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A study on the effects of multicollinearity, autocorrelation and four sampling designs on the predictive ability of the 1994 and 1995 variable-exponent taper functions Bartel, Joseph

Abstract

In British Columbia, government, industry and consulting firms have used taper functions since the late sixties. Most recently, Kozak's (1988) variable exponent model has been used since 1989. One practical problem with the model is that, it does not estimate total or merchantable volume without bias. These biases were found to be more pronounced for red cedar (Thuja plicata Donn ex D.Don) and western hemlock (Tsuga heterophylla (raf). Sarg.). Because of this problem, a second equation known as the 1994 equation was developed. However, reviewers identified some theoretical problems concerning multicollinearity and autocorrelation in the 1994 equation. These prompted the development of a third equation that possesses a lesser amount of multicollinearity referred to as the 1995 equation. The three principal objectives of this research were: (1) to study the effects of multicollinearity and autocorrelation on the predictive ability of the 1994 and 1995 variableexponent taper functions; (2) to study the effects of four sampling strategies on the predictive ability of the 1994 and 1995 taper equations; and (3) to examine the possibility of localizing the 1994 taper equations. The effects of multicollinearity and autocorrelation and the four sampling designs were studied using Monte Carlo simulations. The results of the study indicated that the presence of severe multicollinearity and autocorrelation in the data did not seriously affect the predictive ability of the equations. Stratified random sampling, with equal allocation of observations selected from each stratum, gave the smallest variability of the estimated coefficients compared to simple random sampling, and stratified random sampling, with the number of samples proportional to the size of the strata. However, the average estimated regression coefficients were somewhat different from the population parameters.Therefore, simple random sampling is recommended for selecting trees from the population if the main objective is the estimation of the population parameters. If the equations are to be used for prediction, then a wider range of the data (stratified sampling) should be used. The results indicated that no adjustment or scaling is required for the western hemlock equation for the two subzones studied.

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