• Multicollinearity within Selected Western North American Temperature and Precipitation Data Sets

      Cropper, John Philip; ProSight Corporation (Tree-Ring Society, 1984)
      This paper is concerned with examining the degree of correlation between monthly climatic variables (multicollinearity) within data sets selected for their high quality. Various methods of describing the degree of multicollinearity are discussed and subsequently applied to different combinations of climate data within each site. The results indicate that higher degrees of multicollinearity occur in shorter data sets. Data consisting of 12 monthly variables of a single parameter (temperature or precipitation) have very low degrees of multicollinearity. Data set combinations of two parameters and lagged variables, as commonly used in tree-ring response function analysis, can have significant degrees of multicollinearity. If no preventative or corrective measures are taken when using such multicollinear data, erroneous interpretations of regression results may occur.
    • Response Functions Revisited

      Blasing, T. J.; Solomon, A. M.; Duvick, D. N.; Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 57851 (Tree-Ring Society, 1984)
      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.
    • Usefulness of Annual Growth Rings of Cypress Trees (Taxodium Distichum) for Impact Analysis

      Ewel, Katherine Carter; Parendes, Laurie A.; School of Forest Resources and Conservations, University of Florida, Gainesville, Florida (Tree-Ring Society, 1984)
      Because of the propensity of cypress trees (Taxodium distichum) to form false or incomplete annual rings, the use of their growth rings for impact analysis is limited. However, the error associated with reading growth rings can be estimated by comparing two cores from the same tree, and the error inherent in a single core can be reduced by averaging the growth estimate over 6-10 years.