Proc nlmixed significant variance interpretation

[Caetreviop543]

I’m conducting a tobit model using proc nlmixed, and was wondering how to interpret the variance parameter. Here is my model:

proc nlmixed data=mydat XTOL=1E-12 method=GAUSS qpoints=100;
parms b0=1.6 b1=-.04 sigma2_u=2 sigma2=5;
bounds sigma2_u sigma2 >=0;
pi = constant("pi");
mu = b0 + b_0j + b1*time;
if log_y > 0 then 
ll = (1 / (sqrt(2*pi*sigma2))) * exp( -(log_y-mu)**2 / (2*sigma2) );
if log_y = 0 then 
ll = probnorm( (log_y - mu) / sqrt(sigma2) );
L = log(ll);
model log_y ~ general(L);
random b_0j ~ normal(0, sigma2_u) subject=id;
run;
quit;

And my output:

How do I interpret the significant, fixed and random variance parameters (sigma2, sigma2_u)? Does a significant value mean the variance is larger than expected, or something else?

[SteveDenham · Accepted solution]

The tests are about a null hypothesis of the parameter being zero.  If you wish to test against some other value, you would have to re-parameterize the model.

SteveDenham