Optimal Plans_Calculated ResponsesGood morning,
I wanted to launch an Optimal Plan with mixture plan factors and categorical parameters (see below):
- % Compound A (mixture)
- % Compound B (mixture)
- % Compound C (mixture)
- Compound type D (categorical): D1 / D2 / D3
- % Compound D
- Compound type E (categorical): E1 / E2 / E3
- % Compound E
I'm measuring several experimental responses and calculating the cost price of a formula based on its components. When checking if my model is correct, I wanted to see if it accurately predicted the price of a given formula. The problem is that the predicted value is completely wrong. I've tried adding more experiments, but nothing has helped. What do you think I should do?
Thank you in advance for your feedback.
Re: Optimal Plans_Calculated ResponsesHello @SquaresJackal10 ,
It's difficult to provide more precise assistance without an anonymized dataset or more information and context. Why are you trying to model a calculated response? Don't you already have access to the price equation?
A calculated price response is usually quite simple, using a linear additive model based solely on principal effects. Since your design includes mixing factors and continuous factors expressed as percentages, perhaps the model's price considers the proportions but not the quantity of raw materials, unlike the calculated price (which uses prices in €/kg or per L)? A simple calculation based on the total quantity, rather than the proportions, might help.
Another avenue to explore is how the model was specified, particularly in light of the diversity of factors.
Hopefully these initial suggestions will be helpful.
Re: Optimal Plans_Calculated ResponsesHello @Victor_G ,
Thank you for your reply. Here is the anonymized file with my 3 answers:
- Prix (€/kg)
- Alkalinity (mg KOH/g)
- Duration (min)
Regarding the price, I tried calculating it in two ways: directly in JMP and as a value using an Excel calculation => no change because the model doesn't predict the correct value. I wanted to add this data as an answer because I have a price limit to reach.
Normally, the quantities are represented in the mixture columns and the other two columns in the categorical columns. This is the first time I've used this type of plan because I usually have no problems with mixture plans.
Afterwards I realize that I will need to increase the size of my plan to gain more accuracy in my other answers and validate my model because it is far from perfect.
Thank you again for your help.
Re: Optimal Plans_Calculated ResponsesHello @SquaresJackal10 ,
I may have missed something, but by using the "Fit Model" script directly in the data table and applying it to the responses, I get results that seem quite satisfactory for the majority of responses (there is still some possible improvement in precision on alkalinity for example, but the trend remains good).
- For the Price response, I simply performed a Box-Cox Y Transformation, available in the red triangle > Factor Profiling > Box-Cox Y Transformation. I performed this transformation because the residuals exhibited a non-random pattern, indicating a missing term in the model (though this is quite unlikely for the Price response, which should be linear and additive), or a necessary transformation. JMP calculates a lambda value around 0 (logarithmic transformation), so I refitted the response with lambda = 0 (red triangle of the Box-Cox transformation, then "Replace with Transform").
- For the alkalinity response, no modifications were made to the default model; it seems to be suitable.
- Regarding the Duration answer, it appears that the value 30000 was used as the upper limit: either the experiment stopped at this value (censorship) or the upper limit was mentioned by default because it wasn't measured. Therefore, you have two options:
- JMP PRO: Either use a "Detection Limits" column property and create a generalized regression model that will take this detection limit into account.
- JMP: The approach is two-step: First, create a model that detects whether the duration is long or short (30,000 or other), then, for the "low" values, create a standard regression model (excluding values 30,000 from the model). The problem (and solution) is quite similar to this topic: https://community.jmp.com/t5/Discussions/Windows-11-gt-JMP-19-gt-Fit-Model-gt-Standard-Least-Square-gt/mp/936972#M109215 This is the option I've chosen by default for your data.
You will find attached your file containing the analysis scripts and prediction formulas.
Hopefully this answer will help you.
Re: Optimal Plans_Calculated ResponsesThank you so much for your help. Indeed, the model's price prediction is correct in theory, but when I calculate it manually, it's not accurate in JMP. I just realized that this is because JMP doesn't link the "H Name" column to the price, as H1 (€10.18/kg), H2 (€1.3/kg), H3 (€1.86/kg), and H4 (€2.3/kg) have different prices.
Indeed, if we put the following proportions into the simulation section:
- A (%) : 35%
- B (%) : 30%
- C (%) : 2%
- D (%) : 8%
- E (%) : 8%
- F (%) : 12%
- G Nom : G1
- G (%) : 0%
- H Name: H1
- H (%) 5%
JMP predicts a price of €2.237/kg. However, the actual result should be around €2.414/kg. And when I switch from H1 to H2, the price doesn't change, even though H2 has a different price. I assumed JMP would link the price variations to the proportions and names of the compounds used, but it might not be that simple. Which isn't illogical in itself. Is there a way to correct this and tell him that H1 is worth €10.18/kg...?
Thank you again
Re: Optimal Plans_Calculated ResponsesSorry, I hadn't noticed that there was a link between certain columns, for the choice and concentration of an additive for G and H.
I see two possible options:
- Either add the interactions between G name and G, and H name and H, to reflect the price difference depending on the type of additive chosen.
- The table could be modified from its current "TALL" format (with one column specifying which G and H are used) to a "WIDE" format (one column for each type of G and H), and when specific G and H compounds are not part of the experiment, their values should be set to 0. This maintains a linear additive model with main effects, but provides a different coefficient (slope) depending on the type of additive chosen for G and H. In this new format, the columns Hname and Hname would be replaced by four columns: H1, H2, H3, and H4, each containing the concentration values for each experiment.
I have added the formula and analysis script corresponding to the first option in the attached file.
Hopefully these options will suit you.
