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Cited by 109Advanced Statistical Methods and ModelsStatistical Methods and ApplicationsData Analysis with R

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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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Olea, Pedro P., Mateo-Tomás, Patricia, de Frutos, Ángel·2010·PLoS ONE
DOI 10.1371/journal.pone.0011698PMC PMC2908144
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Abstract

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.
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.CC BY · PubMed Central
Figure 2 Probability of a variable changing ranking position obtained from the averaged general linear mixed model. Solid lines: Effect of the difference in independent variance explained (IVE) between a particular variable and the previous one in the ranking (established for explaining the response variable) on the probability of changing the position for data sets formed by 10, 11 and 12 explanatory variables in analysis of hierarchical partitioning. Note that no change is expected when the difference in explained variance between a variable and the previous one in the ranking is >17.1. Dotted lines: upper and lower limits according to the standard error of the averaged mixed-model coefficients.
Figure 2 Probability of a variable changing ranking position obtained from the averaged general linear mixed model. Solid lines: Effect of the difference in independent variance explained (IVE) between a particular variable and the previous one in the ranking (established for explaining the response variable) on the probability of changing the position for data sets formed by 10, 11 and 12 explanatory variables in analysis of hierarchical partitioning. Note that no change is expected when the difference in explained variance between a variable and the previous one in the ranking is >17.1. Dotted lines: upper and lower limits according to the standard error of the averaged mixed-model coefficients.CC BY · PubMed Central

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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)
DOI
10.1371/journal.pone.0011698
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
Licence
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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