Nonlinear Estimation Evaluating the Fit of the Model - Variance/Covariance Matrix for Parameters

When a model is grossly misspecified, or the estimation procedure gets "hung up" in a local minimum, the standard errors for the parameter estimates (which are optionally computed by the program via finite difference approximation) can become very large. This means that regardless of how the parameters were moved around the final values, the resulting loss function did not change much. Also, the correlations between parameters may become very large, indicating that parameters are very redundant; put another way, when the estimation algorithm moved one parameter away from the final value, then the increase in the loss function could be almost entirely compensated for by moving another parameter. Thus, the effect of those two parameters on the loss function was very redundant.