Getting back-transformed contrasts via test_predictions in models with log transformed responses

[gp-esteves]

Hello all. Firstly, thank you for your work and dedication on this package, it certainly has helped me immensely.
I have a question on an issue I recently encountered in my work using ggeffects.

I have a model with a log-transformed outcome variable. When trying to get predictions using the model, and later conducting hypothesis tests, I realized that while I could back-transform the predictions (via ggpredict) to the original scale, the same could not be done with the contrasts obtained via test_predictions.

I noticed that one could use the scale argument in test_predictions to exponentiate the contrasts, ie:

test_predictions(model, ..., scale = "exp")

But this seems to return the ratio of the predicted responses in each level of the categorical factor (ie pred1/pred2 with 95CIs), instead of the mean difference of the responses on the original scale (ie pred1 - pred2 with 95CIs). I was wondering if this was somehow possible inside of the ggeffects/marginaleffects framework.

A reproducible example follows using mtcars:

library(ggeffects); library(tidyverse)

dat <- mtcars |> mutate(am_cat = as.factor(am))

m2 <- lm(log(disp) ~ am_cat, dat)

# predictions on the log scale

ggpredict(m2, terms="am_cat", back_transform=FALSE) 
#> Model has log transformed response. Predictions are on transformed
#>   scale.
#> # Predicted values of disp
#> 
#> am_cat | Predicted |     95% CI
#> -------------------------------
#> 0      |      5.59 | 5.38, 5.81
#> 1      |      4.83 | 4.57, 5.09

test_predictions(m2, "am_cat") 
#> # Pairwise comparisons
#> 
#> am_cat | Contrast |     95% CI |      p
#> ---------------------------------------
#> 0-1    |     0.76 | 0.42, 1.10 | < .001

# predictions on the original response scale

ggpredict(m2, terms="am_cat", back_transform=TRUE) 
#> Model has log-transformed response. Back-transforming predictions to
#>   original response scale. Standard errors are still on the transformed
#>   scale.
#> # Predicted values of disp
#> 
#> am_cat | Predicted |         95% CI
#> -----------------------------------
#> 0      |    268.60 | 216.77, 332.81
#> 1      |    125.73 |  97.02, 162.93

test_predictions(m2, "am_cat", scale="exp") # this returns the ratio
#> # Pairwise comparisons
#> 
#> am_cat | Contrast |     95% CI |      p
#> ---------------------------------------
#> 0-1    |     2.14 | 1.53, 2.99 | < .001
#> 
#> Contrasts are presented on the exponentiated scale.

# as shown by

ggpredict(m2, terms="am_cat", back_transform=TRUE)$predicted[1]/
  ggpredict(m2, terms="am_cat", back_transform=TRUE)$predicted[2]
#> Model has log-transformed response. Back-transforming predictions to
#>   original response scale. Standard errors are still on the transformed
#>   scale.
#> Model has log-transformed response. Back-transforming predictions to
#>   original response scale. Standard errors are still on the transformed
#>   scale.
#> [1] 2.136294

^{Created on 2024-10-28 with reprex v2.1.1}

Thank you.

[strengejacke]

FWIW, it works with emmeans engine, but I'll look into this:

library(ggeffects)
dat <- mtcars
dat$am_cat = as.factor(dat$am)
m2 <- lm(log(disp) ~ am_cat, dat)
ggpredict(m2, terms="am_cat") |> test_predictions(engine = "emmeans")
#> Model has log-transformed response. Back-transforming predictions to
#>   original response scale. Standard errors are still on the transformed
#>   scale.
#> # Pairwise comparisons
#> 
#> am_cat | Contrast |        95% CI |      p
#> ------------------------------------------
#> 0-1    |   142.87 | 76.70, 209.03 | < .001

^{Created on 2024-11-15 with reprex v2.1.1}

[gp-esteves]

Thank you. I was aware that back-transformed contrasts were possible in emmeans using the "regrid" function, but it's very handy to know that the emmeans engine seems to achieve this as well.