Examining the Gain in Model Prediction Accuracy Using Serial Autocorrelation for Dominant Height Prediction

Abstract

Abstract Within-subject serial correlation (autocorrelation) has long been a concern in forest growth and yield modeling but has been ignored for predictive purposes in most studies. In this study, we used linear prediction theory combined with linearized (with respect to random effects) nonlinear mixed models to investigate the improvement in model prediction achieved with autocorrelation. In this setting, predictions rely on estimates of common parameters obtained from a set of previous growth series and prior observations of new growth series, allowing the response variable for the new series to be projected either backward or forward in time. The prediction gains associated with using autocorrelation were evaluated using stem analysis data sets for black spruce (Picea mariana [Mill.] BSP) and red alder (Alnus rubra Bong.). The evaluations involved splitting the data and comparing models with one or more random parameters, with and without use of autocorrelation. Autocorrelation improved the projection of dominant height (site index) over short ranges (10–20 years), but the gain was trivial for the long range (>20 years). Consequently, in cases of dominant height projection based on one single observation, for practical purposes, autocorrelation can be ignored in both model-fitting and prediction stages. Cross-comparison between models with different random effects indicated that simple models with one random effect had the best predictive performance. Rather than excluding such models solely on the basis of certain fit statistics, it is recommended that the predictive abilities of models with a single random effect be evaluated, with and without correlated errors, relative to their counterparts with more random effects.