Remove outliers and reduce yLim appropriately for each facet in ggplot2 - r

Question

I am currently making a facet multi box plot using ggplot2, where I have cleared the outliers and set the yLim to 5000.
However, not all of the boxplots (the ones at the beginning of the image below) go anywhere near 5000. How can I reduce the y axis for only a select few of these boxplots in the image? I've tried multiple answers from the community, but they seem to be outdated.
Here is the code I am using:
require(reshape2)
require(ggplot2)
data_frame <- read.csv("results.csv", header=T)
p <- ggplot(data=data_frame, aes(x='', y=value)) + geom_boxplot(outlier.shape=NA, aes(fill=policy))
p <- p + facet_wrap( ~ level, scales="free") + coord_cartesian(ylim = c(0, 5000))
p <- p + xlab("") + ylab("Authorisation Time (ms)") + ggtitle("Title")
ggsave("bplots.png", plot=last_plot(), device=png())

Answer 1

As noted above, you pretty much have to filter before plotting, but this doesn't need to be done by editing any files, or even by creating new dataframes. Using dplyr you can just chain this into the processing of your data. I've done a hopefully reproducible example below with some made-up data (as I don't have yours). I created a function to filter by the same procedures as the boxplot is using. It's a bit hacky, but hopefully works as one potential solution:
require(ggplot2)
require(dplyr)
data_frame <- data.frame(value = c(rnorm(2000, mean = 100, sd = 20), rnorm(2000, mean = 1000, sd = 500)),
level = c(rep(1,2000), rep(2, 2000)),
policy = factor(c(rep(c(rep(1, 500), rep(2, 500), rep(3, 500), rep(4, 500)), 2))))
# filtering function - turns outliers into NAs to be removed
filter_lims <- function(x){
l <- boxplot.stats(x)$stats[1]
u <- boxplot.stats(x)$stats[5]
for (i in 1:length(x)){
x[i] <- ifelse(x[i]>l & x[i]<u, x[i], NA)
}
return(x)
}
data_frame %>%
group_by(level, policy) %>% # do the same calcs for each box
mutate(value2 = filter_lims(value)) %>% # new variable (value2) so as not to displace first one)
ggplot(aes(x='', y=value2, fill = policy)) +
geom_boxplot(na.rm = TRUE, coef = 5) + # remove NAs, and set the whisker length to all included points
facet_wrap( ~ level, scales="free") +
xlab("") + ylab("Authorisation Time (ms)") + ggtitle("Title")
Resulting in the following (simplified) plot: