Define a covariate

[#1]

My understanding is this:

• A factor is categorical variable
• A covariate is a continuous variable

Why do JMP define and use covariate differently?

What is  the correct definition of a covariate?

[#2 · Accepted solution]

The term 'covariate' is used differently in different contexts. You seem to be asking about a covariate in the context of design of experiments. In this context, a covariate is a variable or factor that affects the response but is not controlled like the other factors. Instead, it co-varies with the change in the factor levels from one treatment to the next.

If the covariate levels are known for each run, then it can be included in the response model like any other factor. If you can determine the covariate levels prior to conducting the experiment, then record these values in a separate data table and then Add Factor > Covariate in the design window. The number of rows in this table must be at least as large as the number of runs in the design.

If you cannot determine the covariate levels before conducting the experiment, then Add Factor > Uncontrolled. This way you will have a placeholder in the data table for recording the level during the run and you will be able to include this factor in the model specification.

[#3]

Hi @Mark_Bailey ,

Thank you for this insightful definition of covariate vs uncontrolled factors. it has helped me to better understand the differences in JMP for this 2 terms in DoE. I asked  a question about this in this thread : Solved: Unexpected change in controlled variable in DOE - JMP User Community

I still have some gaps in being able to differentiate one from the other in certain cases. For example, what about if i have some powders I am going to use for my experiment. i know their weights in advance because I measure them, but it is something I cannot really control. here we have that characteristic of "knowing in advance" typical of covariates, but I am more inclined to think that this is an "uncontrolled" factor in my DoE.

Regards,

Julian

[#4]

It sounds like you will determine the weight of the powder used in each run as you run the experiment, not beforehand. I would use the Uncontrolled factor type in this situation. You can still specify the model terms that involve this factor when you design the experiment.

[#5]

Hmmm.  "i know their weights in advance because I measure them".  I'm not sure I understand the requirement of knowing the value before the experiment.  You need to know the value for each treatment (during the experiment) and since this variable is not controlled by the experimenter, you can treat this as a contributor to the MSE of the experiment (random errors) or it can be assigned as a random variable in the model (covariate).  ANCOVA accounts (adjusts) for the variation of the covariate to then assess the other terms in the model. The adjustment hopes to prevent the covariate from inflating the MSE. What am I missing?

Many authors call the covariate a concomitant variable.  See Montgomery page 569

Montgomery, Douglas C. (1991)  “Design and Analysis of Experiments.”  Wiley (ISBN 0-471-52000-4)

[#6]

Thank you @statman for your explanaitions,

I'll be more specific. Let's not talk about powder weight but rather powder humidity. This is a powder property that is always measured irrespective of doing a doe or not later on. Then the powders can be used in real experiments with the doe factors (imagine temperature and pressure) to process them into something else. Therefore, we know powder humidity before any doe trial and that it is also a variable that can vary in an uncontrolled way.

I am inclined to treat this powder humidity as an uncontrolled variable just to check if there is an impact. What confuses me is that it is said that "covariates" are those variables you know in advance. Despite the fact that my variable powder humidity is known in advance, it really does not co-varies with the change in the factor levels from one treatment.

[#7]

Just a quick clarification, the name co-vary comes from the variable co-varying with the Y's not the x's.

So here's the question, Are you willing to manage the moisture content (what you call humidity) of the powder?  If so there are more efficient/effective ways to study this in an experiment.  If you are not willing to manage the moisture content of the powder, than you can account for this variation in a couple of ways:

1. Confound it with a block (measure and group low moisture content with one block and high moisture content with the other block), or

2. Measure the moisture content for each treatment and assign it as a covariate in the model.

[#8]

Thank you @Mark_Bailey for your answer. I'll be more specific. Let's not talk about powder weight but rather powder humidity. This something you cannot control but you just measured for all trials. Then the powders are used in the real experiments with the doe factors (imagine temperature and pressure).

I am inclined to treat this powder humidity as an uncontrolled variable just to check if there is an impact. What confuses me is that it is said that "covariates" are those variables you know in advance. Despite the fact that my variable powder humidity is known in advance, it really does not co-varies with the change in the factor levels from one treatment.

[#9]

I agree with that direction. The whole point of an Uncontrolled factor is that it serves as a covariate in the model, but its value is not known at the time you design the experiment. It is a placeholder. You will measure the value of the uncontrolled factor during the run.

[#10]

Thank you @Mark_Bailey  for your view on my case. In some cases the difference between covariates and uncontrolled factors is quite tricky.