title 'no EVR';
data semex;
input X Y Z;
cards;
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-0.285903650628292	0.251069095255313	1
;
run;
;
proc nlmixed data = semex tech = trureg hess corr itdetails;
*Starting values;
parms MNX =  .01, MNY =  0.001, DX0 = 0.01, DY0 = 0.4, DR0 = 1.0, DX1 = 0.01, DY1 = 0.01, DR1 = -0.3;
title 'EVR false';
*This is the model;
MUX = MNX;
MUY = MNY;
DEVX = X - MUX;
DEVY = Y - MUY;
DX = DX0 + DX1*Z;
DY = DY0 + DY1*Z;
SX = exp(DX);
SY = exp(DY);
RHO = (exp(DR0 + DR1*Z)-1)/(exp(DR0 + DR1*Z)+1);
ll = ((SX**2)*(DEVY**2) - 2*RHO*SX*SY*DEVX*DEVY + (SY**2)*(DEVX**2))/(2*(RHO**2-1)*(SX**2)*(SY**2)) - log(2*3.145927) - 0.5*(log(1 - RHO**2) + log(SX**2) + log(SY**2));
model Y ~ general(ll);
run;
;
proc nlmixed data = semex tech = trureg hess corr itdetails;
*Starting values;
parms MNX =  .01, MNY =  0.001, DX0 = 0.01, DY0 = 0.36, DR0 = 1.0, D1 = 0.01, DR1 = -0.3;
title 'EVR true';
*This is the model;
MUX = MNX;
MUY = MNY;
DEVX = X - MUX;
DEVY = Y - MUY;
DX = DX0 + D1*Z;
DY = DY0 + D1*Z;
SX = exp(DX);
SY = exp(DY);
RHO = (exp(DR0 + DR1*Z)-1)/(exp(DR0 + DR1*Z)+1);
ll = ((SX**2)*(DEVY**2) - 2*RHO*SX*SY*DEVX*DEVY + (SY**2)*(DEVX**2))/(2*(RHO**2-1)*(SX**2)*(SY**2)) - log(2*3.145927) - 0.5*(log(1 - RHO**2) + log(SX**2) + log(SY**2));
model Y ~ general(ll);
run;
;
proc nlmixed data = semex tech = trureg hess corr itdetails;
*Starting values;
parms MNX =  .01, MNY =  0.001, DX0 = 0.01, DY0 = 0.36, DR0 = 1.0, DY1 = 0.01, DR1 = -0.3;
title 'HoV for X';
*This is the model;
MUX = MNX;
MUY = MNY;
DEVX = X - MUX;
DEVY = Y - MUY;
DX = DX0;
DY = DY0 + DY1*Z;
SX = exp(DX);
SY = exp(DY);
RHO = (exp(DR0 + DR1*Z)-1)/(exp(DR0 + DR1*Z)+1);
ll = ((SX**2)*(DEVY**2) - 2*RHO*SX*SY*DEVX*DEVY + (SY**2)*(DEVX**2))/(2*(RHO**2-1)*(SX**2)*(SY**2)) - log(2*3.145927) - 0.5*(log(1 - RHO**2) + log(SX**2) + log(SY**2));
model Y ~ general(ll);
run;
;
proc nlmixed data = semex tech = trureg hess corr itdetails;
*Starting values;
parms MNX =  .01, MNY =  0.001, DX0 = 0.01, DY0 = 0.36, DR0 = 1.0, DY1 = 0.01;
title 'HoV X and equal corr';
*This is the model;
MUX = MNX;
MUY = MNY;
DEVX = X - MUX;
DEVY = Y - MUY;
DX = DX0;
DY = DY0 + DY1*Z;
SX = exp(DX);
SY = exp(DY);
RHO = (exp(DR0)-1)/(exp(DR0)+1);
ll = ((SX**2)*(DEVY**2) - 2*RHO*SX*SY*DEVX*DEVY + (SY**2)*(DEVX**2))/(2*(RHO**2-1)*(SX**2)*(SY**2)) - log(2*3.145927) - 0.5*(log(1 - RHO**2) + log(SX**2) + log(SY**2));
model Y ~ general(ll);
run;