An Ordinal Response Model for the Control of Eucalyptus grandis Cut Stumps of Multiple Stem Origin

Broadfoot, Lynn Beresford (2000) An Ordinal Response Model for the Control of Eucalyptus grandis Cut Stumps of Multiple Stem Origin. MSc(R) thesis, University of Glasgow.

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Abstract

It has been suggested that an effective predictor of the survival of Eucalyptus grandis cut stumps of multiple stem origin in trials using selected herbicide, may be found from measurements taken on the dimensions of the cut stumps (or stools). To examine this conjecture, data on stool diameter, sum of cut surface diameters and highest height of coppice growth was collected from 714 cut stumps during a study of cut stumps to assess the efficacy of five different types of herbicide in combination with three methods of application, carried out in the KwaZulu-Natal Midlands region of South Africa. Although the measurements were available they were not used in the final analysis of the trial. Little, Maxfield and Kritzenger (1997), found that those stumps treated with herbicide using a basal frill method of application were more efficient at killing stumps on the first and second applications. It was reported that there were no statistical differences between the herbicides. The work described in this thesis follows on from, and extends their analysis. By considering the continuous measurements of stool dimensions in addition to the treatment factors and modelling the total number of applications until a kill is achieved, as an ordinal response it was hoped to construct an accurate predictor of cut stump survival. In Chapter 1, an outline is given of the forestry background to the control of the Eucalyptus grandis cut-stumps problem, and the original KwaZulu-Natal experiment is more fully described. A resume of Little, Maxfield and Kritzenger's results follows. A preliminary examination of the data is described in Chapter 2. One outlier from the continuous variates was identified and changed to a more meaningful value. Stool diameter, sum of cut surface diameters and highest height were considered to be potential predictors of cut stumps survival because of varying degrees of linearity when plotted against the cumulative sample logits with stool diameter showing the strongest linear trend. More complicated functions of the continuous variates were assessed in the same way but with little success. One of the new variables was derived from stool diameter and sum of cut surface diameters to produce the ratio of the stool diameter to sum of cut surface diameters, by seeking to account for the poor performance of the cut surface method of application in cut-stumps of multiple stem origin. This poor performance is in contrast to the relatively largely successful results seen in trials of a similar nature on cut-stumps of single stem origin. No evidence was found from this sample that the ratio of stool diameter to the sum of cut surface diameters had a systematic effect on the total number of applications until a kill is achieved. However, for thoroughness and continuity this variable was assessed in a best subsets approach to selecting the best linear predictor in Chapter 4 and then later used in an additional analysis. This meant that there were 3 strong possible predictors for modelling the survival of cut-stumps in this study: stool diameter, highest height and sum of cut surface diameters. As a small proportion of the trial had been terminated before its completion the response contained some 29 missing values. The occurrence of missing values was scrutinised. The pattern of missing data appeared to be random. The present case is an example of the general polytomous data problem with 4 response categories (representing total number of applications until a tree stump is killed). So, in Chapter 3, approaches to ordinal response data in general use are discussed including the use of cumulative logit models. An outline of the benefits of using cumulative logit models for ordinal response data is given which leads to the presentation of the proportional odds model as a suitable model for analysing the cut-stump data. An introduction to generalised linear models is given with a close look, in the general case, at the estimation of parameters using the method of maximum likelihood. The likelihood functions for the multinomial distribution are derived in the final section. (Abstract shortened by ProQuest.).

Item Type: Thesis (MSc(R))
Qualification Level: Masters
Additional Information: Adviser: Keith Little
Keywords: Statistics
Date of Award: 2000
Depositing User: Enlighten Team
Unique ID: glathesis:2000-76465
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 19 Nov 2019 14:18
Last Modified: 19 Nov 2019 14:18
URI: http://theses.gla.ac.uk/id/eprint/76465

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