[R-sig-ME] P-values of averaged mixed model parameters in MuMIn

[Ben Bolker]

    (I've been meaning to respond to this for a few days ...)

    If you look at MuMin:::summary.coefTable you'll see code that looks 
like this:

tvalue <- object[, 1L]/object[, 2L]
     if (all(is.na(object[, 3L]))) {
         pvalue <- 2 * pnorm(-abs(tvalue))
         rval <- cbind(object, tvalue, pvalue)
         cn <- c("z value", "Pr(>|z|)")
     }
     else if (any(is.finite(tvalue))) {
         pvalue <- 2 * pt(-abs(tvalue), object[, 3L])
         cn <- c("t value", "Pr(>|t|)")
     }


   This shows that the p-values are simply calculated from Z/t 
statistics, which are in turn calculated from estimates and 
appropriately adjusted standard errors.

   My personal opinion is that you should be **very** cautious with 
inference/p-values on model-averaged coefficients:

   * some of the strongest proponents of information-theoretic/model 
averaging approaches  (White, Burnham, Anderson) are against mixing 
frequentist null-hypothesis testing with model averaging approaches

   * there's a medium-sized literature that suggests that _most_ (if not 
all) approaches to inference on model-averaged parameters are overly 
optimistic (= overly narrow confidence intervals = low coverage = overly 
low p-values = inflated type 1 error); one example is

Kabaila, Paul, A. H. Welsh, and Waruni Abeysekera. “Model-Averaged 
Confidence Intervals.” Scandinavian Journal of Statistics 43, no. 1 
(March 1, 2016): 35–48. https://doi.org/10.1111/sjos.12163.


On 1/18/21 9:54 PM, Vitor Vieira Vasconcelos wrote:
>    Hi,
>    Our research team is using the MuMIn package, and we got in doubt about
> how it calculates probability values (p-values) for the averaged
> coefficients of the respective resulting averaged models. In our case, we
> are averaging generalized linear mixed models of the glmmTMB package. In
> the details of the par.avg() function, I understood how the unconditional
> standard errors are calculated, but I could not find there (neither in the
> provided references) how the p-values are calculated.
>      We are aware that p-values in generalized linear mixed models has been
> a controversial topic, but we also noted that calculating p-values from
> simulation or bootstrapping has becoming increasingly popular.
>       We would be immensely grateful if anyone could provide us some
> information about how the p-values are calculated in this context in MuMIn
> package.
> 
> Best regards,
> Vitor Vieira Vasconcelos
> 55-31-99331-1593
> 
> 	[[alternative HTML version deleted]]
> 
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