Model Ii Regression User’s Guide, R Edition

Function lmodel2 computes model II simple linear regression using the following methods: major axis (MA), standard major axis (SMA), ordinary least squares (OLS), and ranged major axis (RMA). Information about these methods is available, for instance, in section 10.3.2 of Legendre and Legendre (1998) and in sections 14.13 and 15.7 of Sokal and Rohlf (1995). Parametric 95% confidence intervals are computed for the slope and intercept parameters. A permutation test is available to determine the significance of the slopes of MA, OLS and RMA and also for the correlation coefficient. This function represents an evolution of a Fortran program written in 2000 and 2001. Bartlett’s three-group model II regression method, described by the above mentioned authors, is not computed by the program because it suffers several drawbacks. Its main handicap is that the regression lines are not the same depending on whether the grouping (into three groups) is made based on x or y. The regression line is not guaranteed to pass through the centroid of the scatter of points and the slope estimator is not symmetric, i.e. the slope of the regression y = f(x) is not the reciprocal of the slope of the regression x = f(y). Model II regression should be used when the two variables in the regression equation are random, i.e. not controlled by the researcher. Model I regression using least squares underestimates the slope of the linear relationship between the variables when they both contain error; see example in chapter 5.4 (p. 11). Detailed recommendations follow.