Models for predicting lumber bending MOR and MOE based on tree and stand characteristics in black spruce

In this study, a stepwise method was introduced to identify the best variables for predicting lumber static bending modulus of elasticity (MOE) and modulus of rupture (MOR) based on stand and tree characteristics in black spruce (Picea mariana). In the initial development of the technique, the two equations were fitted independently using ordinary least squares (OLS). A test for cross-equation correlation using black spruce data showed highly significant correlation between the two equations. Since the cross-equation correlation exists between the two equations, more efficient parameter estimation can be achieved through joint-generalized least squares, better known as seemingly unrelated regression (SUR). A simultaneous system of two equations was derived for black spruce. The two methods were evaluated and compared for some statistical parameters. The results indicated that there is a small difference between the two methods, but parameter estimates from seemingly unrelated regression estimation had smaller standard errors in all cases as compared to those from ordinary least squares estimates. Therefore, the system estimation methods theoretically perform better for simultaneously interdependent systems of equations and the appropriate system estimation approaches are recommended for estimating coefficients in simultaneously interdependent systems of forestry equations.