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Abstract Multiscale geographically weighted regression (MGWR) extends geographically weighted regression (GWR) by allowing process heterogeneity to be modeled at different spatial scales. While MGWR improves parameter estimates compared to GWR, the relationship between spatial scale and correlations within and among covariates—specifically spatial autocorrelation and collinearity—has not been systematically explored. This study investigates these relationships through controlled simulation experiments. Results indicate that spatial autocorrelation and collinearity affect specific model components rather than the entire model. Their impacts are cumulative but remain minimal unless they become very strong. MGWR effectively mitigates local multicollinearity issues by applying varying bandwidths across parameter surfaces. However, high levels of spatial autocorrelation and collinearity can lead to bandwidth underestimation for global processes, potentially producing false local effects. Additionally, strong collinearity may cause bandwidths to be overestimated for some processes, which helps mitigate collinearity but may obscure local effects. These findings suggest that while MGWR offers greater robustness against multicollinearity compared to GWR, bandwidth estimates should be interpreted with caution, as they can be influenced by strong spatial autocorrelation and collinearity. These results have important implications for empirical applications of MGWR.
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Estimation and interpretation problems and solutions when using proportion covariates in linear regression models
Proportion variables, also known as compositional data, are very common in ecology. Unfortunately, few scientists are aware of how compositional data, when used as covariates, can adversely impact statistical analysis. We describe here how proportion covariates result in multicollinearity and parameter identifiability problems. Using simulated data on bird species richness as a function of land use, we show how these problems manifest when fitting a wide range of models in R, both in a frequentist and Bayesian framework. In particular, we show that similar models can often generate substantially different parameter estimates, leading to very different conclusions. Dropping a covariate or the intercept from the model can solve the multicollinearity and parameter identifiability problems. Unfortunately, these solutions do not fix the inherent challenges associated with interpreting parameter estimates. To this end, we propose focusing the interpretation on the difference of slope parameters to avoid the inherent unidentifiability of individual parameters. We also propose conditional plots with two‐axes and marginal plots as visualization techniques that can help users better interpret their modeling results. We illustrate these problems and proposed solutions using empirical data from the North American Breeding Bird Survey. The practical and straightforward approaches suggested in this article will help the fitting of linear models and interpretation of its results when some of the covariates are proportions.
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- Award ID(s):
- 2040819
- PAR ID:
- 10581477
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Ecology
- Volume:
- 105
- Issue:
- 4
- ISSN:
- 0012-9658
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1002/ecy.4256
