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I have a question about the interpretation of residual diagnostics using DHARMa.

I fitted a binomial mixed model and used DHARMa for model diagnostics.

library(DHARMa)
simulationOutput <- simulateResiduals(m1_test, n = 1000, seed = 123)
plot(simulationOutput)
testResiduals(simulationOutput)

This is what the DHARMa plots look like:

enter image description here enter image description here

Given that I have a lot of data (n = 9587) and according to the DHARMa vignette there will very likely be significant patterns with large sample sizes, the plots look pretty good to me. However, I'm not sure if I should be concerned about underdispersion since the dispersion test yields a dispersion parameter of 0.80552:

enter image description here

The DHARMa vignette suggests that e.g. a dispersion parameter of 5 is reason for concern about overdispersion, but I cannot find anything about when a value indicating underdispersion should be taken seriously. Should I worry about underdispersion or is it fine? I also plotted the residuals against individual predictors. There are some significant deviations, but nothing outstanding that would point to large deviations.

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1 Answer 1

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The default dispersion parameter estimated by DHARMa is essentially observed/expected variance, so 0.8 means that there is 20% lower variance than expected, which I would consider a small to moderate deviation.

Regarding the vignette: I never meant to suggest that 5 is a cut-off for concern. In the vignette, I just provide numerical examples for small / large values of the dispersion parameter, in the spirit to the comment above.

About your question: the main effect of the over/underdispersion is on the CIs / p-values, with overdispersion leading to anti-conservative and underdispersion to conservative bias. Based on this, I wouldn't be super concerned about a small underdispersion such as 0.8, but you might get slightly higher power by fitting a variable dispersion model.

Disclaimer: I'm the developer / maintainer of DHARMa. For technical questions about DHARMa and error reports, please use https://github.com/florianhartig/DHARMa/issues

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