Re: minimum objective function

From: KENNETH.G.KOWALSKI@monsanto.com Subject: Re: minimum objective function Date: 02 Dec 1998 14:25:47 -0600 Ian, I'm assuming that you checked your models and that the models are hierarchical. That is, for the model with both THETA(1) and THETA(2) you can set either to some null value (typically 0 or 1) such that it reduces to the THETA(1) or THETA(2) alone model. If that is the case then it should be that OF3<OF1 and OF3<OF2. If this is not being met, then you may not have achieved the global optimum (minimum objective function) for the model with both THETA(1) and THETA(2) in the model. Perhaps your model is overparameterized making it difficult to achieve the optimum. Let's suppose that you found OF2<OF3 yet they're supposed to be hierachical. You should be able to use final estimates obtained from the THETA(2) alone model and set THETA(1) to its null value for absence in the model with both THETA(1) and THETA(2) and have the same objective function value (OF2). You might start from there with perhaps only slightly changing the starting value for THETA(1) from its null value and see if you can get it to iterate and converge such that OF3<OF2. Of course if that happens, there is still no guarantee that you have achieved the absolute minimum. Good luck! Ken