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Code for figure 2 from Bellégo and Papeis 2019
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library(ggplot2) | |
# For figure 2 of paper https://www.semanticscholar.org/paper/Dealing-with-Logs-and-Zeros-in-Regression-Models-Bellégo-Pape/546a6f45433b413721f9a60f0be8e3e2b69fe103 | |
set.seed(1) | |
beta <- 1 | |
x_max <- 1 | |
x <- x_max * runif(10000) | |
y <- sapply(x, function(x) rpois(1, lambda=exp(beta * x + 1))) | |
df <- do.call(rbind, lapply(seq(.01, 1, by=.01), function(delta){ | |
beta_hat <- unname(lm(log(y + delta) ~ x)$coefficients['x']) | |
bias <- 100 * abs(beta_hat - beta) / beta | |
data.frame(bias=bias, delta=delta) | |
})) | |
ggplot(df, aes(x=delta, y=bias)) + geom_line() | |
# Adaptation w/ realistic parameterization + log base | |
set.seed(1) | |
beta <- 1 | |
x_max <- 7 | |
x <- x_max * runif(10000) | |
y <- sapply(x, function(x) rpois(1, lambda=2**(beta * x + 1))) | |
df <- do.call(rbind, lapply(seq(.01, 1, by=.01), function(delta){ | |
beta_hat <- unname(lm(log2(y + delta) ~ x)$coefficients['x']) | |
bias <- 100 * abs(beta_hat - beta) / beta | |
data.frame(bias=bias, delta=delta) | |
})) | |
ggplot(df, aes(x=delta, y=bias)) + geom_line() |
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