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I've used lme4 to fit a mixed model and could obtain p-values by using the lmerTest or afex packages. However due to heteroskedasticity (Levene Test) I also fit a robust model (rlmer command in the robustlmm package). Unfortunately lmerTest and afex do not work with rlmerMod objects. So I was looking for other ways to obtain p-values.

Doing some online-research I found the recent publication by Geniole et al. (2019) and they used the Satterthwaite-approximated degrees of freedom generated by the lme4 model in combination with the output of the robustlmm model to obtain p-values for the robust model (see their Supplemental Material).

As the the summary of the rlmer model gives me a t-value I could calculate the p-values for the robust model with the help of the Dfs from the non-robust model via the following formula:

p.value.robust = 2*pt(abs(t.value.robust), Satterthwaithe.DF.non.robust, lower=FALSE)

Is that a correct way to do this? Do you know other ways to calculate p-values for the robust model?

Literature:

Geniole Shawn N., Proietti Valentina, Bird Brian M., Ortiz Triana L., Bonin Pierre L., Goldfarb Bernard, Watson Neil V. and Carré Justin M. 2019. Testosterone reduces the threat premium in competitive resource division. 286. Proceedings of the Royal Society B. http://doi.org/10.1098/rspb.2019.0720

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