Covariance estimate is zero for random compoment

Question

My dataset consists of 4 variable: values, dil, exp and sample. There are 170 values obtained for variable values; there are 5 levels for the variable dil, 10 levels for the variable exp and 5 levels for the variable sample.

I fitted a mixed model in SAS to find the variance component estimates:

proc mixed;
by sample;
model values = dil;
random exp;
run;

So here dil is fixed and experiment is random.

When I fit the model, the covariance estimate for for exp is zero. It says that "Convergence criteria met but final hessian is not positive definite". Can anyone give some help on this? Thank you!

Also there are a few na values in the dataset.

Answer 1

By covariance estimate do you mean the error term for experiment is 0? I wouldn't call this a covariance estimate.

This is a common problem with mixed models. The most common explanation of a zero error estimate is that there are too many levels of the random random effect and not enough fixed observations within each random level to be able to calculate the error term.

I think you should look into fitting your data into one model instead of 'by sample'. I don't know enough about your design. Is 'sample' repeated measurements on the same observation? If not you can probably just remove the 'by sample' statement, else you need to modify the code to introduce correlation among the repeated effects.

If you post your data with more explanation we may be able to determine the correct model. However in some situations, when the experimental design was poor, you may not be able to get around this.