Generalized linear regression

generalized_linear_regression/example_data.R

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+# 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)
+
+library(tidyverse)
+# 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 trisomy_21_dx
+# sample from a normal distribution for BPD/FL, but use a higher mean if trisomy_21_dx == 1
+data <- data.frame(trisomy_21_dx = sample(x = c(0,0,0,1), 
+                                          size = n, 
+                                          replace = TRUE)) |> 
+  mutate(`BPD/FL` = ifelse(trisomy_21_dx == 1, 
+                           rnorm(n, mean = 1.6, sd = .2),
+                           rnorm(n, mean = 1.5, sd = .2)))
+
+
+base_plot <- ggplot(data, aes(y=trisomy_21_dx, x=`BPD/FL`)) + 
+  geom_point() + 
+  theme_bw() + 
+  labs(y = "Trisomy 21 Dx")
+
+# 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")
+
+
+