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Abstract:
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Ordinary Least Squares (OLS) regression assumes that the independent variables are measured without error. However, it can be argued that any measured independent variables – those whose underlying distributions are continuous or nearly continuous – are actually measured with error. Alternative models, such as Reduced Major Axis (RMA) regression - also known as geometric mean regression, have been proposed to account for the errors in independent variables. Despite this, OLS regression remains the standard model in science even in cases where independent variables are almost certainly measured with error. The reliance on OLS may be partly due to well-developed theory behind OLS regression compared to RMA. Here we fill the theoretical gap for RMA by deriving the estimators for RMA regression in the 0-intercept case. We also examine the performance of both methods in different settings, including where some independent variables are measured with error and others are not. We conclude with a case study on allometric models.
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