Evaluation of Goodness-of-Fit Statistics from Precon to Estimate the Strength of Multivariate Tree Growth-Climate Associations

Although the primary purpose of response function analysis is to identify climate variables that have significant associations with tree radial growth, many researchers are also interested in assessing the strength of these associations. Existing response function programs use a liberal criterion to determine how many climate variables should be included in the analysis. The resulting response function models include a large number of predictor variables. The objective of this analysis is to determine if these response function models are over-fitted to the data used to calibrate them, resulting in over-estimation of strength of associations. PRECON was used to produce response functions for white oak chronologies from n = 149 sites, with separate response functions using 34 monthly climate variables or 10 seasonal climate variables. An analysis of goodness-of-fit statistics for response function calibration provided strong evidence of over-estimation of strength of associations. The degree of over-estimation was greater when 34 monthly climate variables were included in the models compared to models with10 season variables. There was much less evidence of over-fitting for the R-verif statistic that reflects strength of association between predicted and actual tree-ring indices that were not included in model calibration. The PRECON R-verif statistic is the best measure of the strength of multivariate growth-climate associations currently available.