How to extract stat_smooth curve maxima in gpplot panel (facet_grid)? - ggplot2

Question

I have created this plot with 18 grids using facet_grid command and two different fitting equations (for Jan - Apr, and May - Jun). I have two things that I need help with:
(may sound obvious, but) I haven't been able to find on the internet working codes extract a curve maximum for a stat_smooth fit. I'd appreciate if someone could show and explain what the codes mean. This is the closest I could find, but I am not sure what it means:
gb <- ggplot_build(p1)
curve_max <- gb$data[[1]]$x[which(diff(sign(diff(gb$data[[1]]$y)))==-2)+1]
How to add a vertical line to indicate max value on each curve?
Data file (rlc2 <- read_excel)
Plot
plot <- ggplot(rlc2, aes(par, etr, color=month, group=site))+
geom_point()+
stat_smooth(data = subset(rlc2, rlc2$month!="May" & rlc2$month!="Jun"),
method = "glm",
formula = y ~ x + log(x),
se = FALSE,
method.args = list(family = gaussian(link = "log"), start=c(a=0, b=0, c=0)))+
stat_smooth(data = subset(rlc2, rlc2$month=="May" | rlc2$month=="Jun"),
method = "nlsLM",
formula = y ~ M*(1 - exp(-(a*x))),
se = FALSE,
method.args = list(start=c(M=0, a=10)))+
facet_grid(rows = vars(month), cols = vars(site))
plot
field_rlc_plot
Any other advice are also welcome. I am educated as programmer so my codes are probably a bit messy. Thank you for helping.

Answer 1

Try this:
First, fit the data and extract the maximum of the fit.
my.fit <- function(month, site, data) {
fit <- glm(formula = etr ~ par + log(par),
data = data,
family=gaussian(link = "log")
)
#arrange the dersired output in a tibble
tibble(max = max(fit$fitted.values),
site = site,
month = month)
}
#Apply a custom function `my.fit` on each subset of data
#according to month and site using the group_by/nest/map method
# the results are rowbinded and returned in a data.frame
my.max<-
rlc2 %>%
dplyr::group_by(month, site) %>%
tidyr::nest() %>%
purrr::pmap_dfr(my.fit)
Next, join the results back on your data and plot a geom_line
rlc2 %>%
dplyr::left_join(my.max) %>%
ggplot(aes(x = par, y = etr))+
geom_point()+
stat_smooth(data = subset(rlc2, rlc2$month!="May" & rlc2$month!="Jun"),
method = "glm",
formula = y ~ x + log(x),
se = FALSE,
method.args = list(family = gaussian(link = "log"), start=c(a=0, b=0, c=0)))+
stat_smooth(data = subset(rlc2, rlc2$month=="May" | rlc2$month=="Jun"),
method = "nlsLM",
formula = y ~ M*(1 - exp(-(a*x))),
se = FALSE,
method.args = list(start=c(M=0, a=10)))+
geom_line(aes(y=max), col="red")+
facet_grid(rows = vars(month), cols = vars(site))