I am using JMP in order to find a relation between response (Y) and factors (B, CU, T, pH), with the following details:
Y (Product of a biochemical reaction): I don't want neither maximizing/minimizing the response, nor matching it to a specific value. I want to find a relation between changing the factors and amount of Y.
B: This is a factor at three levels of 10, 100, 1000. I want to investigate the effect of the factor at just these specific values, not at the points between. (Should I define this factor as discrete numeric in JMP?)
CU: This is a factor at three levels of 0.5, 1, 1.5.
T: This is a factor at three levels of 20, 30, 40.
pH: This is a factor at three levels of 7, 8, 9.
In the last three factors, I want to see the effect of any value between the levels. Should I define these factors as continuous factor in JMP? If so, should i define three levels for the continuous factors as mentioned in this link http://www.jmp.com/support/notes/35/417.html ?)
In all factors increasing the levels is not linearly resulted.
It is known, that level increasing for each factor increases the response Y, if all other factors remain at constant level.
I also want to study the second order interaction between the factors.
I am going to use "custom design" platform for design of my experiments in JMP. Could anyone suggest using another type of design, like 'response surface design'?
Hi, I have not any experience with JMP, but I know something about DOE and RSM.
If you need to see the effect of the factors over the response (Y), I propose the usage of the Full Factorial Experiment - which is all combinations of lower (10, 0.5, 20, 7) and upper (1000, 1.5, 40, 9) bounds of the factors. Then you construct regression model with linear terms only y=b0+sum(bi*xi). The values and signs of the coefficient will give you how the factors affect the response.
If you need to explore the behavior of the response at different values of the factors, then you can construct regression model based on second order polynomial, y=b0+sum(bi*xi) + sum(bij*xi*xj)+sum(bii*x2) and to perform optimization, by keeping the first factor at the levels you want and by (e..g.) scanning the rest of the factors with some appropriate step.
In my opinion you don't need to bother with "continuous" factors at the stage of designing of the experiment. You have three levels - this is completely OK to build a model which covers the whole space defined by the upper and lower bounds. It is different story if, provided that you have built the regression model, you want to vary the factors continuously. According to the definition of your task you can do it, by varying the first factor as discrete one (only at the levels, 10, 100, 1000).
For the both regression models above you can check the significance of the coefficients and to see whether they differs from zero (statistically) if some coefficient is significant, than the respective factor (or interaction) is significant.
I strongly advice you to "code" the factors - to replace with -1, 0 +1, the real values of the factors, than to calculate the regression model, than to do the optimisation (again with values of the factors between -1 and +1) and at the end to recalculate the real values of the factors at the points in the factor space you are interested in. This will help you to avoid the influence of the values of the factors - you have values which vary from 0.5 to 40 - this will affect the accuracy of the calculations anyway. Its better to do this only for the last three ones. The first one (at levels 10, 100, 1000) is not symmetrical, so keep it as is.
Not to forget - please do several (about 5) experiemtns at the center of the space, to check the variance (simply saying whether they are repetitive or not) of your experiments and to use the data for checking the statistical significance of your model (Fisher test).
There is e good method to study a reaction like this and it is knowing the model of the kinetics of the reaction, because factorial design just give you a model of what are the factors and how they influence your yield, but for a chemist is more important to recognize the kinetics of the reaction, in this case is better the use of a model that can give you the order of the reaction and k.
Factorial design is not so good for this kind of study there are more interesting types, have you ever used the StatGraphics, in this software there are all kind of grahs that give you a continuous answer of your factors.
I would use the custom option in JMP and create an optimal response surface. You will want to take the log of B. in your design. This will make your levels 1, 2, 3. This equal distance between each level will benefit your model. If you leave them as 10, 100, 1000, you will have some issues of collinearity among your factors in interactions.
A full factorial is far too large. Optimal Respones Surface or a Box Behnken Design will work well with a minimum of samples. (27 or less)
Yes, you can use SPSS or StatGraphics, both are good, I usually use the second one. If you have an especific case to plan the design and you need some help, please do not hesitate, here i am. I am writing a book about it.
JMP is probably the best software to use for all around data analysis. I use Design Expert for designing and analyzing experiments and STATA or SAS for most of my observational data analysis.
SPSS will have some issues with the interaction terms in the model. JMP codes the levels as -1, 0, 1. So, when you look at the correlation of these factors and their interactions, the VIF is 1.00. SPSS will show the VIF for these sane interactions as much higher. The Std Err will be larger too leading to a bad model.
Follow Kalins advice. Code the factors. JMP is a tool, like the other packages. If you rely too much on your tools, you are going to make mistakes....JMP will produce a good model, but you need to lead it. Do several iterations, and look at the residuals and the p-values of the estimates. Keep trimming them out until only valid ones remain. I see people just rely on JMP too much and produce a wonderfully fitting model that is garbage because the DOF is too high.
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