| Author | Message | ||
     Sirinnapa Saranwong |
I suppose that we can use the variables that have relationship to each other (collinearity) as Xs in MLR equation. However, I experiance a difficulty in finding an English statistical reference to answer one of referees. Please suggest me some. | ||
| hlmark |
Sirinnapa - I'm not sure what the original question is, but Draper and Smith's "Applied Regression Analysis", Wiley (3rd ed 1998, although you could use any edition for this info) contains information for just about anything you might want to know about multiple regression, including some discussion of correlation among the X variables. There is some more information about specialized topics in Daniel and Wood's "Fitting Equations to Data", Wiley (1971). If you could be more specific about your question, we might be able to give more specific answers. Howard \o/ /_\ | ||
| Sirinnapa Saranwong |
Dear Howard, Thank you very much for your help. My problem is I have 2 collinear variables which are not NIR spectra (R = 0.69). And I use them to predict another chemical variable (Y). Even if there are collinear but I can get the better SEP (from a separate test set) from using both of variables compared with using only one. Anyway, the referee of my paper said this is wrong. The person said I cannot use the collinear variables in MLR equation. Hope that it's clearer this time. Thanks, Sirinnapa | ||
| hlmark |
Sirinnapa - There is a problem with using correlated variables, but that is not that it destroys the usability of the model; correlated variables can still make good models. The problem is that it inflates the variance of the two estimators involved, so that each are individually less reliable than they should be even though as a pair they can work together very well; this is discussed in Draper and Smith. There is a graphical description of this situation on page 34 of Mark, H. "Principles and Practice of Spectroscopic Calibration"; Wiley (second ed. 1991) I have heard Cuthbert Daniel (of Daniel and Wood) state that correlations of up to 0.99 are not disastrous, although I don't know that he ever wrote that down anywhere, and he's now deceased. So your correlation coefficient of 0.69 is not all that bad. In fact, you might try something: perform a simple (one variable) regression of one of your X's on the other. You might find from this that the regression statistics (t-test for the variable, or F-test for the regression) turn out to be statistically non-significant. This should be a fairly convincing answer to the reviewer. Unfortunately I don't know of very much else written about the subject of correlated variables, although the basics of the variance inflation effect are well-known and written in most Statistics books. Another approach would be to compute Principal Components and use those; you can compute two Principal Components from your data and those are orthogonal by definition. The two PCs will give calibration results otherwise identical to your two current variables. Howard \o/ /_\ | ||
| Sirinnapa Saranwong |
Howard - Thank you very much. Sirinnapa | ||
| Sirinnapa Saranwong |
Howard - Thank you very much. Sirinnapa |