Re: Response Surface Analysis

Your lack of fit is likely due to the fact that the design has no corner points. You might consider taking data at the 8 corner points.

I don't know what you mean by "and build your model/response surface from that." You shouldn't discard terms because they are not significant. You have established that they are not exceptionally large under the null hypothesis, but you have no evidence that they are negligible. A test for "negligibility" would use the other tail of the F-distribution. In general for response surface problems, one uses the full model. The exceptional case, where one needs to "boil down" the model for publication is tricky and requires some expertise.

The coefficients in a response surface model are not usually of prime interest. The predictions and contour plot are of principal interest.

You would be better off not to scale the three variables, since you lose unit information. Center them, but don't scale them.

Forget the eigenvalues. For three variables, the contour plot is all you need. By the way the axis limits on a contour plot should correspond to the actual data limits, else one tends to be swayed by an extrapolated picture.

Until you resolve the lack-of-fit problem, you shouldn't put much credence on the minimum, since the missing extreme points of the region may well twist things and create saddle points. The design that you have chosen precludes interactions from being informative, and may confound some interaction effects with the quadratic terms.

Scott Mcclintock wrote:
Im trying to do a response surface analysis using SAS but am somewhat confounded. Ive taken a number of stat classes but will be the first to admit that
Im rather weak when it comes to experimental designs and linear models.

Im working with three numeric variables x1, x2, x3 and a number of response variables. I gathered data using a circumscribed central composite design.

Ive been using proc rsreg but am not entirely sure how to go about interpreting the data and in what order to interpret it. On the offchance of
interest here is some sample output: http://www.id.unizh.ch/software/unix/statmath/sas/sasdoc/stat/chap56/sect5.htm

My understanding is to look at the pvalues for each of the 9 (10 with intercept) coefficients and build your model/response surface from that.

Then look at the eigenvalues to check to see if its the expected optimum. If its not the expected optimum(saddlepoint for instance), or if the expected
optimum is occuring at x values far outside the specified range then I need to use the ridge command to 'recalibrate' and run the study again.

Im not certain of how to interpret the tests on linear/quadratic/crossterm. Do I only consider checking the pvalues of the linear
coefficients if the linear test is significant? Same with quadratic and crossterm? For instance I think I have one dependent variable where
the crossterm test is insignificant but x1*x3 is significant. Should that be ignored?

What can or should be done if the lack of fit is significant?

How does one interpret/use/ignore the 4 df tests on x1, x2, x3?

Finally what if my model says that, for instance, x1 and x2 are significant but x3 is not. Then when I look at the eigenvalues I have
positives for x1 and 2 and negative for x3. Since Im not including x3 would this no longer be a saddlepoint? Would it now be
a minimum? Or should I still follow the ridge suggestions and run more experiments?

Answers to any questions, of any shallowness or depth are dearly appreciated. Im rather groping blindly and could use any sort
of pity/help that the statistical cosmos has to offer.

Best regards,
--Scott




--
Bob Wheeler --- http://www.bobwheeler.com/
        ECHIP, Inc. ---
Randomness comes in bunches.
.

Relevant Pages

  • Re: how to analyze the orthogonal experiment data with strong dependence.
    ... linear) in order to do so. ... Takeaki Kariya and Hiroshi Kurata Generalized least squares. ... Wiley series in probability and statistics. ... If the orthogonal design was not the correct design for those ...
    (sci.stat.consult)
  • [RtS is back] Re: CB Radio, alt.usenet.kooks
    ... couple of linear amps in my time, neither were more than 50 watts or so. ... I took that design to a tech and asked him if it ... the amp so the tubes were put in parallel so I could add more later if I ...
    (misc.transport.trucking)
  • Re: Design of Experiments: Lack of fit
    ... I have a simple question about design of experiments. ... So I have now the linear models for output. ... Your extra middle level experiments may cause loss of significance in linear ... Run your analysis data with just 16 base experiments using normal linear ...
    (sci.stat.math)
  • Re: Expandable CASE
    ... designed to match single values efficiently. ... Even single values are not matched efficiently, because it uses linear ... some might say that a sufficiently smart compiler might optimize ... if you want a more efficient CASE, design a language ...
    (comp.lang.forth)
  • Re: Lightspeed exceeded
    ... get in>> your> way when you design and carry out the tests. ... of the experiment as a confirmation of GR, ... Your claim is clearly that Vessot chose to interpret the outcome ... | Gravity probe A verified GR's predictions for the rate of the maser ...
    (sci.physics.relativity)