Multinomial regression on imputed data with MICE - Why are coefficient names not showing?

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I am running a multinomial regression using the multinom function of the R package nnet. The dataset I am using is an imputed one using MICE, and is therefore a mids object. I have not managed to obtain the coefficient names in the summary output of the multilevel model.

Here is a reproducible example using the dataframe on mice:

library(mice)
library(nnet)

test <- mice(nhanes2, meth=c('sample','pmm','logreg','norm'))

m <- with(test, multinom(age ~ bmi, model = T))
summary(pool(m))

m1 <- with(nhanes2, multinom(age ~ bmi, model = T))
summary(m1)

With the code above, the output of 'm' lists the coefficients as 1, 2, 3 and 4 instead of their variable names, which come out correctly with the output of 'm1'. Seems to be an issue with running the multinomial command on a mids object. Any suggestions on why this happens and what I can do about it?

It makes it really difficult to interpret the output, as in my actual model I will have several predictors.

Thanks!

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