4 0 US !=ABACBA0CBAconstrains all parameters corresponding to A to be equal, similarly for B and C. The 7th parameter would be left unconstrained. This sequence applied to an unstructured 4 x 4 matrix would make it banded, that is

A

B A

C B A

0 C B A

site.gen 2 # G header line site 0 US .3 !=0A0AA0 !GPUPUUP .1 .4 .1 .1 .3 gendefines a structure for the genotype by site interaction effects in a MET in which the genotypes are independent random effects within sites but are correlated across sites with equal covariance.

site 0 FA2 !G4PZ3P4P !=00000000VVVV 4*.9 # initial values for 1st factor 0 3*.1 # initial values for 2nd factor, first fixed at 0 4*.2 # initial values for site variancesdefines a 2 factor Factor Analytic model for 4 sites with equal variance. The first loading in the second factor is constrained equal to 0 for identifiability. P places restrictions on the magnitude of the loadings and the variances to be positive.

xfa(site,2) 0 XFA2 !=VVVV0 !4P4PZ3P 4*.2 # initial specific variances 4*1.2 # initial loadings for 1st factor 0 3*.3 # initial loadings for 2nd factordefines a 2 factor Factor analytic model in which the specific variances are all equal.

where

if the coefficient is 1 you may omit the * 1,

if the coefficient is -1 you may write

the meaning of the coefficients is as follows

typically

a variance parameter may only be included in constraints once,

5 -7 parameter 7 is the negative of parameter

32 34 35 37 38 39 for a 4 by 4 US matrix given by parameters 31...40, the covariances are forced to be equal. units -uni(check) parameter associated with model

term uni(check) has the same magnitude but opposite sign to the parameter associated with model term units