GPS-X Technical Reference

383 Optimizer
Use specified standard deviations as reference (ON - OFF): Determines if the
standard deviation of errors should be used as reference values for the purpose of
counting the proportion of weighted residuals falling outside reference bounds at a given
level of significance. These reference bounds are calculated using the reference standard
deviations. In addition, if this option is ON a chi-square test is performed on the sum of
squares of the standard deviations of the weighted residuals divided by the reference
standard deviations. This option is set to OFF by default. It does not affect the outcome
of an optimization run.
Level of significance: This value is used for computing the reference bounds if use
specified standard deviations as reference is set to ON . This value cannot affect the
outcome of an optimization run.
Heteroscedasticity model (ON - OFF): Determines if the variance model given in
Equation 14.8 is used. If this option is turned off the heteroscedasticity parameters are
set to zero.
Heteroscedasticity parameters: A vector containing the heteroscedasticity parameter for
each response variable. If heteroscedasticity model is set to OFF, all heteroscedasticity
parameters are ignored.
Derivative Information Sub-Section
Report objective function gradient and Hessian ( ON - OFF ): Controls the printing of
the gradient and the Hessian of the objective function at the solution. When this option is
ON, the gradient and Hessian are printed to the Log window and if necessary to the
stats.txt file. The gradient of the objective function is a vector containing the derivatives
of the objective function with respect to each optimized parameter. The relative gradient
is a scaled version of the gradient. The Hessian is a matrix containing the second
derivatives of the objective function with respect to the optimized parameters. A Gauss-
Newton Hessian approximation is used. The Hessian is only reported when the maximum
likelihood or the sum of squares objective functions are used.
Report model sensitivity coefficients (ON - OFF): Controls the printing of the model
sensitivity coefficients at the solution. When this option is ON the sensitivity coefficients
are printed to the Log window and if necessary to the stats.txt file. For each target
variable, the model sensitivity coefficients are the derivatives of the target variable with
respect to each optimized parameter at each data point. These derivatives are used in the
calculation of the Hessian, variance-covariance, and correlation matrices and the
confidence limits.
Finite-difference relative perturbation size: The gradient vector elements and the
model sensitivity coefficients are calculated using a finite-difference formula, specifically
a forward-difference formula. The step size used in calculating the derivatives is
calculated by multiplying the finite-difference relative perturbation size by the
absolute value of the parameter of interest. Note that this setting affects the calculation of
the confidence limits.
GPS-X Technical Reference