On the Choice of Linear Regression Algorithms for Biological and Ecological Applications

Abstract

Model II regression (i.e. minimizing residuals obliquely) is the adequate alternative to Model I regression by Ordinary Least Squares (i.e. minimizing residuals vertically) given the absence of well-established dependence relationships or x measured with error. Yet, it has no perfect solution. Determining the true slope from errors-in-the-variables models requires the errors in x and y estimated from higher order moments. However, their accurate estimation requires enormous data sets and thus they are not applicable to most ecological problems. The alternative Reduced Major Axis (RMA) is dependent on a strict set of assumptions, hardly met with real data, making it prone to bias, whereas Principal Components Analysis (PCA) becomes less reliable with decreasing correlations while x and y presenting approximate variances. We used artificial data (allowing for the determination of the true slope) to demonstrate when RMA or PCA should be preferred. Consequently, we propose using PCA whenever r 2 +s 2 x /s 2 y is higher than 1.5. Otherwise, we suggest generating artificial data manipulated to match the structure of the original, and to test which method provides closer estimates to the input true slope. We provide a user-friendly script to perform this task. We tested the use of RMA and PCA with real data about intraspecific and interspecific biomass-density relations in algae and seagrass, algae frond growth, crustacean and bird morphometry, sardine fisheries and social sciences data, commonly finding widely divergent slope estimates leading to severely biased parameter estimations and model applications. Their analyses support the suggested approach for method selection summarized above.

A machine learning-based quantitative model (LogBB_Pred) to predict the blood–brain barrier permeability (logBB value) of drug compounds

“…For comparison, we also developed prediction models based on other machine learning algorithms: RF ( Svetnik et al 2003 ), k NN ( Song et al 2017 ), ANN ( Tadeusiewicz 2015 ), MLR ( Vieira et al 2016 ), AdaBoost ( CAO et al 2014 ), XGBoost ( Ogunleye and Wang 2020 ), and SVM ( Ben-Hur et al 2008 ). RF is an ensemble learning method that combines multiple decision trees to improve model accuracy and generalization.…”

“…MLR is a statistical method used to model a linear relationship between a dependent variable and one or more independent variables. The objective of MLR is to find the best-fit line that represents the relationship between variables ( Vieira et al 2016 ). SVM is a supervised learning algorithm used for classification and regression analysis.…”

A meta-analysis shows that seaweeds surpass plants, setting life-on-Earth’s limit for biomass packing

“…We add a numerical argument for a careful selection of the data from such stands: these are randomly scattered below the IBL, leading their distribution to approximate a circle. In these cases the slopes estimated by ordinary least squares (OLS) tend to 0, those estimated by reduced major axis (RMA) tend to 1, and those estimated by principal components analysis (PCA) become erratic [49–52]. We estimated the boundary line using quantile regression (QR).…”

A model for the biomass–density dynamics of seagrasses developed and calibrated on global data

“…PCA and RMA tend to be complementary, with one excelling where the other fails. However, when applied to biomass–density data, PCA often performs better than RMA [39–41]. With these seagrass data, both methods were generally equally good, and RMA performed conspicuously less well only when applied to Cymodocea nodosa (Ucria) Ascherson (1870).…”