Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

- JMP User Community
- :
- Discussions
- :
- Re: color map on correlations and estimation efficency

- Subscribe to RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Printer Friendly Page

Highlighted

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Dec 2, 2019 11:34 AM
(1577 views)

I am working on a design with 2 continuous factors and one discrete numeric factor and I can't go above 12 runs for this design. When I look at the color map of correlations of this design, it shows correlation among the factors. I have tried different number of runs to see it gets better but it doesn't. If I go below 12 run, power of design decreses and I can't go more than 12 runs. Is there anything I can do about the orthogonality of the design? Also, does looking at estimation efficiency help in this case?

1 ACCEPTED SOLUTION

Accepted Solutions

Highlighted

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

There is nothing wrong with using a Discrete Numeric factor. It is essemtially a continuous factor but you specify the levels and JMP specifies the terms in the model. You could also use a Continuous factor and specifiy the terms, then JMP specifies the levels. I got a better design in 12 runs this way. I saved the table here for you.

Your example appeared to use a model with all main effects and two-factor interactions and a single quadriatic term for exhaust temp. That model is the one I used.

Learn it once, use it forever!

8 REPLIES 8

Highlighted

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

There is nothing wrong with using a Discrete Numeric factor. It is essemtially a continuous factor but you specify the levels and JMP specifies the terms in the model. You could also use a Continuous factor and specifiy the terms, then JMP specifies the levels. I got a better design in 12 runs this way. I saved the table here for you.

Your example appeared to use a model with all main effects and two-factor interactions and a single quadriatic term for exhaust temp. That model is the one I used.

Learn it once, use it forever!

Highlighted
##

@markbailey Thank you for your reponse. Using continuous factor instead of discrete numeric factor does help but I think the quadriatic term for exhaust temp was added when I used discrete numeric factor. Now if I only include main effects and two-factor interactions I see correlations again. Is this expected or am I doing something different?

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

Highlighted
##

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

Correct, as I said, if you define the levels using a Discrete Numeric factor then JMP defines the terms. You must have a quadratic term in the model to keep all three factor levels.

The reason for the non-zero correlations is the addition of a center point and the imbalance in the design. You will still have correlations if you omit the center point. Each main effect is correlated (r = +/- 1/3) with the interaction effect involving the other two factors in this case using 12 runs. You need to go to 8 runs or 16 runs to eliminate the correlations.

Why are you concerned about this much correlation in the estimates? Do you have high variance response to begin with? Do you have small effects of changing factor levels?

Learn it once, use it forever!

Highlighted
##

@markbailey I am concerned about correlation because of small changes with factor levels. But correlation is better when using continuous factor instead of discrete numeric so I guess this will work for me in this case. Thank you for explaining it. Appreciated

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

Do you mean that the inflation caused by the correlations is severe because you expect small effects due to limited factor ranges? Is there a reason that you cannot widen the factor ranges and produce a larger effect?

Learn it once, use it forever!

Highlighted
##

That was my thought but with the design you suggested correlation between factors declined so that should be the case.

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

Highlighted
##

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

If your expected effects are at least 3x the standard deviation of the response then the power is quite high with the 12 runs:

This result can be expected even with the correlations (+/- 1/3) seen here:

The correlations result in NO bias of the estimates. The correlations inflate the variance of the estimates, which causes a lengthening of the confidence intervals:

The CI are about 6% longer, a very modest inflation. I don't think these correlations compromise the design performance much.

Learn it once, use it forever!

Highlighted
##

- Mark as New
- Bookmark
- Subscribe
- Mute
- Subscribe to RSS Feed
- Get Direct Link
- Email to a Friend
- Report Inappropriate Content

Re: color map on correlations and estimation efficency

I forgot to address your specific request for orthogonality. As you discovered, it can be very expensive to achieve this characteristic. It requires a fully balanced design and all the estimation columns must be balanced, too. We can often produce economical and effective designs without orthogonality. The 12 runs that I found seem to have a few low correlations and, therefore, a few inflated confidence interval lengths. See if the correlation is acceptable for you case.

Learn it once, use it forever!

Article Labels

There are no labels assigned to this post.