GPS-X Technical Reference

405 Optimizer
To check for violation of the independence assumption, the standardized residual plots
should be examined for any noticeable trends. The presence of trends provides evidence
of serial correlation. Serial correlation occurs when residuals taken in sequence are
correlated with each other.
To check the assumption that the errors are normally distributed, the standardized
residual plots should be examined to see if the residuals are randomly scattered about
zero. In addition, the values of the standardized residuals should be examined to check
whether approximately 95 percent of the residuals lie between +2 and -2.
The standardized residual plots are scaled to fit in the Log window. The largest
standardized residual for each response variable is represented by the maximum number
of " * " characters, which is seven. The remaining standardized residuals for a response
variable are scaled relative to this maximum residual for the purposes of calculating how
many " * " characters to print. You should consult the actual values of the standardized
residuals provided in the Log window to determine whether the actual magnitudes of the
residuals for a response variable are large.
If the assumption that the residuals are independent and normally distributed is violated it
provides evidence that our model is inadequate to represent the experimental data. If the
process model structure is correct, it should account for the non-random variability in the
data.
The assumption that the residuals should be independent if the measurement errors are
independent is not strictly correct but is fine for practical purposes. The residuals are
always correlated to some extent as a result of the fact that there are n measurements but
only (n - p) degrees of freedom, where p is the number of parameters to be estimated
(Draper and Smith, 1981).
Portmanteau Statistic
The Portmanteau test is used to detect trends in the weighted residuals. If trends are
present, the residuals are not independent. This violates one of the assumptions of the
maximum likelihood method and indicates that the model does not account for all of the
non-random variability in the data. The Portmanteau test is designed for data taken in
sequence (e.g. time or space).
GPS-X Technical Reference