Accounting for serial correlation and its impact on forecasting ability of a fixed- and mixed-effects basal area model: a case study

Abstract

Successfully accounting for serial correlations has always been a vital part of growth and yield modeling when using repeated measurement data. In this case study, 16 alternative functions addressing the serial correlations of errors from a basal area model of black spruce (Picea mariana (Mill.) B.S.P.) were examined and compared. Results from this study showed that functions incorporated into the fixed and mixed models to account for the serial correlations improved model fit. The serial correlation of the residuals from the fixed model with directly modeled error structure was significantly lower than that from the fixed model without a modeled error structure. For the mixed model, modeling error structure resulted in only a moderate reduction in serial correlation of residuals. The comparison of the fixed and mixed models with and without directly modeling the error structure showed that for fixed model, a substantial improvement in forecasting ability was achieved when the error structure was directly modeled to account for serial correlation, and when the forecasts were adjusted based on the estimated correlation. But for the mixed model, further modeling of the error structure to account for more serial correlation resulted in worsened or comparative forecasting ability of the fitted model.

Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for Oaks (Quercus spp.) Considering Forest Structural Diversity

“…Although introducing random effects could correct or reduce autocorrelation and heteroscedasticity [65,68,87,88], our mixed-effects model still exhibited autocorrelation and heteroscedasticity. We therefore further introduced three variance functions and three correlation structures to refine our model.…”

Allometric modelling of crown width for white spruce by fixed- and mixed-effects models

“…Mixed models are suitable for analyzing longitudinal data due to their flexibility in dealing with different data structures such as irregular and/or unbalanced data. They are able to handle the lack of independence caused by grouped data structures associated with clustered or repeatedly measured data (Pinheiro and Bates 2004, Temesgen et al 2008, Yang and Huang 2011, Meng et al 2012. This is important in situations where statistical inferences are essential, especially for forest growth and yield models mostly developed from limited sampling data.…”