Imputation to predict height to crown base for trees with predicted heights

Abstract

Height-to-crown-base (HTCB) measurements are frequently used as inputs for growth and yield models. They are essential for reliable projections of stand structure over time required for sustainable forest management. Often, HTCB is measured alongside total height (HT) for only a subsample of trees and must be imputed for unobserved measurements in the sample. Typically, HTCB models require HT as a covariate, requiring a “double” imputation for missing HTCB measurements, leading to potentially substantial error propagation issues. We compared the effects of subsample size, imputation method, and use of imputed rather than measured HT on the accuracy of HTCB predictions. HT and HTCB were imputed using a nonlinear fixed-effects model (NFEM), a NFEM with a correction factor estimated using an ordinary least squares (OLS) regression on the subsampled measurements, and a nonlinear mixed-effects model (NMEM) with stand- and plot-level random parameters. Using cross-validated bias and root mean squared error (RMSE), our results indicated that NMEM obtained the smallest RMSE at subsample sizes greater than one, with RMSEs ranging between 2.19 and 2.51 m. However, while NMEM provided generally smaller RMSEs, biases ranging between −0.92 and −0.29 m existed at subsample sizes less than three trees per plot, and −2.86 m when no subsample was available. We observed negative bias when using imputed rather than measured HT for both the correction factor and mixed-effects model that is mitigated to a range of −0.51 m to −0.08 m with subsample sizes of at least two trees. Following this, we recommend using NMEMs for HTCB imputation with at least four trees per plot.