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UBC Theses and Dissertations

A structured covariance model for Douglas-fir PSP data and some implications for sampling Northway, S.


The error structure resulting from the repeated measurements of permanent sample plots (PSPs) can be addressed using a general linear model. Maximum likelihood methods provide a unified approach for estimating the parameters and subsequent inferences. Utilizing a predicted error structure, the efficiency of proposed PSP sampling schemes can be compared, prior to sampling. This can be done because the sampling errors of the model parameters are independent of the dependent variable. A sampling scheme is defined by the independent variables' intended frequencies and a sample size. Statistical and cost efficiency can be calculated by combining the sampling scheme with the sampling costs and the predicted error structure. In the data set examined, the correlation in the error structure was constant among the measured increments within a plot. The third increment on a plot was no more independent of the first increment than the second. This symmetric error structure was a better fit than the more usually assumed autoregressive structure. The data set, with an assumed symmetric error structure, was used to address two questions as examples of how this type of analysis might be used. In the first example, two sampling schemes were compared. Sampling Scheme 1 involved three increments on 150 plots, resulting in a total of 450 increments at a cost of $540,000. Sampling Scheme 2 involved two increments on 150 plots and one increment on 111 plots, resulting in 411 increments at a cost of $642,000. The second scheme resulted in fewer increments, but more measurements and more plots. The two schemes had nearly identical statistical efficiencies. Scheme 2 was more efficient per increment, but less cost efficient. The cost efficiency of remeasuring the same PSP overwhelms the increased statistical efficiency of independent increments. However, for modelling purposes, repeated measurements from the same PSP does not represent an irreplaceable asset. If a PSP is lost to development, a reasonable cost recovery would be the cost of its last remeasurement and the first measurement of a replacement. As a second example, sampling Scheme 3 composed of 150 plots with a 5-year and a subsequent 10-year increment was compared to Scheme 4 which combined 141 plots with three 5-year increments and nine plots with one 5-year increment. Scheme 3 utilizes 300 increments at a cost of $420,000, while Scheme 4 utilizes 432 increments at a cost of $525,600. The parameter covariance matrices of Scheme 3 and 4 are nearly identical, resulting in the same precision in their respective estimates. Scheme 3 is therefore statistically more efficient per increment and is more cost efficient. Comparing these two schemes tests the trade off of skipping an intermediate measurement on all the plots against making all the measurements on a subset of the plots. Skipping an intermediate measurement is far more efficient, both statistically and financially.

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