Use and misuse of the reduced major axis for line-fitting.
Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X-axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry-asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate.
Department of Anthropology, Washington University, St. Louis, MO 63130, USA. rjsmith@wustl.edu
Richard J
RJ
Smith
D003627:Data Interpretation, Statistical; D016018:Least-Squares Analysis; D012107:Research Design