Uncertainty, Emergence, and Statistics in Dendrochronology - Dendroclimatology - page 94

case at least, the answer appears to be 'No,' but how do we know? Recall that we
withheld the 1897-1930 data from response function estimation for model valida-
tion purposes. We can use these data now to objectively test each response function
model for skill prior to the 1931-1996 calibration period. For comparison, we have
also done this using only the significant climate months in the correlation function
as predictors: the single month that exceeds the a posteriori 95% significance level
(current June precipitation) and the four months that exceed the a priori 95% signif-
icance level (prior-July, prior-September, and current June precipitation, and current
May temperature). The results of these runs are shown in Table 4.2 .
Note that the calibration period R 2 increases as the number of predictors in the
model increases. This is expected even by chance alone (Morrison 1976 ) . In par-
ticular, there is a big jump in R 2 from one predictor (current June precipitation)
to four predictors (prior-July, prior-September, and current June precipitation, and
current May temperature) and a corresponding substantial reduction in the AIC.
This jump in R 2 is also strongly maintained in the form of increased skill in the
verification period of the four-predictor model; i.e., the RSQ, RE, and CE statis-
tics are all substantially higher for the four-predictor model compared to that based
on only one predictor. So the four monthly variables selected by a priori testing of
the monthly correlations are collectively more important to eastern hemlock growth
than the one variable selected by the stringent a posteriori test. In this case anyway,
the multiplicity problem discussed earlier is not a problem at all!
The results of the full response function tests based on using all 32 monthly cli-
mate variables in the eigenanalysis, and using either the EV1 or PVP cutoffs for
retaining candidate eigenvectors, are even more interesting. As we saw previously,
the response function based on the candidate predictor pool selected by PVP resulted
in a higher R 2 and smaller AIC than those selected by EV1. Yet, the verification
statistics are somewhat better for the full response function based on the EV1 pool
(especially for RE and CE). This result illustrates that while the AIC is useful for

Table 4.2 Comparisons of climate models used to estimate the Mohonk Lake hemlock
chronology

Calibration period statistics Verification period statistics

R 2

# PREDICTORS NEIG AIC RSQ RE CE

1 1/1 0.209 − 11.27 0.094 0.039 0.039

4 2/2 0.343 − 21.34 0.226 0.173 0.173

32 EV1 13/4 0.342 − 16.63 0.269 0.251 0.251

32 PVP 25/6 0.413 − 19.37 0.248 0.111 0.110

The calibration period is 1931-1996 and the verification period is 1897-1930.
# PREDICTORS

=

number of monthly climate variables used in each principal components
regression model; NEIG the number of candidate climate eigenvectors/the number of climate

eigenvectors entered into the model; R 2

=

= cumulative fractional variance of the model; AIC =

Akaike information criterion; RSQ = square Pearson correlation; RE = verification reduction of

error; CE verification coefficient of efficiency. Higher RSQ, RE, and CE mean better verification

of the fitted model.

=