Equivalence between model based::estimate_means() and marginal effects::avg_predictions

[rbcavanaugh]

I'm hoping to get some guidance on equivalencies between modelbased::esimate_means() and marginaleffects::avg_predictions() since modelbased uses marginaleffects on the backend.

for example in a multiple regression model:

library(modelbased)
library(marginaleffects)
data(penguins)
model <- glm(sex ~ species + island + body_mass, family = binomial, data = penguins)

I was expecting these to be the same (which they are, but of course "average" is not)

estimate_means(model, by = "species", estimate = "typical")

Estimated Marginal Means

species   | Probability |       95% CI
--------------------------------------
Adelie    |        0.98 | [0.95, 0.99]
Chinstrap |        0.97 | [0.90, 0.99]
Gentoo    |    2.22e-03 | [0.00, 0.01]

Variable predicted: sex
Predictors modulated: species
Predictors averaged: island, body_mass (4.2e+03)
Predictions are on the response-scale.

avg_predictions(model, variables = "species", newdata = "balanced")

 species Estimate Std. Error     z Pr(>|z|)   S    2.5 %  97.5 %
 Adelie     0.98009    0.01004 97.66   <0.001 Inf  0.96042 0.99976
 Chinstrap  0.96604    0.02097 46.06   <0.001 Inf  0.92493 1.00715
 Gentoo     0.00229    0.00188  1.21    0.225 2.2 -0.00141 0.00598

Type: response

As well as these: (but this one I'm less sure about).

estimate_means(model, by = "species", estimate = "average")

Average Predictions

species   | Probability |       95% CI
--------------------------------------
Adelie    |        0.55 | [0.42, 0.67]
Chinstrap |        0.53 | [0.37, 0.69]
Gentoo    |        0.56 | [0.40, 0.70]

Variable predicted: sex
Predictors modulated: species
Predictions are on the response-scale.

avg_predictions(model, variables = "species", newdata = NULL)

 species Estimate Std. Error    z Pr(>|z|)     S 2.5 % 97.5 %
 Adelie       0.692     0.0205 33.7   <0.001 823.1 0.652  0.732
 Chinstrap    0.653     0.0289 22.6   <0.001 374.1 0.596  0.709
 Gentoo       0.186     0.0104 17.9   <0.001 235.0 0.166  0.207

Type: response

or perhaps it would make sense that "average" and "mean" return the same output"

avg_predictions(model, variables = "species", newdata = "mean")
 species Estimate Std. Error    z Pr(>|z|)     S     2.5 %  97.5 %
 Adelie     0.97484    0.01501 65.0   <0.001   Inf  0.945423 1.00425
 Chinstrap  0.95722    0.03222 29.7   <0.001 641.8  0.894063 1.02037
 Gentoo     0.00171    0.00131  1.3    0.192   2.4 -0.000858 0.00427

Type: response

Would it be possible to create a quick map between the arguments for modelbased and marginal effects that create the same estimates?