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Staff

## Re: How to look for optimum mean with low variation from DOE

I am using the latest version of JMP (13.1.0) but it won't matter for your question. I fit the main effects only linear predictor against the Shrinkage response. Here is the Fixed Effect Tests report for the model of the mean response:

You can see that five of the seven factors have significant main effects. That is, there is strong evidence that they affect the mean response.

Here is the Variance Effect Likelihood Ratio Tests report for the model of the variance of the response:

So it appears that none of the factors affect the variance of the response. This result means that the ordinary least squares regression with a model that includes normally distributed errors with constant variance is sufficient.

This result also means that none of these factors can be used to reduce the variability of the Shrinkage.

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Level II

## Re: How to look for optimum mean with low variation from DOE

Hi Mark,

Thanks for the elaboration on the subject, any reason in the example it actually states that the hold time is the factor that will affect the variance?Or its just for example purpose only

Rgrds

Irfan
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Staff

## Re: How to look for optimum mean with low variation from DOE

I honestly can't say. It is not my example. I am only stating my conclusions based on the logvariance model and analysis that I did with this example data table. I hope that the steps I showed (and direction to the JMP guide) will help you with your own analysis.

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Level II

## Re: How to look for optimum mean with low variation from DOE

Dear mark, i was trying to replicate your analysis using JMP 5.1.2 but I'm not sure which model did you use to do this, are you able to show how you do this. When i tried to use the standard least square model the effect tests indicate that only 2 factors have a signficant main effects.

Effect Tests

Source Nparm DF Sum of Squares F Ratio Prob > F
MoldTemp 1 1 770.0625 12.7571 0.0038
Screw Speed 1 1 5076.5625 84.0998 <.0001
Hold Time 1 1 3.0625 0.0507 0.8256
Gate Size 1 1 7.5625 0.1253 0.7295
Cycle Time 1 1 0.5625 0.0093 0.9247
Moisture 1 1 0.5625 0.0093 0.9247
Pressure 1 1 95.0625 1.5748 0.2334

How do you run the variance effect likelihood ratio test in JMP 5.1.2, is this feature available in my JMP version

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Staff

## Re: How to look for optimum mean with low variation from DOE

The key is to change the fitting personality. Click the Standard Least Squares button in the upper right corner of the Fit Model launch dialog and select Loglinear Variance for the personality. You should see two tabs now for effects. The first one is for the terms in the linear predictor for the mean and the second is for the variance. You need to separately specify the linear predictor for both.

Let me know if there is still some confusion about how to set it up.

Learn it once, use it forever!
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Level II

## Re: How to look for optimum mean with low variation from DOE

Dear Mark,

Thank you for the continous support, but unfortunately after selecting the personality and selecting the loglinear variance option, when I tried to add in all the factors into the contruct model effects i have to put in the logvariance effects attributes for all the 7 factors.

Variance Parameter Estimates

Term Estimate Std Error t Ratio exp(Estimate) exp(2|Estimate|)
Intercept 5.1223121 0.31623 16.1982 167.723 28130.9
MoldTemp&Variance -0.143491 0.35355 -0.4059 0.86633 1.3324
Screw Speed&Variance 2.3306542 0.35355 6.5921 10.2847 105.774
Hold Time&Variance 0.5258412 0.35355 1.4873 1.69188 2.86246
Gate Size&Variance -0.278257 0.35355 -0.7870 0.7571 1.74458
Cycle Time&Variance -0.458603 0.35355 -1.2971 0.63217 2.50229
Moisture&Variance -0.312123 0.35355 -0.8828 0.73189 1.86684
Pressure&Variance 0.311134 0.35355 0.8800 1.36497 1.86315

btw is there a way for me to paste a picture in this discussion so that I can show what am I getting

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Staff

## Re: How to look for optimum mean with low variation from DOE

First, save the picture. macOS and Windows both include utility apps for screen capture. Each is sufficient for this purpose. Then click the Photos button in the menu bar for your reply. A small dialog opens. Click Choose Files to select the file with the image. Wait until the Done button in the lower right corner is active, then click it.

As to the problem, I don't know what you mean. The linear predictor for the mean and the variance are separate. You can independently enter any terms you like for each one.

Learn it once, use it forever!
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Level II

## Re: How to look for optimum mean with low variation from DOE

Hi Mark,

Here is a screenshot of my jmp interface as you can see i can't select both the standard least squares and loglinear variance personality together, it only works with one of these two options

After constructing the model based on the above factors combination here is what i got, how do i interpret the data for the variance table

Another thing using this jmp version how do I do the analysis that you did to determine which factors has a strong impact on the variance and which factors has a strong impact on the mean.

If I want to run the loglinear variance model then I have to add in the logvariance effect from the attributes option

Let me know if my question is not clear and thanks in advance for your help

Rgrds

Irfan

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Staff

## Re: How to look for optimum mean with low variation from DOE

I no longer have JMP 5 installed on my computer so I cannot run through an example in parallel with you. I will do my best to answer your question in spite of that deficiency.

So it looks like you found the Loglinear Variance personality in the drop-down menu in the upper right corner of Fit Model launch dialog - good!  It also looks like you don't have two tabs for the linear predictor, as we would with the current version of JMP, but instead you select a term in the Effects list and apply the LogVariance attribute. That way is correct! You can enter the same term twice, once for the mean model and again for the variance model. JMP won't let you enter the same term twice, though, so in the case that you want to estimate the same effect in both models, enter it, add the LogVariance attribute for the variance model, then add it again for the mean model. A bit clumsy but that is why they changed the interface in a later version! It works.

In your example, you have the MoldTemp, Screw Speed, and their interaction effects in the linear predictor for the mean model and only the HoldTime effect in the linear predictor for the variance model. (Note again that you can have any combination of effects for either model.)

Based on these predictors, the results indicate that all of the terms in the linear predictor for the mean model are significant. The LRT for Equal Variance report for the variance model serves the same purpose as the ANOVA report for the mean model: is the proposed model (active variance effects) significant compared to the reduced model (constant variance). We reject the null hypothesis (constant variance) in this case because the p-value is very small.

Furthermore, the t-test for the Variance Parameter Estimates indicates that the Hold Time estimate has has a large t-ratio. You an also use the interval exp(Estimate) to exp(2|Estimate|) to evaluate the significance. If this interval excludes 1, then the estimate is significant. (This last statement is from distant and often faulty memory, so take it with 'a grain of salt.')

Hint: if you select Tools > Help (?) and then click on a table of results in a report (e.g. parameter estimates), JMP will go directly to the explanation of that information!

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