GPS-X Technical Reference

Optimizer 398
Detailed Statistical Report
The detailed statistical report provides additional information that is helpful when doing
parameter estimation. It allows the user to assess how well their model fits the measured
data. The detailed statistical report is activated by setting the detailed statistical report
option to ON in the Static sub-section of the Optimizer form. The statistics included in
the detailed statistical report are discussed below.
Variance-Covariance and Correlation Matrices
The variance-covariance matrix is defined by Equation 14.22 for the sum of squares
objective function and by Equation 14.24 for the maximum likelihood objective
function. This matrix contains the variances of the individual parameter estimates
(diagonal elements) and the covariances between the different parameter estimates (offdiagonal
elements). Parameters with large variances may be unnecessary.
The elements of the correlation matrix are calculated as follows:
Equation 14.28
where
( V ˆ) k , l
is the (k,l) element of the variance-covariance matrix.
By definition, the elements of the correlation matrix are always between zero and one.
Unless some parameters are on their bounds the diagonal elements are always equal to
one. The off-diagonal elements indicate the degree of correlation between pairs of
parameters. A large off-diagonal element indicates a high degree of correlation between a
pair of parameters. This provides evidence that some of the parameters in the model are
unnecessary and the model is over parameterized. This may indicate that the model is not
adequate for the task at hand or that the data do not provide enough information to allow
estimation of all of the model parameters (Draper and Smith, 1981).
The variance-covariance and correlation matrices 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