Program for Model II regression with permutation tests
Pierre LegendreJanuary 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 threegroup model II regression method, described by the abovementioned 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

MacOSXIntel version
 Fortran source code (file modelII.f), which can be compiled using a Fortran compiler. The user may modify the Parameter statement at the beginning of the program, which fixes the size (nmax, mmax) of the largest data matrix which may be analysed.
 Compiled version of the program for Intel Macs
 Program documentation, in Adobe Acrobat format
 Sample files

MacOS9 version
 Fortran source code for MacOS9 ("Classic") (file ModelII.f), which can be compiled using a Fortran compiler. The user may modify the Parameter statement at the beginning of the program, which fixes the size (nmax, mmax) of the largest data matrix which may be analysed.
 Compiled versions of the program for any Macintosh computer (fat binary)
 Program documentation, in Adobe Acrobat format
 Sample files
 32bit DOS version (The executable file is a Win32 "console" executable, not a DOS executable. Therefore it cannot run under plain DOS, nor in a DOS window under Windows 3.x, only in Windows 95/98 or Windows NT consoles)
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.