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Estimating and Modelling Bias of the Hierarchical Partitioning Public-Domain Software: Implications in Environmental Management and Conservation
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BACKGROUND: Hierarchical partitioning (HP) is an analytical method of multiple regression that identifies the most likely causal factors while alleviating multicollinearity problems. Its use is increasing in ecology and conservation by its usefulness for complementing multiple regression analysis. A public-domain software "hier.part package" has been developed for running HP in R software. Its authors highlight a "minor rounding error" for hierarchies constructed from >9 variables, however potential bias by using this module has not yet been examined. Knowing this bias is pivotal because, for example, the ranking obtained in HP is being used as a criterion for establishing priorities of conservation. METHODOLOGY/PRINCIPAL FINDINGS: Using numerical simulations and two real examples, we assessed the robustness of this HP module in relation to the order the variables have in the analysis. Results indicated a considerable effect of the variable order on the amount of independent variance explained by predictors for models with >9 explanatory variables. For these models the nominal ranking of importance of the predictors changed with variable order, i.e. predictors declared important by its contribution in explaining the response variable frequently changed to be either most or less important with other variable orders. The probability of changing position of a variable was best explained by the difference in independent explanatory power between that variable and the previous one in the nominal ranking of importance. The lesser is this difference, the more likely is the change of position. CONCLUSIONS/SIGNIFICANCE: HP should be applied with caution when more than 9 explanatory variables are used to know ranking of covariate importance. The explained variance is not a useful parameter to use in models with more than 9 independent variables. The inconsistency in the results obtained by HP should be considered in future studies as well as in those already published. Some recommendations to improve the analysis with this HP module are given.
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![Figure 1 Number of studies using the HP package of Walsh and Mac Nally [9] for the R software over time. The subject categories with most number of studies are shown. Filled circles: number of total studies using HP package (n = 128). Filled squares: “Ecology” subject category. Opened circles: “Biodiversity conservation” subject category. Filled triangles: “Environmental sciences” subject category. Filled diamonds: “Geography physical” subject category. Red filled circles and dashed line: Number of studies using the HP package with more than 9 variables (n = 26). Note that a same study can pertain to more than 1 subject category and thus the sum of the number of studies from all the categories is higher than the number of total of studies.](/paper-figures/c1f884f444fe4023871604a33e32d46b/estimating-and-modelling-bias-of-the-hierarchical-partitioning-public-domain-figure-1.jpg)
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“Olea et al. (150) have shown that for more than nine explanatory variables, the order in which variables are entered in an HP analysis can affect the amount of independent variance explained by a given predictor.”
From Climate-driven declines in arthropod abundance restructure a rainforest food web (2018) · cites this paper as [150]
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Leiva-González, E. M., Gutierrez, D. A. N., Ruíz-Montoya, L., Santos‐Moreno, A., Kraker‐Castañeda, C., & García-Bautista, M. (2018) · Mammal Research · doi:10.1007/s13364-018-0403-z · Cited by 1
Metadata
- Authors
- Olea, P. P., Mateo-Tomás, P., & de Frutos, Á.
- Affiliations
- IE University (ES)
- Corresponding author
- Olea, Pedro P.
- ORCID
- Olea, Pedro P.
- Venue
- PLoS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2010-07-21
- Volume
- 5
- Issue
- 7
- Pages
- e11698
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC2908144
- OpenAlex
- W2089525213
- Cited by
- 109
- References
- 34
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 6 · 2023: 11 · 2022: 10 · 2021: 10 · 2020: 6 · 2019: 4 · 2018: 11 · 2017: 5 · 2016: 6 · 2015: 9 · 2014: 6 · 2013: 4 · 2012: 7
- FWCI
- 4.36
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- PLoS ONE (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Figshare (submittedVersion, cc-by)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Data Analysis with R
- Keywords
- hierarchical partitioning, multicollinearity, explained variance, conservation prioritization, environmental management, ecological inference, numerical simulation
- MeSH terms
- Conservation of Natural Resources, Environmental Monitoring, Models, Theoretical, Software, Bias
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