Additivity and maximum likelihood estimation of nonlinear component biomass modelsThis article is part of a larger document. View the larger document here.
Since Parresol's (2001) seminal paper on the subject, it has become common practice to develop nonlinear tree biomass equations so as to ensure compatibility among total and component predictions and to fit equations jointly using multi-step least squares (MSLS) methods. In particular, many researchers have specified total tree biomass models by aggregating the expectations of nonlinear component equations. More recently, an alternative approach has been used wherein compatibility is ensured by specifying a total biomass equation plus one or more component disaggregation functions. Yet calibration of such equations typically has not recognized the additivity of the biomass data or the implied stochastic constraints necessary for development of a valid probability model. For model selection based on information criteria, stochastic simulation, Bayesian inference, or estimation with missing data, it is important to base estimation and inference on probabilistic models. Thus, we show how to specify valid stochastic models for nonlinear biomass equation systems and how to estimate parameters using maximum likelihood (ML). We also explain how ML procedures can accommodate unobserved or aggregated component biomass data. We use Parresol’s slash pine data set to contrast model forms and demonstrate Gaussian ML from complete and missing data using open-source software.