The structural relationship: regression in biology

Abstract

Most biologists are now aware that ordinary least square regression is not appropriate when the X and Y variables are both subject to random error. When there is no information about their error variances, there is no correct unbiased solution. Although the major axis and reduced major axis (geometric mean) methods are widely recommended for this situation, they make different, equally restrictive assumptions about the error variances. By using simulated data sets that violate these assumptions, the reduced major axis method is shown to be generally more efficient and less biased than the major axis method. It is concluded that if the error rate of the X variable is thought to be more than a third of that on the Y variable, then the reduced major axis method is preferable; otherwise the least squares technique is acceptable. An analogous technique, the standard minor axis method, is described for use in place of least squares multiple regression when all of the variables are subject to error.

Allometric scaling of foraging rate with trail dimensions in leaf-cutting ants

“…Standard errors of parameter estimates are identical for RMA and OLS regression [23], and we used the OLS standard errors calculated in R to determine 95% confidence intervals (CIs) for the slope coefficients.…”

Productivity, carbon isotope discrimination and leaf traits of trees of Eucalyptus globulus Labill. in relation to water availability

“…RMA regression is more appropriate than ordinary least squares regression when neither variable has a very small error variance and the correlation coefficient is less than 0.9, i.e. R 2 < 0.8 (McArdle 1988). The significance of the slope and the correlation coefficient are calculated the same for both OLS and RMA regressions.…”

Multivariate and geometric morphometrics in the analysis of sexual dimorphism variation in Podarcis lizards

“…The scaling of head characters with SVL was examined (after log-transformation of variables), treating the two sexes separately. To do this, reduced major axis (RMA) regression was applied, using the software developed by Bohonak (2002), as ordinary least-squares regression would provide biased values for the allometry equations due to the presence of measurement error in both the independent and the dependent variables (McArdle, 1988;Sokal and Rohlf, 1995). Deviation from isometry was tested using the formulae given in Clarke (1980).…”