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extendedFamily

extendedFamily adds new links to R’s generalized linear models. These families are drop in additions to existing families.

Links:

• loglog
• logc
• identity
• odds-power

Logit and Loglog: Mathematical Comparison

For the binomial family, the link is usually the logit but there are other options. The loglog model assigns a lower probability for X ranging from -5 to 2. For X over 2, the models are essentially indistinguishable. This can lead to improved performance when the response rate is much lower than 50%.

Logit and Loglog: Model Performance on Real World Data

The heart data contains info on 4,483 heart attack victims. The goal is to predict if a patient died in the next 48 hours following a myocardial infarction. The low death rate makes this dataset a good candidate for the loglog link.

data(heart)

heart %>%
  summarise(deathRate = mean(death))
#>    deathRate
#> 1 0.03925942

Only the family object needs to change to use the loglog link.

glmLogit <- glm(
  formula = death ~ anterior + hcabg + kk2 + kk3 + kk4 + age2 + age3 + age4,
  data = heart, family = binomial(link = "logit")
)
glmLoglog <- glm(
  formula = death ~ anterior + hcabg + kk2 + kk3 + kk4 + age2 + age3 + age4,
  data = heart, family = binomialEF(link = "loglog")
)

AUC improved by changing the link.

predictions <- heart %>%
  select(death) %>%
  mutate(
    death = factor(death, levels = c("0", "1")),
    logitProb = predict(object = glmLogit, newdata = heart, type = "response"),
    loglogProb = predict(object = glmLoglog, newdata = heart, type = "response")
  )

roc_auc(data = predictions, truth = death, event_level = "second", logitProb)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 roc_auc binary         0.797

roc_auc(data = predictions, truth = death, event_level = "second", loglogProb)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 roc_auc binary         0.801

Tidymodels

The family objects integrate with Tidymodels.

library(tidymodels)

heart <- heart %>%
  mutate(death = factor(death, levels = c("0", "1")))

parsnip_fit <-
  logistic_reg() %>%
  set_engine("glm", family = binomialEF("loglog")) %>%
  fit(death ~ anterior + hcabg + kk2 + kk3 + kk4 + age2 + age3 + age4, data = heart)

testPredictions <- parsnip_fit %>%
  predict(new_data = heart, type = "prob")
testPredictions <- heart %>%
  select(death) %>%
  bind_cols(testPredictions)

testPredictions %>%
  roc_auc(truth = death, event_level = "second", .pred_1)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 roc_auc binary         0.801

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.