Robustness to failure of assumptions of tests for a common slope amongst several allometric lines--a simulation study

In allometry, researchers are commonly interested in estimating the slope of the major axis or standardized major axis (methods of bivariate line fitting related to principal components analysis). This study considers the robustness of two tests for a common slope amongst several axes. It is of particular interest to measure the robustness of these tests to slight violations of assumptions that may not be readily detected in sample datasets. Type I error is estimated in simulations of data generated with varying levels of nonnormality, heteroscedasticity and nonlinearity. The assumption failures introduced in simulations were difficult to detect in a moderately sized dataset, with an expert panel only able to correct detect assumption violations 34-45% of the time. While the common slope tests were robust to nonnormal and heteroscedastic errors from the line, Type I error was inflated if the two variables were related in a slightly nonlinear fashion. Similar results were also observed for the linear regression case. The common slope tests were more liberal when the simulated data had greater nonlinearity, and this effect was more evident when the underlying distribution had longer tails than the normal. This result raises concerns for common slopes testing, as slight nonlinearities such as those in simulations are often undetectable in moderately sized datasets. Consequently, practitioners should take care in checking for nonlinearity and interpreting the results of a test for common slope. This work has implications for the robustness of inference in linear models in general.