Comparison of fitting approaches with biomass expansion factor equations

Biomass equations for the biomass expansion factor (fBEF) have been widely applied for accurate stand biomass estimations. The question here is how to improve the fitting precision of these biomass expansion factor (fBEF) equations by using different methodologies. Stand biomass data were obtained from 53 permanent sample plots located in Cunninghamia lanceolata plantations of Anhui and Fujian Provinces across China. The least squares approach, the nonlinear mixed model approach, and the hierarchical Bayesian approach were applied to establish BEF equations so as to test the effect of regions. Split-plot design with regions of Anhui and Fujian Provence and sample plots as replications. Results showed significant differences between Fujian and Anhui Provinces for stand biomass, volume, and fBEF at different ages. The R2 and mean deviation (dMD) values for the least squares approach was R2 = 0.643, dMD = 0.376; for the nonlinear mixed model approach was R2 = 0.802, dMD = 0.233; and for the hierarchical Bayesian approach was R2 = 0.804, dMD = 0.228. Also, there were highly significant differences in fitted results between the least squares and the nonlinear mixed model approaches, as well as between the least squares and the hierarchical Bayesian approaches (P < 0.01). However, no significant differences were found between the nonlinear mixed model approach and the hierarchical Bayesian approach (P = 0.547). Thus, both the mixed model approach and the Bayesian hierarchical approach were effective methods for estimating stand biomass at the regional scale.