In the study of ecological community structure, the multivariate niche model has always been the assumed structural model. This model is closely connected to the multivariate two-sample problem. Important to the understanding of species interactions in a community is the measurement of the degree to which the niches of two species overlap, or to measure the similarity between the resource use distributions of the species. Discriminant analysis is the tool used most often to analyze the similarity. In this study, we discuss the most commonly used similarity measures, and develop measures that are less dependent on the assumptions of the usual discriminant analysis. Specifically measures arc derived assuming normal distributions with heterogeneous variance-covariance matrices arc derived.
The problem of estimating the measures and their precision and accuracy is investigated. Two methods, the jackknife and the bootstrap, arc described for estimating the bias and variance of an estimated measure. The performance of these methods was evaluated using simulation. When the number of variables involved in the model is large, the estimates of these measures may be severely biased, and the bias is consistently negative. By collecting larger samples the bias can be reasonably adjusted. Two potentially important factors affecting results arc the disparity in the means and the heterogeneity of the variance-covariance matrices. It is shown that when the mean separation is small, the heterogeneity of the covariance matrices has a moderate effect on the bias, but the effect is diminished when the mean separation becomes larger. The variance of the similarity estimates is also related to the value of the measure and is a quadratic function of the similarity. The logarithmic transformation of the similarity is seen to linearize the variance of the similarity estimate.
The jackknife method gives good adjustment of the bias of the estimated measures. Generally, the bootstrap method performs worse than the jackknife method. In some cases, especially when there are many redundant variables neither method gives reliable results. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/74739 |
| Date | January 1986 |
| Creators | Lu, Ruey-Pyng |
| Contributors | Statistics, Smith, Eric P., Good, Irving J., Holtzman, Golde, Lentner, Marvin, Schulman, Robert S. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | ix, 144 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 15280212 |
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