Toy Example with Explosive Coefficients

library(knitr)
library(janitor)
library(broom)
library(tidyverse)

Create a data set

set.seed(123)
outcome <- c(rep("Yes", 40), rep("No", 60))
predA <- rnorm(100, mean = 0, sd = 1)
predB <- rbinom(100, 1, 0.3)
predX <- c(rep("Low", 10), rep("Middle", 15), 
           rep("High", 50), rep("Middle", 25))

temp_data <- tibble(outcome, predA, predB, predX) %>%
    mutate(predX = fct_relevel(
        factor(predX), "Low", "Middle", "High"))

Fit logistic regression model for outcome with A and B

mod01 <- glm(outcome == "Yes" ~ predA + predB, 
             family = binomial, data = temp_data)
tidy(mod01, exponentiate = TRUE, conf.int = TRUE) %>%
    select(term, estimate, std.error, conf.low, conf.high) %>%
    kable(digits = 3)

term	estimate	std.error	conf.low	conf.high
(Intercept)	0.736	0.241	0.456	1.177
predA	0.915	0.226	0.582	1.426
predB	0.722	0.459	0.286	1.751

Fit logistic regression model for outcome adding in X

mod02 <- glm(outcome == "Yes" ~ predA + predB + predX, 
             family = binomial, data = temp_data)

tidy(mod02, exponentiate = TRUE, conf.int = TRUE) %>%
    select(term, estimate, std.error, conf.low, conf.high) %>%
    kable(digits = 3)

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

term	estimate	std.error	conf.low	conf.high
(Intercept)	45567353.559	1245.579	0.000	NA
predA	0.892	0.249	0.542	1.452000e+00
predB	0.767	0.500	0.276	2.002000e+00
predXMiddle	0.000	1245.579	NA	4.149098e+33
predXHigh	0.000	1245.579	NA	3.311521e+33

Why does this explosion in the standard error happen? Why are we getting all of these warnings?

temp_data %>% tabyl(outcome, predX)

 outcome Low Middle High
      No   0     25   35
     Yes  10     15   15

If predX is Low, we know that outcome = Yes.

How can we fix this?

Collapse the predX categories, or redefine them in some other way.

temp_data <- temp_data %>%
    mutate(newpredX = fct_recode(predX, 
                                 "Not_High" = "Low",
                                 "Not_High" = "Middle",
                                 "High" = "High"))

temp_data %>% tabyl(outcome, newpredX)

 outcome Not_High High
      No       25   35
     Yes       25   15

Fit logistic regression for outcome adding in new X

mod03 <- glm(outcome == "Yes" ~ predA + predB + newpredX, 
             family = binomial, data = temp_data)

tidy(mod03, exponentiate = TRUE, conf.int = TRUE) %>%
    select(term, estimate, std.error, conf.low, conf.high) %>%
    kable(digits = 3)

term	estimate	std.error	conf.low	conf.high
(Intercept)	1.128	0.317	0.605	2.120
predA	0.897	0.231	0.565	1.411
predB	0.699	0.469	0.271	1.728
newpredXHigh	0.420	0.421	0.180	0.948