Created
May 17, 2019 17:12
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A comparison of std.errors of the treatment effect from an additive DGP experiment where a pre-treatment variable is interacted maximally, only additive no interaction, or unadjusted for.
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library(tidyverse) | |
library(lme4) | |
library(broom) | |
N <- 1e4 | |
generate_data <- function() { | |
tibble( | |
intercept = 1, | |
pretreatment_var = case_when(rbinom(N, 1, p = 0.5) == 1 ~ 0.5, TRUE ~ -0.5), | |
treatment_effect = case_when(rbinom(N, 1, p = 0.5) == 1 ~ 1, TRUE ~ 0), | |
discrepancy = rnorm(N), | |
y = intercept + pretreatment_var + treatment_effect + discrepancy | |
) | |
} | |
extract_std_error <- . %>% | |
tidy() %>% | |
filter(term == "treatment_effect") %>% | |
pull(std.error) | |
seq_len(1e2) %>% | |
map_dbl(~ generate_data() %>% | |
lm(y ~ treatment_effect*pretreatment_var, data = .) %>% | |
car::deltaMethod("treatment_effect") %>% | |
tidy() %>% | |
filter(column == "SE") %>% pull(mean)) %>% | |
ecdf() %>% | |
plot(col = "green", lwd = 3, xlim = c(0.019, 0.023), | |
main = "std.error of treatment_effect") | |
seq_len(1e2) %>% | |
map_dbl(~ generate_data() %>% | |
lm(y ~ treatment_effect + pretreatment_var, data = .) %>% | |
extract_std_error()) %>% | |
ecdf() %>% | |
lines(col = "black", lwd = 3) | |
seq_len(1e2) %>% | |
map_dbl(~ generate_data() %>% lm(y ~ treatment_effect, data = .) %>% extract_std_error()) %>% | |
ecdf() %>% | |
lines(col = "purple", lwd = 3) | |
legend("topleft", legend = c("maximal", "additive", "unadjusted for"), | |
col = c("green", "black", "purple"), | |
lwd = 5) |
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