GPS-X Technical Reference

397 Optimizer
For the maximum likelihood objective function, the variance-covariance matrix of the
parameter estimates is defined as (Bard, 1974):
Equation 14.24
The matrix Ĥ -1 is the inverse of the Gauss-Newton Hessian approximation to the
maximum likelihood objective function at the solution.
For both the sum of squares and the maximum likelihood objective functions, the
100(1-a)% confidence limits for parameter k are:
Equation 14.25
The variable t(n – p; a / 2) is the Student’s t-statistic, with n-p degrees of freedom, and a
significance level of a / 2. In this case, n is the number of data points per response,
except for the sum of squares objective function where it is the total number of data
points. The variable a is the significance level for the parameter estimates. It is defined
by the following expression:
Equation 14.26
where δ is the confidence coefficient. The confidence coefficient corresponds to the
confidence level for confidence limits parameter found in the Confidence Limits subsection
of the Optimizer form. The default value is 0.95 so that by default GPS-X reports
95 percent confidence limits.
Equation 14.27
The confidence limits are only reported when the printing of confidence limits switch in
the Confidence Limits sub-section in the Optimizer form is set to ON.
GPS-X Technical Reference