Need help understanding interaction variable

[#1]

Hello

I am trying to conduct a simple 2 way analysis of an experiment; each factor has 3 levels with one replicate each. Both variables are continuous. When running the analysis and looking at the output and parameter estimates I see the following:

Intercept

Factor 1

Factor 2

(Factor 1 - x) * (Factor 2 - y) where x and y seem to be some averaged/arbitrary value

Can somebody explain how I would use (Factor 1 - x) * (Factor 2 - y)  in the regression equation?

Also, what is the best way to determine which levels of the different factors are most significant.

thanks

[#2 · Accepted solution]

First after fitting your model go to the red triangle and choose save columns> "prediction formula"

This saves the prediction formula for your model to the data table.

Go to your JMP data table and you will notice that a new column has been added at the far right named prediction formula

Double click on the column heading and a dialog box will appear.

Under the column properties pulldown highlight Formula

click edit formula button

go to the red triangle pulldown and chose simplify

That will give you the simplified parameter estimates.

The reason you obtained strange parameter estimates was because you probably chose a 3 level design. You could have accomplished the same thing with a two level design and just added center points which might have been simpler.

[#3]

I understand now, thanks.

One other question... If I have a data set with 2 factors, but there is only 1 replication/observation (as shwon below), I can't do any interaction analysis because of inssuficient DoF, correct??

Factor A     Factor B     Response

1                a                y1

1                b                y2

1                c                y3

2                a                y4

2                b                y5

2                c                y6

3                a                y7

3                b                y8

3                c                y9

[#4]

You should be okay. If the are both 3 level categorical factors the model is pretty saturated but you get the interactions terms delineated. You could also try a stepwise regression to make the model more parsimonious. If one factor is continuous and one is categorical then it appears to me when utilizing the "simulate responses" under the red triangle that you have enough DoF for interactions and the error. Alternatively you could also add an additional row and replicate one of the other combinations.

[#5]

The 2 factors are quantitative, but can be classified as Nominal.

The reason I asked is because when I run the fit model command with the 2 factors and the cross of the 2 factors as a the model effects, the F test for the model's effects are null. I think it's because each factor has 2 degree of freedom and the interaction has another 4, which makes 8 degrees of freedom. This leaves no degrees of freedom for the error term which is why the F test can't show any results. Isn't that right? If I run the ANOVA without the interaction terms it runs fine. And if I changed one of the factors to a continuous variable it runs fine, but I think in my case they should both be set as nominal.

I was looking online and it seems that as a general rule you cannot properly analyze the interaction between 2 factors with only 1 replicate/combination. I just would like to be sure about this fact.

[#6 · Accepted solution]

You are correct. The null is due to the fact that all of your degrees of freedom are used up. That is why I asked you if they could be treated as continuous. Did you try to model using the stepwise model personality?

[#7]

Thanks for this explanation as I had the same issue. 

I have another question, after simplifying the formula, is there anyway to simply have x1*x2 in the "parameters estimates" table instead of (x1-a)*(x2-b) ? 

Thanks ! 

[#8]

Ah, yes. I believe you also asked this question in another thread. The centering is done to reduce the collinearity that is caused by scale differences. It is a way of JMP helping you with your analysis.

For example, suppose factor X1 has the range 100 to 200 and factor X2 has the range 1 to 2 with this design:

X1    X2     X1*X2

100   1         100

100   2         200

200   1         200

200   2         400

The interaction would have the range 100 to 400. The correlation between X1 and the X1*X2 interaction is 0.688 which is quite high. If I center X1 and X2 before multiplying, the correlation between X1 and the centered X1*X2 interaction is 0. This is a good thing which is why JMP does it. Further, JMP provides the tools needed to understand the model and evaluate it with the centering in place.

Can you turn this off? Yes. In the Fit Model dialog box, click the red triangle in the upper left and "uncheck" the Center Polynomials choice before clicking Run. However, keep in mind that by doing this you will be increasing the multicollinearity in the model which, in turn, increases the variance of parameter estimates and affects the statistical testing and significance for those parameter estimates.