MANOVA - Error "Note: Sphericity test not performed due to insufficient error degrees of freedom"

[#1]

Hi,

I tried to run some outcomes by Timepoint, subject and Timepoint*subject (no random effect) using MANOVA in Analysis-> Fit Model and the following error message was displayed:

"Note: Sphericity test not performed due to insufficient error degrees of freedom".

Does anyone know why it occurred? 

Thanks.

[#2 · Accepted solution]

What happens if you remove the term for the interaction effect?

[#3]

Hi Mark,

JMP only performs Sphericity Test in a repeated-measures design if subject is removed from the Construct Model Effects.

[#4 · Accepted solution]

Hi Rei,

Short answer: When performing a MANOVA in JMP you do not include "Subject" as a term in the Model Effects section. You need to do this for a mixed model (when data are stacked in long form) so that you can model subject-level effects and their interactions, but with the MANOVA it isn't necessary and, as you discovered, leads to problems estimating model effects (and tests of assumptions). 

Longer answer: "Subject" is modeled implicitly in a MANOVA because the data are arranged with one subject per row, and a MANOVA is calculated by forming contrasts across columns. To take a more familiar example, in a dependent measures t-test, if you were to calculate a column of difference scores (time 1 - time 2, for example), you wouldn't include an effect of "Subject" in your hypothesis test (a one-sample t-test of the mean of the difference scores against 0, in this case). The "effect" of subject has already been accounted for by forming that difference score. In a conceptually similar way, the MANOVA accounts for subject effects in the formation of the contrasts across columns, and the hypothesis test (of a centroid now, rather than a single mean) requires no additional specification of "subject." 

@julian

[#5]

Hi @julian, thank you for your explanation! Great!

So, if I have some variables (outcome and predictors) for a repeated-measures design, all of them should be drag to the Y Column and keep the Timepoint only in the Construct Model Effect. If I do it, it works! :)

[#6 · Accepted solution]

Predictors (those that are between-subject) should not be included in the Y, Columns role for a MANOVA. The columns that make up your outcomes are the only thing you should include in the Y, Columns role, and once you launch the MANOVA you will define the repeated structure of those outcomes (for example, they could be levels of a single factor, or some combination of multiple factors -- JMP will need to know this in order to define the contrasts across columns).

You might want to run through the MANOVA example in the JMP documentation, and also check out the One Page Guide on MANOVA here. These cover how to set up the model effects and also cover a bit of the interpretation from the MANOVA. 

You might also be interested to read through this post from a while back where I work through the fitting and interpreting the output in a MANOVA. 

@julian

[#7 · Accepted solution]

BTW I liked the JMP Help  Univariate Tests and the Test for Sphericity found in the JMP online help for Multivatiate Response models.  It describes MANOVA  using the data table Dogs.jmp.

I do not have much recent experience with repeated measures. To brush off the rust and to see what is new, I found a website I like. Maybe I like it because the author's comments align with my beliefs An Introduction to Sphericity  Footnote 12 states "... At some point you've got [to] look at the data (using graphical methods, descriptive statistics and so forth) and make a considered judgement about what procedures to use."

I use Variability Chart's std dev plot and compute delta and compare, difference from Mean Effects, especially when the Mean Effects are large. The delta plots, with Mean Effects removed, display raw variation not just the std dev in a common scale.   It is easy to look for outliers etc.

Julian and Mark provided excellent suggestions and links to additional help.