Coping with Multicollinearity: An Example on Application of Principal Components Regression in Dendroecology

摘要

The objectives of this study are: to present a step-by-step procedure for estimating a response function using principal components regression; to provide a formula for estimating the standard errors of the principal component estimators of the coefficients of the independent variables; to introduce the appropriate test statistic for assessing the significance of the regression coefficients obtained using principal component regression; to explore the effects of the various methods of selecting principal components on characteristics of the response function; and to demonstrate the methods (detrending and autoregressive modeling) used to transform ring-width series to produce a growth measure that reflects the variation in climate.