*Holland (2006) Crop Sci. 46:642-654 genotypic correlation macro
This version is for RCBD of one test involving genotypes

dataset need to be named "tall"
variables names are rep & geno
do the correlation two variables at a time, which ones are defined in the call of the macro
;

%macro gencorr(TraitI, TraitJ);
data subset; set tall; if trait 5 "&TraitI" or if trait 5"&TraitJ";
*Perform multivariate REML estimation of variance
and covariance components, using the "asycov" option
of proc mixed to obtain the asymptotic variancecovariance
matrix of the estimates;
proc mixed data5subset asycov;
class trait rep geno;
*Treat environments and replications as fixed effects to
speed computation of the variance and covariance
estimates of interest. Note that the F-tests associated
with these factors are testing the hypothesis that there
are no significant differences among environments or
among replications for the two traits combined. Such
hypothesis are generally not of real interest, instead
tests of main effects of environments and replications,
if they are of interest, should be conducted on each
trait separately with univariate analyses;
model y 5 rep(trait);
* Treat genotypes ("geno") and genotype-by-environment
interactions ("geno*env") as random effects and
estimate their variance and covariance components
for the two traits with the following codes;
random trait/subject 5 geno type 5 un;
* Model the residual error term ("rep*geno(env)") to
allow for covariances between error effects on the two
traits measured on the same plot, but not between
different plots;
repeated trait/ sub 5 rep*geno type 5 un;
*Output the estimates of variance and covariance
components to a data set called "estmat" and output
the asymptotic variance-covariance matrix of those
estimates to a data set called "covmat";
ods output covparms 5 estmat asycov 5 covmat;
run;
*Read variance and covariance estimates ("estmat"
data set, to be read into a vector called "e") and their
variance-covariance matrix ("covmat" data set, to be
read into a matrix called "cov") into proc iml to estimate
correlations and their standard errors using the
delta method;
proc iml;
use estmat; read all into e;
use covmat; read all into cov;
*Obtain the "C" matrix by removing the extra first column
of the "cov" matrix;
C 5 cov(|1:nrow(cov), 2:ncol(cov)|);
*Obtain genotypic covariance (CovG) and variance
components (VG1 and VG2) from the elements of the
"e" vector;
CovG 5 e(|2,1|); VG1 5 e(|1,1|); VG2 5 e(|3,1|);
*Obtain phenotypic covariance (CovP) and variance
components (VP1 and VP2) from the elements of the
"e" vector;
CovP 5 CovG 1 e(|5,1|);
VP1 5 VG1 1 e(|4,1|); VP2 5 VG2 1 e(|6,1|);
*Create a module called "correl" that will estimate genotypic
and phenotypic correlations and their standard
errors;
start correl(C, CovG, VG1, VG2, CovP, VP1, VP2, RG,
RP, SERG, SERP);
RG 5 CovG/sqrt(VG1*VG2);
* Make the derivative vector for rg, note that the order
of the rows and columns of the variance covariance
matrix is VG1, CovG, VG2, VGE1, CovGE, VGE2,
VError1, CovError, VError2;
dg5 (21/(2*VG1))//(1/CovG)//(21/(2*VG2))//0//0//0;
*Compute the variance of the estimate of the genotypic
correlation using the delta method, then take its square
root to obtain the standard error of the genotypic correlation
estimate ("serg");
varrg 5 (RG**2)*dg9*C*dg; serg 5 sqrt(varrg);
RP 5 CovP/sqrt(VP1*VP2);
*Make the derivate vector for rp;
d1p 5 21/(2*VP1); d2p 5 1/CovP; d3p 5 21/
(2*VP2);
dp 5 d1p//d2p//d3p//d1p//d2p//d3p;
*Compute the variance of the estimate of the phenotypic
correlation using the delta method, then take
its square root to obtain the standard error of the phenotypic
correlation estimate ("serp");
varrp 5 (RP**2)*dp‘*C*dp; serp 5 sqrt(varrp);
finish correl;
* Run the "correl" module and display the results;
call correl(C, CovG, VG1, VG2, CovP, VP1, VP2, RG,
RP, SERG, SERP);
print "Genotypic Correlation Between &TraitI and
&TraitJ";
print RG serg;
print "Phenotypic Correlation Between &TraitI and
&TraitJ ";
print RP serp;
quit;
run;
* End the macro;