Generalized linear regression (#896)

* notes from glm workshop * Flesh out explanation of continuous and unbounded, and add box on probs, odds, and logits. * Update metadata, add quick review of linear models * Flesh out linear models review * Start example with code * Finish example * Add R code used in module and missing image file * Put in metadata, improve quiz questions * Add missing metadata * Correct version number after super handy autochecker caught my mistake! * Update data example to sepsis * Replace example data * Reordering sections for improved flow (hopefully!) * Reorder generalized linear regression (#914) * fix mathjax * general structure/reordering * reordering/naming sections * Rearrange example content and add quiz on outcome variables * Add brief explanation of terms in linear model * Add more explanation before linear model sepsis example * Rework "probability and odds" section as "talking about chance", reordering some headings * improve hyperlink text Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Improve hyperlink text Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking punctuation for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking punctuation for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking wording for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking wording for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking wording for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking punctuation for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Clarifying * Improve quiz answer Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking punctuation for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking wording for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * Tweaking punctuation for clarity Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com> * clarify convergence Co-authored-by: Rose M. Hartman <rosemm@users.noreply.github.com> * update answser explanation for clarity Co-authored-by: Rose M. Hartman <rosemm@users.noreply.github.com> --------- Co-authored-by: drelliche <99294374+drelliche@users.noreply.github.com> Co-authored-by: franzenr <87659159+franzenr@users.noreply.github.com>
arcus · Apr 12, 2024 · 91a786f · 91a786f
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diff --git a/generalized_linear_regression/example_data.R b/generalized_linear_regression/example_data.R
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+library(tidyverse)
+# show the relationship between probability, odds, and logits
+logit_demo <- data.frame(Logit = c(-Inf, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, Inf)) |> 
+  mutate(Odds = exp(Logit),
+         Probability = ifelse(Odds < Inf, Odds / (1 + Odds), 1))
+knitr::kable(logit_demo, digits = 3)
+
+# set the random seed so results replicate exactly with the random number generators
+set.seed(24601)
+
+# sample size
+n <- 100
+
+# random sampling of 0 and 1 for sepsis
+# sample from a normal distribution for heart_rate and temp, but use a higher mean if sepsis == 1
+data <- data.frame(sepsis = sample(x = c(0,0,0,1), 
+                                          size = n, 
+                                          replace = TRUE)) |> 
+  mutate(heart_rate = ifelse(sepsis == 1, 
+                           rnorm(n, mean = 100, sd = 10),
+                           rnorm(n, mean = 95, sd = 10)),
+         temp = ifelse(sepsis == 1, 
+                           rnorm(n, mean = 102, sd = 1),
+                           rnorm(n, mean = 101, sd = 1)))                           
+
+
+base_plot <- ggplot(data, aes(y=sepsis, x=temp)) + 
+  geom_point() + 
+  theme_bw() + 
+  labs(y = "Sepsis", x = "Temperature")
+
+# try plotting the data with just a linear model
+base_plot + 
+  stat_smooth(method = "lm")
+ggsave("linear_prediction.png", width = 5, height = 5, units = "in")
+
+base_plot + 
+  stat_smooth(method = "glm", method.args = list(family = "binomial"))
+ggsave("logit_prediction.png", width = 5, height = 5, units = "in")