So I have created an LRT using hyphy which obviously requires two separate models be optimized and then compared. The problem is that the alternative model (fewer constraints) always seems to come out with a lower likelihood than the null. I optimize and then use ClearConstraints to change the null into the alternative model. When I check parameter starting values for the alternative they are the same before and after the clear constraint. Shouldn't the null optimized values be the starting point for the second optimization and therefore a negative LRT not possible? Now in this case the null value for some of the parameters is not possible in the alternative model but it is set to be very very close (difference of 0.0001) and under other simulations I know this to not be a huge change in likelihood (-0.1 at min). I have included the test simulated data and script. This is an example script that emphasizes the problem.

So my overall question is, is there a way to eliminate negative LRT's (at least to the -0.1 level) or am I doing something wrong? I hope that makes sense. Thanks for any help.