ANOVA with multiple repeated measures factors

[#1]

I am new to JMP and having a hard time running a repeated measures ANOVA.  The problem is that I have two factors and BOTH are repeated measures.  All of the examples find online show repeated measures ANOVA with one between subjects factor and one within.  Can anyone help? Here is a description.  

One group of subjects.  This is a face recognition task with eye tracking.  The dependent variable is the duration of looking time.  

Repeated measures factor 1: Face Half (upper face vs lower face)

Repeated measures factor 2: Phase (Learning, Target, and Distractor)

In short, we are interested in seeing if subjects look longer to the upper or lower face and also if their duration of looking time differs across phase (when the learn the face, for target faces, or for distractor faces).  Plus the interaction. 

Help! 

[#2]

Also, I should have clarified that the difficulty is with entering these variables in JMP to do the analysis. I can figure out how to do it with one repeated measure, but can find an option to specify that I have two. I was able to make it work using stacked data but only if I specify subject as a random effect, which I do not want to do.

[#3]

If you haven't looked at this addin, I suggest you down load it from the file exchangw

Full Factorial Repeated Measures ANOVA Add-In

[#4]

Thanks! I'll look into it!

[#5]

This solved it. Thank you so much!

[#6]

Jim solved your problem but I just want to make sure that his note in the JMP Knowledge Base is also part of your answer.

Why wouldn't you want to treat subject as a random effect? How is a fixed effect of subject meaningful?

[#7]

I am so glad you asked! This question has been killing us! We have been trying to figure out why our output in SPSS comes out so different than in JMP. In the end, we figured it must have to do with JMP treating subject as a random effect. Turns out, if I use the add-in recommended above, the result comes out identical to that of SPSS. So, can you please tell us!? Why does subject need to be included as a random effect? I have been looking in statistics books, online resources, everywhere I can think of to figure out why JMP does this, when other statistical packages do not! If someone here can provide the answer, you will make my day!

[#8]

The fact is that software was generally unable to properly estimate the random effects properly except in special cases until a recent times. So most analyses used a standard ANOVA or regression analysis and (incorrectly) treated all effects as fixed effects. Many textbooks have yet to catch up with more modern practice.

The choice between fixed or random is based on your inference about the effect of a source of variation. We are generally interested in the fixed effects of factors such as treatment. We see this effect as fixed because our inference is about specific levels and we believe that each level always produces the same effect. On the other hand, some sources of variation represent only a sample. The effect of subject is such an case. We are generally uninterested in the effect of an individual subject because it doesn't generalize but instead care about the population. In this case, we are interested in the variance across subjects. The random effect is this variance.

[#9]

Thank so much for the quick reply. Do you have any resources you can point me to on this topic? I ended up analyzing my data first in SPSS with a "traditional" repeated measures ANOVA (I'll call this "SPSS Traditional" for simplicity). Then, I conducted the same analysis in JMP, but including subject as a random effect (JMP Mixed Effects) and, of course, got a slightly different result. Then, I used the add-in recommended above to do a repeated measures ANOVA (JMP Traditional) and got a result that is identical to my SPSS Traditional analysis. Finally, I was able to use SPSS Mixed to do a repeated measures ANOVA with subject as a random effect (SPSS Mixed Effects) and produced an identical result as what I had gotten with "JMP Mixed Effects." So, in essence, the two programs are doing the same thing, it is simply easier to do the Mixed Effects analysis in JMP. Now, what I am still confused about is WHY subject should be included as a random effect when it seems to me that this is not what most people are doing (or at least not what the majority of SPSS users are doing). Doesn't a "traditional" repeated measures ANOVA already treat subject as a random effect to some degree? Can you point me to any resources that demonstrate the difference between what the traditional model is doing and what including subject as a random effect is doing? Many thanks for helping me to sort this out. I want to make sure I really understand it.

[#10]

I don't know for certain that the majority of SPSS users treat subject as a fixed effect but I believe you. The majority is not always right and in statistics the majority is often simply behind in terms of adopting new methods. It takes about twenty years for methods to prevail and another decade for them to be covered in textbooks and taught in school.

You are correct: if one used a traditional MANOVA for a repeated measures analysis, the subject is a random effect.

It isn't wrong to treat subject as a fixed effect but what is the use of this interpretation? Subject has nothing to do with treatments. Subject is only part of the experimental unit.