko.

Have you considered searching the chemometric literature? Many of the approaches developed for analysing spectroscopy data are based on highly colinear data [I know that my own data had VIF scores >1000 when I checked out of interest]... For example you may wish to consider PLS-DA . A lot will depend on just how colinear your data are, as the chemometric literature has mainly been developed for sampling points at regular intervals from an underlying curve.

I would also agree with the PCA course of action.

Some time ago I also used something "simpler" that I found in the following paper to orthogonalize my variables:

Burrill, Donald F. "Modeling and interpreting interactions in multiple regression." accessed July 2 (1997): 2007.

I hope it'll be useful.

another viewpoint is to centre the variables that are displaying collinearity. That is subtract the mean or median from the columns and the shift will reduce the collinearity without reducing the predictability of the variables

Warning: this is a weird answer, but I think it might work for you.

Have you thought of trying exploratory factor analysis to pull out profiles of proteins? That way, you might be able to find clusters of collinear proteins and rename the clusters as singular covariates with states (e.g., high, medium, low, or some sort of integer or ratio as a numerical index). This essentially what people do when trying to develop psychometric instruments that have indices (e.g., the NEO-PI-R personality test, which has 5 indices for personality traits).

Here's an example of confirmatory factor analysis (not exploratory like yours. This is when you have hypothesized clusters) that is a typical way factor analysis is used: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3218373/

Here is a recent way exploratory factor analysis is being used for lipid profiles that mirrors pretty much what I am suggesting you try with the proteins: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3552685/

My opinion is that the reason why this wonderful tool, factor analysis, has not been used as much in biomedical research is because it has been mainly on the radar of the sociologists and psychologists. It is one of their main tools. I am in public health, and it is not emphasized in our basic biostatistics curriculum. In fact, I have not noticed it taught at all anywhere in public health. I learned it myself while collaborating with an organizational psychologist on an interdisciplinary project.

It is possible you have too many proteins and this would not work because you have too much data. Sometimes that is good, and sometimes that is a problem!

The genetics people who have too much data try to use multifactor dimensionality reduction (MDR): http://en.wikipedia.org/wiki/Multifactor_dimensionality_reduction At first blush, it looks great, but the reality is, to quote what happens to be on Wikipedia today, "As with any data mining algorithm there is always concern about overfitting. That is, data mining algorithms are good at finding patterns in completely random data."

This is why I have never used this MDR approach; I find factor analysis more informative. I just try to get rid of some columns empirically if I have too many and make it so I can use factor analysis.

I hope this helps you. Good luck with your project!

-Monika

One way of identifying multicollinearity is to scan a correlation matrix of all of the predictor variables and see if any correlate very highly (by very highly I mean correlations of above .80 or .90). This is a good ‘ball park’ method but misses more subtle forms of multicollinearity.

For multiple regression SPSS produces various collinearity diagnostics, one of which is the variance inflation factor (VIF). The VIF indicates whether a predictor has a strong linear relationship with the other predictor(s). Although there are no hard and fast rules about what value of the VIF should cause concern, Myers (1990) suggests that a value of 10 is a good value at which to worry. What’s more, if the average VIF is greater than 1, then multicollinearity may be biasing the regression model (Bowerman & O’Connell, 1990). Related to the VIF is the tolerance statistic, which is its reciprocal (1/VIF). As such, values below 0.1 indicate serious problems although Menard (1995) suggests that values below 0.2 are worthy of concern.

After these diagnostics you will be sufficiently informed to eliminate the variables of concern.

Thank you very much to all for your responses.