Interpreting variable importance for multinomial logistic regression - `nnet::multinom()` and `caret::varImp()`

[Rodrigue]

Hi @martinctc, First welcome to the community.

You say that you post the same issue on stack. Can u link it here? See the doc in the faq about cross-post

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Posting the same question both here and on other sites Posting the same question to multiple forums at the same time is often considered impolite. We don't completely ban such cross-posting, but we ask you to think hard before you do it and to follow some rules. Cross-post sparingly Rather than post the same thing here and elsewhere from the get-go, post in one place at a time. Let enough time go by (think days, not hours) before you take your question somewhere else. Sometimes people at another site may suggest you post here if your question doesn't fit within the scope of the other site. Always link to your other posts, and update everywhere with any solution…

Now your question. The VarImp here is the sum of absolute value of coef of a variable.

# library(tidyverse)
library(nnet)
library(caret)
#> Le chargement a nécessité le package : lattice
#> Le chargement a nécessité le package : ggplot2

fit <- multinom(Species ~ ., data = iris) # fit model
#> # weights:  18 (10 variable)
#> initial  value 164.791843 
#> iter  10 value 16.177348
#> iter  20 value 7.111438
#> iter  30 value 6.182999
#> iter  40 value 5.984028
#> iter  50 value 5.961278
#> iter  60 value 5.954900
#> iter  70 value 5.951851
#> iter  80 value 5.950343
#> iter  90 value 5.949904
#> iter 100 value 5.949867
#> final  value 5.949867 
#> stopped after 100 iterations

fit
#> Call:
#> multinom(formula = Species ~ ., data = iris)
#> 
#> Coefficients:
#>            (Intercept) Sepal.Length Sepal.Width Petal.Length Petal.Width
#> versicolor    18.69037    -5.458424   -8.707401     14.24477   -3.097684
#> virginica    -23.83628    -7.923634  -15.370769     23.65978   15.135301
#> 
#> Residual Deviance: 11.89973 
#> AIC: 31.89973

^{Created on 2020-02-27 by the reprex package (v0.2.1)}

For instance:
For Sepal.length his importance ( 13.38206) is the sum of abs(-5.458424)and abs(-7.923634).

Hope it help