How can I find the maximum output of a function - r

Question

If I have a GLM, is there any way I can efficiently find the maximum output by changing one covariate and holding the others?
Using my simulated data:
# FUNCTIONS ====================================================================
logit <- function(p){
x = log(p/(1-p))
x
}
sigmoid <- function(x){
p = 1/(1 + exp(-x))
p
}
beta_duration <- function(D, select){
logit(
switch(select,
0.05 + 0.9 / (1 + exp(-2*D + 25)),
0.9 * exp(-exp(-0.5 * (D - 11))),
0.9 * exp(-exp(-(D - 11))),
0.9 * exp(-2 * exp(-(D - 9))),
sigmoid(0.847 + 0.210 * (D - 10)),
0.7 + 0.0015 * (D - 10) ^ 2,
0.7 - 0.0015 * (D - 10) ^ 2 + 0.03 * (D - 10)
)
)
}
beta_sex <- function(sex, OR = 1){
ifelse(sex == "Female", -0.5 * log(OR), 0.5 * log(OR))
}
plot_beta_duration <- function(select){
x <- seq(10, 20, by = 0.01)
y <- beta_duration(x, select)
data.frame(x = x,
y = y) %>%
ggplot(aes(x = x, y = y)) +
geom_line() +
ylim(0, 1)
}
# DATA SIMULATION ==============================================================
duration <- c(10, 12, 14, 18, 20)
sex <- factor(c("Female", "Male"))
eta <- function(duration, sex, duration_select, sex_OR, noise_sd){
beta_sex(sex, sex_OR) + beta_duration(duration, duration_select) + rnorm(length(duration), 0, noise_sd)
}
sim_data <- function(durations_type, sex_OR, noise_sd, p_female, n, seed){
set.seed(seed)
data.frame(
duration = sample(duration, n, TRUE),
sex = sample(sex, n, TRUE, c(p_female, 1 - p_female))
) %>%
rowwise() %>%
mutate(eta = eta(duration, sex, durations_type, sex_OR, noise_sd),
p = sigmoid(eta),
cured = sample(0:1, 1, prob = c(1 - p, p)))
}
# DATA SIM PARAMETERS
durations_type <- 4 # See beta_duration for functions
sex_OR <- 3 # Odds of cure for male vs female (ref)
noise_sd <- 1
p_female <- 0.7 # proportion of females in the sample
n <- 500
data <- sim_data(durations_type = 1, # See beta_duration for functions
sex_OR = 3, # Odds of cure for male vs female (ref)
noise_sd = 1,
p_female = 0.7, # proportion of females in the sample
n = 500,
seed = 21874564)
I am fitting a fractional polynomial GLM:
library(mfp)
model1 <- mfp(cured ~ fp(duration) + sex,
family = binomial(link = "logit"),
data = data)
summary(model1)
Given that I am holding sex as constant, is there any way to find the value of duration within a certain range that gives me the highest predicted value? Something less inefficient than:
range <- seq(10, 20, by = 1e-4)
range[which.max(predict(model, type = "response", newdata = data.frame(duration = range, sex = "Male")))]

Answer 1

You can use optimize here. Just create a function which returns a prediction based on the value of duration:
f <- function(x) predict(model1, list(sex = 'Male', duration = x))
And we can find the value of duration which produces the maximum log odds within the range 0-20 by doing:
optimise(f, c(0, 20), maximum = TRUE)$maximum
#> [1] 17.95679