Verifying the Solution from a Nonlinear Solver: A Case Study

The probit is generally considered to be one of the easiest nonlinear maximum likelihood problems. Nonetheless, in the course of at-tempting to replicate G. S. Maddala’s (1992, pp. 335–38) probit example, Houston Stokes (2003) encountered great difficulty. Of the six coeffi-cients, five coefficients/standard errors he could duplicate, but the sixth was off by more than rounding error. So he tried another package. And another. And another.... Finally, five dif-ferent packages had declared convergence to five solutions that differed only in the sixth coefficient. Estimates of the sixth coefficient ranged from 4.4 to 8.1, and estimates on its standard error ranged from 46 to 114,550.