Factors and Response both are categorical

[#1]

Hello:

What will be the appropriate method of analyzing the significant factors when all of your factors as well as response is categorical.

I am working on manufacturing problem of noise where I have four factors

A: Heat applied, levels Yes and No (half of the samples will be heated)

B: Water immersion, levels Yes and No (half of the samples will be immersed in water)

C: Material, levels Old and New (half of the component is made of different material)

static movement, levels Yes and No (half of the component will be cycled slowly before running an actual high speed test)

Response: Noise Yes and No. ( we will see if there is noise during component high speed testing)

I am trying to see what individual factors or combination of factors result in noise in the component movement. What approach should I follow.

Your help is highly appreciated.

[#2 · Accepted solution]

Hi @VarunK   As you describe it, this is a multiple logistic regression. My question is about the factor settings. There ar 2^4 = 16 possible combinations of factors. How are each of these replicated in the data? i.e., is it balanced (each combination represented the same number of times), or not? If so, how many reps  of each? If not, please detail the imbalance. It’s not enough to know “half the samples will be X” (it depends on which half…as all halves are not created equal). For example, if the same half that is heated is the same half that is immersed in water, then you have no hope of separating the effect of A from the effect of B; A and B would be completely confounded.

A starting point for multiple logistic regression can be found here.

https://www.jmp.com/en_gb/learning-library/topics/correlation-and-regression/multiple-logistic-regre...

[#3]

Thank you for your reply MRB3855,

The DOE is balanced.

Unfortunately, we only have 20 samples available with us and hence there will be no replicates.

What would be better, Have a half factorial with replicate or full factorial with no replicate?

I will go through the link that you have shared.

Your help is highly appreciated.

[#4]

Hi @VarunK : “What would be better, Have a half factorial with replicate or full factorial with no replicate?”

Well…as per usual, it depends. If you expect main effects only (and perhaps a few two way interactions), then 1/2 fraction replicated.  The full factorial doesn’t have any true error (that would come from replicates). The “error” in the full factorial case comes from the higher order interactions. Also, discrimination with logistic models can be challenging; often sample sizes need to be large (so you have lots of degrees of freedom for error) to detect changes in Prob(Noise=Yes) based on changes in factor settings. So, in the name of parsimony and replication, I’d lean towards a replicated 1/2 fraction. Others may disagree…

[#5]

I apologize for my comments and you can ignore them if they don't apply, but I'm confused as to why you took several of what should be continuous factors and decided to treat them as categorical?  You lose efficiency and effectiveness when you do this.

Heat: Vary heat at 2 different temperatures

Water: Vary the water at 2 different levels of water

Movement: Vary the speed at 2 different levels of speed

The only categorical is material type.

In addition, I perhaps do not understand your response, but if  by noise you mean sound, this can certainly be measured with a continuous scale (e.g., decibels, wavelengths)

Continuous variables are much better for DOE as you are attempting to model the effects.  Models with categorical variables are quite limited.

[#6]

Thank you for your reply, statman:

You are right with the noise. I am observing a loud rubbing noise in some parts and hence want to understand what the issue is.

There is no criteria defined in the sound level that is considered as noise. We stand at a certain distance and make decision if it is to be considered as noisy or not.

I can only have heat changed to continuous factor as room temperature and heated temperature ( I will be heating up half the samples and other half will not be heated and so basically room temperature).

I am soaking half of the samples in water and other half not. I believe that heat + water can have an effect in noise

Movement: I will cycle half the parts while other will not be cycled before running the actual test.