I am estimating probit model and some other nonlinear models with Gauss. After it converges at 1e-5 tolerance using optmum or Qnewton to do the optimization, I plug in the estimated coefficients as the starting value. I expect that there will be no iteration since it's already converged. But it iterates again. And the gradient of the first iteration sometimes is even larger than 1e-2. Why is it?

## 3 Answers

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How many places do you save from converged values? The solution is for 16 decimal places and if your start values are less than that, 5 places, say, then it will have to iterate for those remaining 11 places.

0

Thank you! I saved 8 decimal places, and the tolerance is 1e-5. But when it iterates again, some of the gradients are even greater than 1e-4. When it converges again at 1e-5, some of the estimates are different than the starting value (or previous estimates) at 2nd decimal.

Maybe I have a really flat objective function?

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You are likely right about the flat function. Check the condition of your Hessian. I'm not sure what Application you're using, but if it's CMLMT,

struct cmlmtResults out;

out = CMLmt(&lpr,p0,d0,c0);

print log10(cond(out.hessian));

The number printed is the approximate number of places lost in computing the inverse for the covariance matrix of the parameters. If it's greater than 8, it is ill-conditioned indicating a relatively flat function. If it's greater than 16, it is a not positive definite matrix.

## Your Answer

## 3 Answers

How many places do you save from converged values? The solution is for 16 decimal places and if your start values are less than that, 5 places, say, then it will have to iterate for those remaining 11 places.

Thank you! I saved 8 decimal places, and the tolerance is 1e-5. But when it iterates again, some of the gradients are even greater than 1e-4. When it converges again at 1e-5, some of the estimates are different than the starting value (or previous estimates) at 2nd decimal.

Maybe I have a really flat objective function?

You are likely right about the flat function. Check the condition of your Hessian. I'm not sure what Application you're using, but if it's CMLMT,

struct cmlmtResults out;

out = CMLmt(&lpr,p0,d0,c0);

print log10(cond(out.hessian));

The number printed is the approximate number of places lost in computing the inverse for the covariance matrix of the parameters. If it's greater than 8, it is ill-conditioned indicating a relatively flat function. If it's greater than 16, it is a not positive definite matrix.