Very small estimate with a very large standard error in univariate modelling.

Dear all, 

This is the first time to have a post in this forum, and thanks for the platform.

I am a researcher working on the Finnish Twin Cohorts, and I am doing a univariate twin modeling on depression. I have 113 DZ pairs and 69 MZ pairs. The outcome of depression is basically normal-distributed.

Then in the ADE model, I get the data summary and results like this:

data:
$MZ
      dep1            dep2            age1            age2      
 Min.   :1.375   Min.   :1.375   Min.   :34.43   Min.   :34.62  
 1st Qu.:1.750   1st Qu.:1.750   1st Qu.:36.02   1st Qu.:35.92  
 Median :1.875   Median :1.875   Median :37.14   Median :37.25  
 Mean   :1.893   Mean   :1.891   Mean   :37.30   Mean   :37.31  
 3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:38.57   3rd Qu.:38.69  
 Max.   :3.250   Max.   :2.750   Max.   :39.61   Max.   :39.74  

$DZ
      dep1            dep2            age1            age2      
 Min.   :1.250   Min.   :1.250   Min.   :34.55   Min.   :34.49  
 1st Qu.:1.625   1st Qu.:1.750   1st Qu.:35.90   1st Qu.:35.92  
 Median :1.875   Median :1.875   Median :37.16   Median :37.12  
 Mean   :1.889   Mean   :1.869   Mean   :37.19   Mean   :37.18  
 3rd Qu.:2.000   3rd Qu.:2.000   3rd Qu.:38.54   3rd Qu.:38.47  
 Max.   :3.000   Max.   :2.750   Max.   :39.75   Max.   :39.82  

free parameters:
   name   matrix row col   Estimate Std.Error A lbound ubound
1  mean MZ.meanG   1   1 1.88344659  115.8524                
2 beta1     MZ.b   1   1 0.01000000        NA !              
3  VA11    MZ.VA   1   1 0.00194220  303.5822 ! 1e-04!       
4  VD11    MZ.VD   1   1 0.03293261  293.7319 ! 1e-04!       
5  VE11    MZ.VE   1   1 0.05600604  328.6864    1e-04 

The estimates of variance of A, D, or E are quite small, but their SE is large. I am wondering why this thing happened? Is it because of small sample size? 

Besides, there is another warning:

The Hessian at the solution does not appear to be convex. See ?mxCheckIdentification for possible diagnosis (Mx status RED). 

Thank you very much for your insightful suggestions!

Best

Zhiyang