Generalized Least Squares Estimation of Yield Functions

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Abstract:

Data were obtained from 9 measurements of 20 unthinned plots established in Monterey pine plantations in South Australia. A two-stage procedure for estimation of the yield functions was developed, drawing on the theory relating to random coefficients and to seemingly unrelated equations. In the first stage, coefficients relating yield to age for each plot were estimated using ordinary least squares. In the second stage these plot coefficients were then regressed against plot variables such as site index and stocking at age 10. The error terms in the second stage violated the assumptions of ordinary least squares, being heterogeneous across plots and correlated across coefficients. A generalized least squares algorithm was therefore developed and programmed to estimate the final coefficients and other relevant statistics. The algorithm also enabled comparison of the final coefficients based on alternative assumptions about the structure of the error terms. The results showed that the coefficients estimated under the assumption of heterogeneous correlated errors were more efficient than those under other assumptions. Recognition of the correlations between first stage coefficients proved especially important. Comparison of the heterogeneous correlated results with those from ordinary least squares applied to the pooled data from all plots also showed that while the latter estimates of the coefficients seemed robust, their variances were grossly underestimated. Model selection based on ordinary least squares and pooled data may therefore be misleading. Generalized least squares estimators offer substantial advantages in this respect and are consistent and asymptotically efficient. Forest Sci. 24:27-42.

Keywords: Monterey pine; Pinus radiata; Statistical analysis; mathematical models

Document Type: Journal Article

Affiliations: Assistant Forest Resources Officer, Woods and Forests Department of South Australia, currently undertaking Ph.D. studies at the Australian National University

Publication date: March 1, 1978

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