The SOP model: The parameter estimation alternatives

The sop model is a growth and yield model for eucalyptus stands planted in different regions in Portugal. The model's functional form is based on a non-linear difference system of two equations (dominant height and basal area). \ In 1997, the first time that sop was parameterized, the ordinary least squares (OLS), two and three-stage least squares criteria were the methods applied, using more than 3000 re-measurements for the endogenous and exogenous variables corresponding to 3 years of stand measurement observations. Due to the system characteristics, three-stage least squares was considered the best procedure for the estimation process. Using more than 8000 re-measurements, gathered over 5 years, and a more intense regional reality observation, the sop model was re-parameterized using the same set of estimation criteria but using a sequential steps methodology. The OLS criteria application assumes, for the validity of the parameter hypothesis testing, a number of characteristics for the stochastic part of the model, namely zero mean, homoscedasticity, non-autocorrelation and desirable normality. Beyond these, of course, the functional form should reflect the reality, and the equation's right-hand-side (RHS) variables must be deterministic. The sop model parameterization process violates some assumptions. In this chapter a description of the methodology and an indirect analysis of the true meaning of the assumptions are presented.