Residual covariance in bivariate with qt and binary traits

Hi Jiang
I used bivariate reml model with 1 quantitative trait and 1 binary.
I have 333 values for qt trait and 763 for case/controls (333 overlapping and 430 independent).

1)I used only overlapping individuals for both (333 values and case/controls)
I used wo different commands once including --reml-bivar-nocove and once I calculated recidual covariance.
The results are highly different and I need your help for the interpretation.
The first with residual covariance included:

Source Variance SE
V(G)_tr1 18.028821 11.676281
V(G)_tr2 0.046195 0.137366
C(G)_tr12 0.109697 0.910477
V(e)_tr1 4.729939 10.992880
V(e)_tr2 0.205741 0.133265
C(e)_tr12 0.318967 0.870802
Vp_tr1 22.758759 1.937684
Vp_tr2 0.251935 0.021028
V(G)/Vp_tr1 0.792171 0.488189:
V(G)/Vp_tr2 0.183359 0.541333
rG 0.120203 0.959111
logL -593.716
logL0 -593.723 (when rG fixed at 0.000)
LRT 0.014
df 1
Pval 0.4524 (one-tailed test)
n 666

The second without residual covariance

Source Variance SE
V(G)_tr1 19.000041 11.332581
V(G)_tr2 0.058078 0.133082
C(G)_tr12 0.440182 0.142308
V(e)_tr1 3.809812 10.634565
V(e)_tr2 0.194312 0.128821
Vp_tr1 22.809853 1.941344
Vp_tr2 0.252390 0.021075
V(G)/Vp_tr1 0.832975 0.470406
V(G)/Vp_tr2 0.230112 0.522271
rG 0.419033 0.501154
logL -593.782
logL0 -598.809 (when rG fixed at 0.000)
LRT 10.054
df 1
Pval 0.0007601 (one-tailed test)
n 666

Why do they look so different?
Is the sample size too small?

2)I want to run a second model with qt trait for 333 indivs and a case/controls for 430 NOT overlapping indivs.
Can I run a similar model or is better to include all 763 case/controls as trait2 and 333 qt as trait1?

Thanks