RQUADRATIC procedure

Fits a quadratic surface and estimates its stationary point (R.W. Payne).


Options

PRINT = strings
What to print (model, deviance, summary, estimates, correlations, fittedvalues, accumulated, monitoring); default mode, summ, esti

CONSTANT = string
How to treat the constant (estimate, omit); default esti

FACTORIAL = scalars
Limit for expansion of model terms; default 3

POOL = string
Whether to pool ss in accumulated summary between all terms fitted in a linear model (yes, no); default no

DENOMINATOR = string
Whether to base ratios in accumulated summary on rms from model with smallest residual ss or smallest residual ms (ss, ms); default ss

NOMESSAGE = strings
Which warning messages to suppress (dispersion, leverage, residual, aliasing, marginality, vertical, df, inflation); default *

FPROBABILITY = string
Printing of probabilities for variance and deviance ratios (yes, no); default no

TPROBABILITY = string
Printing of probabilities for t-statistics (yes, no); default no

SELECTION = strings
Statistics to be displayed in the summary of analysis produced by PRINT=summary, seobservations is relevant only for a Normally distributed response, and %cv only for a gamma-distributed response (%variance, %ss, adjustedr2, r2, seobservations, dispersion, %cv, %meandeviance, %deviance, aic, sic); default %var, seob if DIST=normal, %cv if DIST=gamma, and disp for other distributions

STATIONARY = scalars
Saves the estimated value of y at the stationary point

SESTATIONARY = scalars
Saves the standard error of the estimated value of y at the stationary point

TYPESTATIONARY = scalars
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)


Parameters

X = variates
X-variates whose linear, quadratic and product terms define the quadratic surface

ESTIMATE = scalars
Estimated value of each x-variate at the stationary point

SE = scalars
Standard error of the estimated value of each x-variate at the stationary point


Description

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 RCHECK, RDISPLAY, RGRAPH, RKEEP, ADD, DROP, SWITCH and so on. It also has options PRINT, CONSTANT, FACTORIAL, POOL, DENOMINATOR, NOMESSAGE, FPROBABILITY, TPROBABILITY and SELECTION which operate similarly to those of FIT, except that PRINT has an additional setting stationary to print the stationary point.

   The x-variates whose linear, quadratic and product terms define the quadratic surface are specified by the X parameter. There are also parameters ESTIMATE and 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 STATIONARY and 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.

 

Options: PRINT, CONSTANT, FACTORIAL, POOL, DENOMINATOR, NOMESSAGE, FPROBABILITY, TPROBABILITY, SELECTION, STATIONARY, SESTATIONARY, TYPESTATIONARY.

Parameters: X, ESTIMATE, SE.


Method

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).


Action with RESTRICT

As in FIT, the y-variate (specified in an earlier MODEL directive) can be restricted to analyse a subset of the data.


Reference

Wu, C.F.J & Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York.