Fits a quadratic surface and estimates its stationary point (R.W. Payne).
|What to print (
||How to treat the constant (
||Limit for expansion of model terms; default 3|
||Whether to pool ss in accumulated summary between all terms fitted in a linear model (
||Whether to base ratios in accumulated summary on rms from model with smallest residual ss or smallest residual ms (
||Which warning messages to suppress (
||Printing of probabilities for variance and deviance ratios (
||Printing of probabilities for t-statistics (
||Statistics to be displayed in the summary of analysis produced by
||Probability level for confidence intervals for parameter estimates; default 0.95|
||Saves the estimated value of y at the stationary point|
||Saves the standard error of the estimated value of y at the stationary point|
||Identifies the type of stationary point (2 for maximum, 1 for maximum on a ridge, -2 for minimum, -1 for minimum on a ridge, or 0 for saddle point)|
||What to plot (
||Colours for the plots|
||X-variates whose linear, quadratic and product terms define the quadratic surface|
||Estimated value of each x-variate at the stationary point|
||Standard error of the estimated value of each x-variate at the stationary point|
||Values at which to evaluate each
RQUADRATIC fits a quadratic surface of several variates, and estimates the stationary point. It is used similarly to
FIT. It must be preceded by a
MODEL statement, and can be followed by
SWITCH and so on. It also has options
PROBABILITY. These operate similarly to those of
FIT, except that
stationary to print the stationary point, and an additional setting predictions to print the predictions (see the
PREDICTIONS option below).
The x-variates whose linear, quadratic and product terms define the quadratic surface are specified by the
X parameter. There are also parameters
SE to save the estimated value of each x-variate, and its standard error, at the stationary point. The y-value at the stationary point, and its standard error, can be saved by the
SESTATIONARY options. The
TYPESTATIONARY option saves a scalar, with one of the following values to identify the type of stationary point: 2 maximum, 1 maximum on a ridge, -2 minimum, -1 minimum on a ridge, or 0 saddlepoint.
PREDICTIONS option can save predictions from the fitted quadratic model. The
LEVELS parameter specifies a variate for each
X, to specify the values at which to form predictions. The predictions are stored in a matrix. The final column contains the predictions, and the earlier columns (one for each
X variate) store the set of x-values at which each prediction was made.
PLOT option specifies which plots to display, with settings:
||for a contour plot, and|
||for surface plot.|
By default nothing is plotted. The
COLOURS option specifies a text or variate to define the colours to use. (This is used as the setting of the
PENFILL parameter of
DSURFACE.) The default is a text containing the values
RQUADRATIC forms variates with the quadratic and product terms of the x-variates, and fits these together with the x-variates themselves. The
RFUNCTION directive is then used to estimate the x- and y-values at the stationary point, with their standard errors. The type of stationary point is identified by an eigenvalue decomposition of the symmetric matrix of estimated regression coefficients of the product and quadratic terms, as described in Section 9.4 of Wu & Hamada (2000).
Wu, C.F.J & Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York.
CAPTION 'RQUADRATIC example',\ 'Second-order Ranitidine experiment (Wu & Hamada 2000, Table 9.12)';\ STYLE=meta,plain VARIATE [VALUES=0,1,-1.41,0,0,0,1,1.41,0,0,-1,-1,0] A & [VALUES=-1.41,-1,0,0,0,0,1,0,1.41,0,-1,1,0] B & [VALUES=6.943,6.248,2.100,2.034,2.009,2.022,\ 3.252,9.445,1.781,1.925,2.390,2.066,2.113] lnCEF PRINT A,B,lnCEF; DECIMALS=2,2,3 MODEL lnCEF RQUADRATIC [PLOT=surface] A,B