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Despite recent advances in algorithmic fairness, methodologies for achieving fairness with generalized linear models (GLMs) have yet to be explored in general, despite GLMs being widely used in practice. In this paper we introduce two fairness criteria for GLMs based on equalizing expected outcomes or log-likelihoods. We prove that for GLMs both criteria can be achieved via a convex penalty term based solely on the linear components of the GLM, thus permitting efficient optimization. We also derive theoretical properties for the resulting fair GLM estimator. To empirically demonstrate the efficacy of the proposed fair GLM, we compare it with other well-known fair prediction methods on an extensive set of benchmark datasets for binary classification and regression. In addition, we demonstrate that the fair GLM can generate fair predictions for a range of response variables, other than binary and continuous outcomes.
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Generalized Linear Models outperform commonly used canonical analysis in estimating spatial structure of presence/absence data
Background Ecological communities tend to be spatially structured due to environmental gradients and/or spatially contagious processes such as growth, dispersion and species interactions. Data transformation followed by usage of algorithms such as Redundancy Analysis (RDA) is a fairly common approach in studies searching for spatial structure in ecological communities, despite recent suggestions advocating the use of Generalized Linear Models (GLMs). Here, we compared the performance of GLMs and RDA in describing spatial structure in ecological community composition data. We simulated realistic presence/absence data typical of many β -diversity studies. For model selection we used standard methods commonly used in most studies involving RDA and GLMs. Methods We simulated communities with known spatial structure, based on three real spatial community presence/absence datasets (one terrestrial, one marine and one freshwater). We used spatial eigenvectors as explanatory variables. We varied the number of non-zero coefficients of the spatial variables, and the spatial scales with which these coefficients were associated and then compared the performance of GLMs and RDA frameworks to correctly retrieve the spatial patterns contained in the simulated communities. We used two different methods for model selection, Forward Selection (FW) for RDA and the Akaike Information Criterion (AIC) for GLMs. The performance of each method was assessed by scoring overall accuracy as the proportion of variables whose inclusion/exclusion status was correct, and by distinguishing which kind of error was observed for each method. We also assessed whether errors in variable selection could affect the interpretation of spatial structure. Results Overall GLM with AIC-based model selection (GLM/AIC) performed better than RDA/FW in selecting spatial explanatory variables, although under some simulations the methods performed similarly. In general, RDA/FW performed unpredictably, often retaining too many explanatory variables and selecting variables associated with incorrect spatial scales. The spatial scale of the pattern had a negligible effect on GLM/AIC performance but consistently affected RDA’s error rates under almost all scenarios. Conclusion We encourage the use of GLM/AIC for studies searching for spatial drivers of species presence/absence patterns, since this framework outperformed RDA/FW in situations most likely to be found in natural communities. It is likely that such recommendations might extend to other types of explanatory variables.
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- Award ID(s):
- 1757351
- PAR ID:
- 10228701
- Date Published:
- Journal Name:
- PeerJ
- Volume:
- 8
- ISSN:
- 2167-8359
- Page Range / eLocation ID:
- e9777
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.7717/peerj.9777
