Reduced Major Axis Regression

Abstract

The theoretical underpinnings of standard least‐squares (LS) regression analysis are based on the assumption that the independent variable (often thought of as x ) is measured without error as a design variable. The dependent variable (often labeled y ) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Thus, the underlying least‐squares regression assumptions can be violated. Reduced major axis (RMA) regression is specifically formulated to handle errors in both the x and y variables. It is an alternative to least squares and demonstrates the importance of understanding the assumptions underlying statistical procedures.

Air pollution scenario over Pakistan: Characterization and ranking of extremely polluted cities using long-term concentrations of aerosols and trace gases

“…Accuracy and errors are reported using the Pearson correlation coefficient (r), the expected error (EE, Equation 4), and relative mean bias (RMB, Equation 5). The slope (, Equation 6) and intercept (, Equation 7) between collocated AquaTerra DTB and AERONET AOD data are calculated using the reduced major axis (RMA) regression which incorporates errors in both independent (AERONET) and dependent (MODIS) variables (Bilal et al 2019a;Harper 2016). The performance of the Terra and Aqua DT, DB, and DTB AOD retrievals is evaluated based on (i) highest correlation coefficient (r), (ii) highest number of collocated retrievals (N), (iii) the highest percentage of retrievals within the EE, and (iv) lowest RMB.…”

Coral Records at the Northern Edge of the Western Pacific Warm Pool Reveal Multiple Drivers of Sea Surface Temperature, Salinity, and Rainfall Variability Since the End of the Little Ice Age

“…Calibrations of Sr/Ca and SST and δ 18 O and SSS were performed using reduced major axis (RMA) linear regressions at monthly and interannual timescales, unless otherwise indicated to facilitate comparison. Compared with the commonly used ordinary least squares (OLS) regression method, RMA accounts for potential errors in both dependent and independent variables, simultaneously minimizing the distance perpendicular to the regression line (Clarke, 1980; Harper, 2016). We found that applying the RMA linear regression method in our monthly and interannual calibrations consistently resulted in steeper slopes and reduced reconstruction errors compared with those of the OLS method (supporting information Figure S3 and Table S3).…”

Design and field campaign validation of a multi-rotor unmanned aerial vehicle and optical particle counter

“…Figure 11 shows the comparative plots for the re-binned data, the regression line, and the corresponding droplet diameter -using the geometric mean diameter of the bins -represented by the colour of the points. Reduced major axis regression (RMAR), as described in Harper (2016), was used since this technique correctly assumes that neither sampling method is perfect. Figure 11b is plotted on a log-log scale for clarity, leading to the appearance of a curved regression line.…”