Modeling and Multivariate Methods - SAS

90 Fitting Standard Least Squares Models Chapter 3
Effect Screening
Estimate
t Ratio
Orthog Coded
Orthog t-Ratio
Prob>|t|
Lists the parameter estimates for the fitted linear model. These estimates can
be compared in size only if the X variables are scaled the same.
The t-test associated with this parameter.
Note: This column appears only for unequal variances and correlated
estimates.
Contains the orthogonalized estimates. These estimates are shown in the
Pareto plot because this plot partitions the sum of the effects, which requires
orthogonality. The orthogonalized values are computed by premultiplying
the column vector of the Original estimates by the Cholesky root of X´X.
These estimates depend on the model order unless the original design is
orthogonal.
If the design was orthogonal and balanced, then these estimates are identical
to the original estimates. Otherwise, each effect’s contribution is measured
after it is made orthogonal to the effects before it.
Lists the parameter estimates after a transformation that makes them
independent and identically distributed. These values are used in the
Normal plot (discussed next), which requires uncorrelated estimates of equal
variance. The p-values associated with Orthog t-ratio estimates (given in the
Prob>|t| column) are equivalent to Type I sequential tests. This means that if
the parameters of the model are correlated, the estimates and their p-values
depend on the order of terms in the model.
The Orthog t-ratio estimates are computed by dividing the orthogonalized
estimates by their standard errors. The Orthog t-ratio values let JMP treat
the estimates as if they were from a random sample for use in Normal plots
or Bayes plots.
Significance level or p-value associated with the values in the Orthog t-Ratio
column.
Saturated Models
Screening experiments often involve fully saturated models, where there are not enough degrees of freedom
to estimate error. Because of this, neither standard errors for the estimates, nor t-ratios, nor p-values can be
calculated in the traditional way.
For these cases, JMP uses the relative standard error, corresponding to a residual standard error of 1. In cases
where all the variables are identically coded (say, [–1,1] for low and high levels), these relative standard errors
are identical.
JMP also displays a Pseudo-t-ratio, calculated as follows:
estimate
Pseudo t = -----------------------------------------------------
relative std error × PSE