Natural variability and the estimation of empirical relationships: a reassessment of regression methods
Ecologists often rely on empirically defined statistical relationships to infer how variables might be related. However, the usual method of estimating such relationships (ordinary least-squares (OLS)) is generally inappropriate because of the substantial natural variability of most ecological varia...
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1995
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crcansciencepubl:10.1139/f95-078 2024-04-28T08:39:36+00:00 Natural variability and the estimation of empirical relationships: a reassessment of regression methods Prairie, Yves T. Bird, David F. Peters, Robert H. 1995 http://dx.doi.org/10.1139/f95-078 http://www.nrcresearchpress.com/doi/pdf/10.1139/f95-078 en eng Canadian Science Publishing http://www.nrcresearchpress.com/page/about/CorporateTextAndDataMining Canadian Journal of Fisheries and Aquatic Sciences volume 52, issue 4, page 788-798 ISSN 0706-652X 1205-7533 Aquatic Science Ecology, Evolution, Behavior and Systematics journal-article 1995 crcansciencepubl https://doi.org/10.1139/f95-078 2024-04-09T06:56:28Z Ecologists often rely on empirically defined statistical relationships to infer how variables might be related. However, the usual method of estimating such relationships (ordinary least-squares (OLS)) is generally inappropriate because of the substantial natural variability of most ecological variables. Natural error variability in the regressor variable can artificially create a significant empirical trend where no underlying or structural relationship exists, or fail to reveal a true structural relationship. In multivariate relationships, natural variability in one variable can induce statistical significance in collinear variables even if they bear no structural relationship. We propose a simple new method, based on instrumental variables, to detect and quantify natural error variability in the regressor variables and to estimate the parameters of the structural relationship. We apply this method to two examples: (1) we show that the structural relationship between adenosine triphosphate concentration (total planktonic biomass) and chlorophyll concentration (autotrophic biomass) does not vary latitudinally in the Southern Ocean despite a significant increase in the OLS slope relating the two at more southerly stations and (2) we demonstrate that the significance of nitrogen in nutrient–chlorophyll relationships in lakes probably reflects natural variability in phosphorus concentration, and not the fertilizing effect of nitrogen. Article in Journal/Newspaper Southern Ocean Canadian Science Publishing Canadian Journal of Fisheries and Aquatic Sciences 52 4 788 798 |
institution |
Open Polar |
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Canadian Science Publishing |
op_collection_id |
crcansciencepubl |
language |
English |
topic |
Aquatic Science Ecology, Evolution, Behavior and Systematics |
spellingShingle |
Aquatic Science Ecology, Evolution, Behavior and Systematics Prairie, Yves T. Bird, David F. Peters, Robert H. Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
topic_facet |
Aquatic Science Ecology, Evolution, Behavior and Systematics |
description |
Ecologists often rely on empirically defined statistical relationships to infer how variables might be related. However, the usual method of estimating such relationships (ordinary least-squares (OLS)) is generally inappropriate because of the substantial natural variability of most ecological variables. Natural error variability in the regressor variable can artificially create a significant empirical trend where no underlying or structural relationship exists, or fail to reveal a true structural relationship. In multivariate relationships, natural variability in one variable can induce statistical significance in collinear variables even if they bear no structural relationship. We propose a simple new method, based on instrumental variables, to detect and quantify natural error variability in the regressor variables and to estimate the parameters of the structural relationship. We apply this method to two examples: (1) we show that the structural relationship between adenosine triphosphate concentration (total planktonic biomass) and chlorophyll concentration (autotrophic biomass) does not vary latitudinally in the Southern Ocean despite a significant increase in the OLS slope relating the two at more southerly stations and (2) we demonstrate that the significance of nitrogen in nutrient–chlorophyll relationships in lakes probably reflects natural variability in phosphorus concentration, and not the fertilizing effect of nitrogen. |
format |
Article in Journal/Newspaper |
author |
Prairie, Yves T. Bird, David F. Peters, Robert H. |
author_facet |
Prairie, Yves T. Bird, David F. Peters, Robert H. |
author_sort |
Prairie, Yves T. |
title |
Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
title_short |
Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
title_full |
Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
title_fullStr |
Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
title_full_unstemmed |
Natural variability and the estimation of empirical relationships: a reassessment of regression methods |
title_sort |
natural variability and the estimation of empirical relationships: a reassessment of regression methods |
publisher |
Canadian Science Publishing |
publishDate |
1995 |
url |
http://dx.doi.org/10.1139/f95-078 http://www.nrcresearchpress.com/doi/pdf/10.1139/f95-078 |
genre |
Southern Ocean |
genre_facet |
Southern Ocean |
op_source |
Canadian Journal of Fisheries and Aquatic Sciences volume 52, issue 4, page 788-798 ISSN 0706-652X 1205-7533 |
op_rights |
http://www.nrcresearchpress.com/page/about/CorporateTextAndDataMining |
op_doi |
https://doi.org/10.1139/f95-078 |
container_title |
Canadian Journal of Fisheries and Aquatic Sciences |
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52 |
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4 |
container_start_page |
788 |
op_container_end_page |
798 |
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1797570563949985792 |