Negative variances?

[#1]

I'm trying to fit a model to data. I add "Random" attribute to all my model effects. My problem is that I some times get negative variances in my output. How can this be?

Since variances cannot be negative, what does that tell me?

Is it an error in JMP or am I misunderstanding something?

Where can I access the exact mathematical formulas used by JMP?

[#2]

You have a repeated-measures design, where repetition is nested within device.  Try again with repetition nested within device, but with the nested term as your random effect.

[#3]

I don't see that. Since all repetitions occur for each device, the repetition should not be nested with device. That was the case if repetitions 0 to 3 occurred for on device while repetitions 4 to 6 occurred for another device? Or am I misunderstanding something?

In any case, negative variances should be a mathematical impossibility (they are averages of squared i.e. positive values). Why does JMP still return negative variances?

[#4]

Uncheck the option "Unbounded Variance Components" to force all positive variance components. Negative variance components can occur if the model is inppropiate for the data or for small sample sizes (in relation to variances).

Check the book (found under Help menu) Modeling and Multivariate Methods page 116.

[#5]

Thank you. I will look into that. I any case you are saying that my model is likely not appropriate for my experimental setup?

[#6]

I do not believe your model is appropriate for your experimental design.  I still think that repetition should be nested within device, with the nested effect as random and the device as fixed.

[#7]

Is each individual device measured repeatedly, or does one repetition represent a different individual device measured only once?  If each device is measured only once, then repetition really doesn't belong in the model and device should be a nominal fixed effect. 

[#8]

Each repetition represents a repeated measurement on the same device. Any variation between repetitions on the same device is thus random (i.e. unaccounted for).