I'm working with partial least square regression with 1 component, and I would like to know where can I find datasets for this model where the number of predictors p is greater than the number of observations n. I know this is a typical framework in chemometrics, but most dataset I found are with more then 1 component. Thanks
1 Answer
Firstly, I'm a little confused by your question. Are you using PLS to reduce the dimensionality of the regression model, remove multicollinearity, or do you only have one independent predictor variable? IMHO, PLS is inappropriate for the latter since PLS transforms your independent variables (X) into uncorrelated components that are then regressed against the dependent variable(s) (Y). There's absolutely no point in applying a PLS transform if you only have one independent predictor variable in your regression model!
I'm not familiar with chemometrics, but the Advanced Soil Geochemical Atlas of England and Wales has a freely available gridded dataset of soil geochemistry. It is a multivariate geospatial dataset; each pixel contains the estimated soil concentrations of approximately 53 elements.
It would require some pre-processing, but this dataset should give you a fairly large number of independent variables for PLS regression analysis. For example, you could choose a subset of the elements to predict another. Moreover, most of the elements are likely correlated with each other, thereby justifying the use of PLS to reduce multicollinearity by transforming the variables into uncorrelated components.