Program for Model II regression with permutation tests

Pierre Legendre
January 2000
Département de Sciences Biologiques
Université de Montréal
This program 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. 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).

Program availability

Legendre, P. & Legendre, L. 1998. Numerical Ecology, 2nd English edition. Elsevier Science BV, Amsterdam. xv + 853 pages. Sokal, R. R. & F. J. Rohlf. 1995. Biometry - The principles and practice of statistics in biological research. 3rd edition. W. H. Freeman, New York.