| Author | Message | ||
     Bob Jordan |
When working in Bernhard Tauschers lab in Germany last year I used their J&M Spectralys system and was intrigued by an algorithm it offered to explore the available wavelength range for its usefulness. It first divided the full range into 10 equal width regions (in either nm or cm-1 terms) and then tried lots of combinations of these 10 bands. Now it was quite efficient at looking at these and did not go through the entire 1023 combinations but I could not work out the criteria that it used to reject certain branches of the search tree. I wonder if this is a published algorithm, and if so if anybody could point me to a source of more information. Unfortunately the German manual did not offer this mono-language kiwi with the clues needed. Can anybody help on the source or theorise on the principle? | ||
| Chris Brown |
Most likely stagewise regression, but there are tens (hundreds?) of methods to efficiently downselect variables which are similar in principle, and (usually) produce nearly identical results. Check out Draper & Smith "Applied Regression Analysis" (Wiley) for an overview of the techniques. ~ C. | ||
| hlmark |
Bob - I think Chris has it basically right. I can offer a couple more ideas, though: however they select the sets of ranges to try, they probably simply use one of the standard calibration statistics (SEC, SEP, SECV or any of the others) to select the final model, and probably also to guide the selection process. As Chris intimated, the same search procedures that are used to select individual wavelengths for MLR calibrations could be applied to selecting the ranges to do the PLS calculations at. According to one scheme of categorization, these can be classified as: 1) Step-up 2) Step-down 3) Select different rangss, keeping the total number of ranges constant (this includes all-possible-combinations) There are also some schemes that combine algorithms from different categories: i.e., step-up from N to N+1 ranges, followed by selecting different candidates to constitute the N+1 ranges. So there are lots of possibilities, but if you need to know exactly what's being done, the only way to be sure is to ask the company. But I agree with Chris that most schemes will produce equivalent results, and in some cases will come up with the same results. Howard | ||
| Bob Jordan |
Thanks for useful comments guys but I think my question is more fundamental. All the points you raise work well with full regression techniques but when PLS is used it raises some further questions. Maybe I am even questioning the iPLS technique that Scott Osborne and I published a few years ago. When you add a range to the PLS you may be adding information that can enhance one of the factors considerably and thus you may need effectively one less factor in the result. So a search being done at say 10 factors would suddenly only need 9 and the extra factor that is now added in moves you one step further towards the 'perfect solution'. Is this taken into account by all of these techniques or does one just blindly proceed with either a fixed number of factors, or does one select the number of factors at each step? I guess my original question is behind the logic of the step procedure. If one removes one region and the solution gets worse, can one assume that all other solutions that have that region removed are also worse? This may work with full regression, but I think not with PLS. In fact there is a classic paper that shows purely random spectra plus a single column containing the y vector that gives a very poor result with PLS. I hope this makes sense. Bob J. | ||
| Chris Brown |
Well ... actually most of the stepwise/stagewise/forward/backward methods DON'T work very well with full regression (on spectroscopic data) due to the multicolinearity that is inherent in the data. Or at least, they don't work well by the means in which they are conventionally implimented (multiple-hypothesis testing). But they do a decent job, even with PLS, IF hypothesis testing ("tests of significance") is avoided and something like more empirical like cross-validation is used instead. In practice, there really isn't great need to complicate things with considerably with PLS. It, like all the multivariate methods, will find wavelengths useful if there is more net analyte signal there than noise. If there's no net analyte signal present in a region, then the wavelength is useless, and merely contributing noise. Given enough samples, PLS/PCR do just fine on their own without wavelength selection (even when there are useless regions of the spectra) because those useless wavelengths will eventually be 'zeroed' in the latent variable model. This is also the case in the example you cited above (the [noise|y] making up X for the regression model). On selecting the appropriate number of factors, I must say (although perhaps unpopularly) that I've rarely seen it to be an important decision. There is a lot of attention given to it in the literature, and I sometimes just wonder whether this isn't just carry-over from classical modeling where the parameters themselves were of interest (rather than predictive ability). Including an 'extra' factor in the latent variable model shouldn't have a significant impact on the utility of the LV model in prediction. If it does, problems are considerably graver (you're working at the multivariate LOD, or your coefficients are wildly unstable/sample-starved). Just my two cents (more like a buck fifty). ~ C. | ||
| David Russell (Russell) |
I use the number of factors suggested by the PLS software as a "guide" but ultimately look at other elements to arrive at the number of factors that I'm "comfortable" with. Key considerations that are favorites of mine are consideration of the error in the reference data and examination of the loadings plots. I'm much more comfortable when the loadings look like spectra. Noisy loadings can be indicative of overfitting or optical anomalies. So my answer would be any time you remove a region you must reconsider the number of factors used. |