Yaffa L. Grossman

Critique of stepwise multiple linear regression for the extraction of leaf biochemistry information from leaf reflectance data

Abstract This study examined the use of stepwise multiple linear regression to quantify leaf carbon, nitrogen, lignin, cellulose, dry weight, and water compositions from leaf level reflectance ( R ). Two fresh leaf and one dry leaf datasets containing a broad range of native and cultivated plant species were examined using unconstrained stepwise multiple linear regression and constrained regression with wavelengths reported from other leaf level studies and wavelengths derived from chemical spectroscopy. Although stepwise multiple linear regression explained large amounts of the variation in the chemical data, the bands selected were not related to known absorption bands, varied among datasets and expression bases for the chemical [concentration (g g −1 ) or content (g m −2 )], did not correspond to bands selected in other studies, and were sensitive to the samples entered into the regression. Stepwise multiple regression using artificially constructed datasets that randomized the association between nitrogen concentration and reflectance spectra produced coefficients of determination ( R 2 s) between 0.41 and 0.82 for first and second derivative log(1/ R ) spectra. The R 2 s for correctly-paired nitrogen data and first and second derivative log (1/ R ) only exceeded the average randomized R 2 s by 0.02–0.42. Replication of this randomization experiment on a larger dry ground leaf data set from the Harvard Forest showed the same trends but lower R 2 s. All of these results suggest caution in the use of stepwise multiple linear regression on fresh leaf reflectance spectra. Band selection does not appear to be based upon the absorption characteristics of the chemical being examined.