A case for beta regression in the natural sciences

Abstract

Data in the natural sciences are often in the form of percentages or proportions that are continuous and bounded by 0 and 1. Statistical analysis assuming a normal error structure can produce biased and incorrect estimates when data are doubly bounded. Beta regression uses an error structure appropriate for such data. We conducted a literature review of percent and proportion data from 2004 to 2020 to determine the types of analyses used for (0, 1) bounded data. Our literature review showed that before 2012, angular transformations accounted for 93% of analyses of proportion or percent data. After 2012, angular transformation accounted for 52% of analyses and beta regression accounted for 14% of analyses. We compared a linear model with angular transformation with beta regression using data from two fields of the natural sciences that produce continuous, bounded data: biogeochemistry and ecological elemental composition. We found little difference in model diagnostics, likelihood ratios, and p‐values between the two models. However, we found substantially different coefficient estimates from the back‐calculated beta regression and angular transformation models. Beta regression provides reliable parameter estimates in natural science studies where effect sizes are considered as important as hypothesis testing.

Methods for Fungicide Efficacy Screenings: Multiwell Testing Procedures for the Oomycetes Phytophthora infestans and Pythium ultimum

“…The comprehensive resume of the efficacy percentages (expressed as proportions) obtained through the BRM and the use of EMMs for the multiple comparisons allowed us to compare simultaneously the two factors (assay type and fungicide concentration). This approach has several advantages compared to the common statistical analyses (e.g., ANOVAs and Kruskal–Wallis); indeed, it does not require any data transformation, handling proportions naturally, and it can address nonconstant dispersion for covariate values (useful in large experiments) through the precision parameter [ 66 ], and it can provide an easily interpretable output ( Table S2 ) through the use of EMMs. The latter represents a very versatile tool for multiple comparisons, since single or multiple factors can be considered starting from the same model (i.e., one-way and two-way data can be handled in the same model) and, since they are equally weighted according to the factor level, can compensate for the imbalance in the data, which is a very common issue in large biological experiments (i.e., presence of outliers) [ 55 ].…”

Oceanic productivity and high-frequency temperature variability—not human habitation—supports calcifier abundance on central Pacific coral reefs

“…We then used beta regression to explore how significant variables identified by the db-RDA related to specific components of benthic cover using the betareg package in R with the logit link function (Cribari-Neto and Zeileis, 2010). Beta regression models are better suited for use with continuous proportional data bounded between [0, 1] than general linear models (Douma and Weedon, 2019;Geissinger et al, 2022). Outliers were excluded from beta regressions based on visual inspection of residual, Q-Q, and Cook's distance plots and evaluated for improved fit by comparison of the precision parameter (j).…”

Higher Early Marine Mortality of Steelhead Associated with Releases of Hatchery Coho Salmon but Not Chinook Salmon

“…2010; Geissinger et al. 2022). We fit separate models for each of the four abundance indices (Chinook Salmon lampara, Chinook Salmon hatchery, Coho Salmon lampara, Coho Salmon hatchery).…”

“…Statistical models.-We used Bayesian beta regression models to estimate the relationship between weekly steelhead survival estimates from the mark-recapture models and abundance of juvenile salmonids (Ferrari and Cribari-Neto 2004;Simas et al 2010;Geissinger et al 2022). We fit separate models for each of the four abundance indices (Chinook Salmon lampara, Chinook Salmon hatchery, Coho Salmon lampara, Coho Salmon hatchery).…”