Response Functions Revisited

Abstract

The use of orthogonalized climatic variables in regression to specify treegrowth/climate relationships, commonly known as response function analysis, involves several a priori decisions and a posteriori interpretations, any of which maybe open to question. Decisions about the number of climatic variables to include, confidence limits, number of eigenvectors to allow as candidate predictors in regression, etc., can affect the response function in unpredictable ways and lead to possible errors in interpretation. To demonstrate the nature of these effects, we compared response functions for particular chronologies with the correlation function, which is simply the series of correlation coefficients between a tree-ring chronology and each of several sequential monthly climatic variables. The results indicate that response functions including high-order eigenvectors should be interpreted cautiously, and we recommend using the correlation function as an interpretive guide. Prior tree-growth variables in regression can mask climatic effects, and the correlation function can also be useful in detecting this masking. Statistical significance is more often attained in response functions than in correlation functions, possibly due to differences in the statistical testing procedures, to the statistical efficiency of eigenvectors in spending degrees of freedom, or to the filtering effects on the climatic data that result from eliminating high-order eigenvectors (noise) from the response function. These filtering effects plus the orthogonalization make response function analysis an efficient method for specifying tree-growth/climate relationships. The examples and guidelines presented here should enhance the usefulness of the method.