GPS-X Technical Reference

407 Optimizer
If the sample autocorrelations for a response variable are independent and normally
n
distributed as mentioned above, then the variables
should
j
be
normally distributed with mean zero and variance one. Due to the fact that the
Portmanteau statistic is a sum of squares of these variables, it is distributed as a chisquared
variable.
n
j
j
(k)
independent and
GPS-X reports the Portmanteau statistic for each target variable and reports the
probability that it is from a chiprobability
for a certain target variable is smaller than the chosen significance level it
provides evidence of a trend in this target variable's weighted residuals. The significance
level is entered in the General Data > System > Parameters > Optimizer form in the
Portmanteau sub-section.
GPS-X provides messages that summarize the results of the Portmanteau test. This test is
only reported when the maximum likelihood or the sum of squares objective functions
are used and the portmanteau test on weighted residuals switch in the Portmanteau
sub-section in the Optimizer form is set to ON.
Summary on Using the Statistical Tests
See Table 4-1 for a summary of how to use the statistics given in the solution report to
assess the adequacy of the fitted model. Keep in mind that many of the tests become
more reliable as the number of measurements increases. Even if the tests indicate that the
model is not adequate, it does not mean that you cannot use the model. A visual
inspection of the plots provided by GPS-X, showing the measured values and the
predicted values, may indicate that the model captures the major trends in the data. This
is often good enough for practical purposes as it may only be important to model certain
aspects of a physical system.
Overparameterization
Overparameterization occurs when there are more parameters in the process model than
necessary to fit the data. This situation leads to correlations between model parameters as
mentioned earlier in the context of the correlation matrix. As a result the objective
function near the solution to the parameter estimation problem has elongated contours
and the solution is not very sensitive to changes in certain parameters.
The user should be careful when choosing the adjustable parameters in a parameter
estimation run. The model should be sensitive to these parameters. It is often not practical
to select the entire model parameters as optimization variables because this slows the
optimization process, and will likely result in meaningless values for certain model
parameters. It is preferable to choose only those parameters that have the greatest affect
on the mismatch between the model and the data. See the Sensitivity Analysis chapter in
the GPS-X User's Guide for details on how to conduct a sensitivity analysis of your
model using GPS-X before doing a parameter estimation run.
GPS-X Technical Reference