Lesson 34: Worksheet

In this worksheet, you are going to use the math300::PIDD data frame. “PIDD” stands for “Pima Indian Diabetes Database” as you can see by giving the ?PIDD command.

Your objective is to choose explanatory variables that give a good stratification of the risk of developing diabetes. First, let’s turn the diabetes categorical variable into a zero-one variable:

PIDD <- PIDD |> mutate(developed_diabetes = zero_one(diabetes, one="yes"))

The commands building and displaying each model follow:

model <- glm(developed_diabetes ~ bmi + insulin, data=PIDD, family="binomial" )
model_plot(model, show_data=FALSE)

Warning: Ignoring unknown aesthetics: fill

Change the explanatory variables (use at most three) to get a model specification that stratifies the risk nicely. Once you have a model that you are satisfied with, let’s look at it a bit more technically.

Scores <- model_eval(model, interval="none") |>
  mutate(diabetes = PIDD$diabetes)

Using training data as input to model_eval().

The variance of the model output is a nice measure of how much stratification of risk your model gives.

Scores |> summarize(vrisk = var(.output))            

       vrisk
1 0.02199098

Choose a threshold for a positive result from your model. This graph will help a lot:

ggplot(Scores, aes(x=diabetes, y=.output)) + 
  geom_jitter(alpha=0.3) +
  geom_violin(fill="blue", alpha=0.2, color=NA)

Using the threshold you just selected, construct the report on false-positives and false-negatives.

threshold <- 0.6 # just demonstrating, but probably not the best choice
Scores |> 
  mutate(test_result = ifelse(.output > threshold, "positive", "negative")) |>
  group_by(diabetes, test_result) |>
  tally()

# A tibble: 4 × 3
# Groups:   diabetes [2]
  diabetes test_result     n
  <chr>    <chr>       <int>
1 no       negative      480
2 no       positive       20
3 yes      negative      235
4 yes      positive       33

From this report, find the sensitivity and specificity of your model/threshold.