Binomial MARS model returns Gaussian coefficients when parsed in tidypredict_fit() and tidypredict_sql()

[brettefaw]

It appears that tidypredict_fit() and tidypredict_sql() are returned a parsed model that has the Gaussian coefficients instead of the Binomial coefficients when a MARS model is fit using the earth package. The example below was done using R version 4.0.2, tidypredict_0.4.8 and earth_5.3.0. A comparison to parsed models using glm() is also included for reference.

library(earth)
library(tidyverse)
library(tidypredict)
data("etitanic", package = "earth")

MARS w/ Binomial

mars.mod.1 <- 
  earth(
    survived ~ age + sex,
    data = etitanic,
    glm = list(family = binomial)
  )
coef(mars.mod.1)

#> (Intercept) sexmale h(9-age) #> 1.0499562 -2.4754699 0.1692326

MARS w/ Gaussian

mars.mod.2 <-
  earth(
    survived ~ age + sex,
    data = etitanic,
    glm = list(family = gaussian)
  )
coef(mars.mod.2)

#> (Intercept) sexmale h(9-age) #> 0.73782144 -0.54239536 0.02975461 The parsed model w/ binomial returns the Gaussian model coefficients with the Sigmoid function applied

tidypredict_fit(mars.mod.1)

#> 1 - 1/(1 + exp(0.737821439264803 + (ifelse(age < 9, 9 - age, #> 0) * 0.0297546135084789) + (ifelse(sex == "male", 1, 0) * #> -0.542395361228247)))

tidypredict_fit(mars.mod.2)

#> 0.737821439264803 + (ifelse(age < 9, 9 - age, 0) * 0.0297546135084789) + #> (ifelse(sex == "male", 1, 0) * -0.542395361228247) Compare tidypredict with predict (fit and pred columns are not the same)

etitanic %>%
  tidypredict_to_column(mars.mod.1) %>%
  mutate(pred = predict(mars.mod.1, type = "response")[,1]) %>%
  head(10) 

#> pclass survived sex age sibsp parch fit pred #> 1 1st 1 female 29.0000 0 0 0.6765193 0.7407665 #> 2 1st 1 male 0.9167 1 2 0.6072916 0.4856151 #> 3 1st 0 female 2.0000 1 2 0.7203309 0.9033125 #> 4 1st 0 male 30.0000 1 2 0.5487016 0.1937987 #> 5 1st 0 female 25.0000 1 2 0.6765193 0.7407665 #> 6 1st 1 male 48.0000 0 0 0.5487016 0.1937987 #> 7 1st 1 female 63.0000 1 0 0.6765193 0.7407665 #> 8 1st 0 male 39.0000 0 0 0.5487016 0.1937987 #> 9 1st 1 female 53.0000 2 0 0.6765193 0.7407665 #> 10 1st 0 male 71.0000 0 0 0.5487016 0.1937987

Contrast with GLM

GLM w/ binomial

glm.mod.1 <-
  glm(
    survived ~ age + sex,
    data = etitanic,
    family = binomial
  )
coef(glm.mod.1)

#> (Intercept) age sexmale #> 1.235414162 -0.004254246 -2.460689180

GLM w/ Gaussian

glm.mod.2 <-
  glm(
    survived ~ age + sex,
    data = etitanic,
    family = gaussian
  )
coef(glm.mod.2)

#> (Intercept) age sexmale #> 0.7734801846 -0.0007286511 -0.5460270483 Coefficients match GLM model 1 above

tidypredict_fit(glm.mod.1)

#> 1 - 1/(1 + exp(1.23541416209053 + (age * -0.00425424604207735) + #> (ifelse(sex == "male", 1, 0) * -2.46068918004127))) Coefficients match GLM model 2 above

tidypredict_fit(glm.mod.2) 

#> 0.773480184644955 + (age * -0.000728651082406954) + (ifelse(sex == #> "male", 1, 0) * -0.546027048277061) Compare predictions (fit and pred match)

etitanic %>%
  tidypredict_to_column(glm.mod.1) %>%
  mutate(pred = predict(glm.mod.1, type = "response")) %>%
  head(10)

#> pclass survived sex age sibsp parch fit pred #> 1 1st 1 female 29.0000 0 0 0.7525094 0.7525094 #> 2 1st 1 male 0.9167 1 2 0.2263259 0.2263259 #> 3 1st 0 female 2.0000 1 2 0.7732765 0.7732765 #> 4 1st 0 male 30.0000 1 2 0.2053963 0.2053963 #> 5 1st 0 female 25.0000 1 2 0.7556650 0.7556650 #> 6 1st 1 male 48.0000 0 0 0.1931799 0.1931799 #> 7 1st 1 female 63.0000 1 0 0.7246003 0.7246003 #> 8 1st 0 male 39.0000 0 0 0.1992178 0.1992178 #> 9 1st 1 female 53.0000 2 0 0.7330082 0.7330082 #> 10 1st 0 male 71.0000 0 0 0.1783852 0.1783852