Prediction equation for randomly chosen factors

[#1]

Hello:

I have three factors two of which are three level factors and one has two levels. All the three factors are continuous.

While analyzing the factors, I switched on the random effects for all the three factors. I have pasted the screen shot of the analysis below. I have some questions based on this as mentioned below:

Q1) How to remove the variables from the model as we generally do in Fixed effect analysis? Will I be required to run the analysis from start each time I need to remove the variable?

Q2) How to make the regression equation for this, do I just add/subtract the BLUP term (Random Effects Prediction) to the Intercept?

Your help is highly appreciated.

[#2]

Any help is appreciated.

[#3 · Accepted solution]

Hi @VarunK,

I don't understand why you switched all your continuous factors as random effects.

The decision to have fixed or random effects is known before the analysis, depending on how you consider these factors, and is often the case for categorical factors (machine A, B, C or operator 1, 2, 3...) or blocking factors (whole plots 1,2,3, and subplots 1,2,3, day of the week, ...). 

Maybe this discussion will help you to understand how you should treat your factors : https://community.jmp.com/t5/Discussions/Random-vs-Fixed-Blocking-Factor-in-DOE/m-p/461743/highlight...

Also the JMP Help about Mixed Model may help you : https://www.jmp.com/support/help/en/17.1/index.shtml#page/jmp/mixed-models-and-random-effect-models....

To answer your questions :

1. There is no automated way to remove terms from a mixed model, but you can use a Standard Least Squares model with fixed and random effects to be able to remove fixed effects (add all the effects and then select the effects that need to be random, click on "Attributes" and select "Random Effect").
   Else, you have to launch the mixed model with your assumed complete model first, and depending on the outcomes (individual p-values for terms in the model, information criteria AICc and BIC of the model, RMSE, ...), you may launch a refined model with the same platform by removing some terms in the Fit Model launch dialog panel.
2. Since you only have your intercept as fixed effects, you will only display the intercept in the equation. However, you can display the Profiler and then click on the red triangle and click on "Conditional Predictions" which will help you see how the response vary depending on fixed and random effects.

I suggest you to read more about the differences between fixed and random effects, as it will help you understand how this affect the model, the difference in effects estimation, and the prediction equation you would like to see.

[#4]

Thank you for your reply, Victor.

I was trying to understand the effect of random vs fixed effect on the regression equation.

Also, I am a bit confused on whether my factors would be fixed or random.

My design variable could have been any value between 2 and 7 (and similarly for other factors), I chose 2, 4.5 and 7. 

I could have chosen any other levels as well so can this be considered as random effect?

Also, if we have a factor with random effect than can we not have a prediction equation?

Your help is highly appreciated.

[#5]

Hi @VarunK,

Fixed effects have an impact on mean (intercept), whereas random effects have an impact on random error (variance).

You can read this section to learn more about Random Effect Models.

Example of Estimating Random Effect Parameters (jmp.com)

The levels you have chosen for your factor don't imply it's a random or fixed effect. It depends on the model you supposed a-priori :

• If you have supposed main effects (and possible 2 factors interactions), then you only need 2 levels to estimate these effects coefficients.
• If you also have supposed quadratic effects, then you need 3 levels to estimate the possible curvature.

I suggest to read the JMP Help documentation about Mixed models and random effects, blocking in DoE, as well as searching in this community, you'll be able to learn more about it.

[#6]

Thank you, Victor:

Sorry for not putting the question with enough clarity.

I know about the levels, but with my statement "My design variable could have been any value between 2 and 7 (and similarly for other factors), I chose 2, 4.5 and 7. " what I meant is I could have chosen 3,5,7 or 2,4,6 etc.

I know that if possible it should be min, max and center for three levels (factor design space limits), but if I think of it as a more generalized statement and say my factor levels have wide range( say 1-100) and I choose 5,25,45 or 30,60,90 or any other combination, will it be considered as random or fixed.

Thank you again for your time.

[#7]

Some clarification about the levels : you do have the possibility to change the levels manually in your design, but this manual change will certainly result in a less optimal design.
Levels choice are selected depending on the factors types, ranges, and assumed model : for main effects and interactions for example, you only need min and max from your continuous factor ranges. If you need quadratic effects, you need a middle point to estimate curvature, etc...
The fact that you have an infinite number of possible values in the range of a continuous factor doesn't make it fixed or random.

Shortly speaking, if this factor may change the response mean and can be changed/repeated in a reproducible way, then it's a fixed effect (no matter the levels used in the design).
If this factor needs to be accounted for the response variance (different variability in the response for different operators, equipments, plot of lands, ...), and only represent a subset/sample of possible values from a population, then this factor can be considered as a random effect.

It's a very rough summary, but hopefully you'll understand the difference and create a more sensible/reasonable model.

Hope this clarify a little bit the topic.

[#8]

Thank you Victor for mentoring me.

This helped me understanding what is a fixed factor and rando factor.

Best Regards,

Varun Katiyar