Questions about dispersion tests about dharma HOT 1 OPEN

Hello, thanks for your questions, which I reply to below:

1. Sorry, yes, this was a typo. Corrected

2. This is an interesting idea, and I have to think about this. I would file this under the general problem of what a good test statistic for working on the simulated data. I have just advised a MSc thesis on this topic, and the student has done extensive simulations. From that, it seems that the problem of this test is not so much a lack of calibration, or bias of the test statistic (which you suggest), but power, but it may be so that the bias from the mechanism that you suggest (which makes sense to me, there should be a small bias) is not visible due to a lack of power.

3. If I understand correctly what you want, this would be the same test as before, just with summing over Pearson residuals instead of Variance? I have considered this, the problem is that this is not general, because there are models that don't report Pearson residuals. I could approximate the variance by simulation, but this could fail if I have a response where all simulated values are, for example, zero.

4. We have also made extensive simulations for this problem. The issue here is the unknown df of the chi2 distribution, which biases a "naive" Pearson chi2, as suggested in many books and on the web, towards underdispersion.

from dharma.