how to draw the log-likelihood graph - r

Question

I am learning how to draw a log-likelihood graph. Please allow me briefly introduce what I want to do specifically:
Assume we have the data/vector as below:
set.seed(123)
sample <- rpois(50, 1.65)
And the log_like function is given as below:
log_like_graph <- function(lambda){
X <- as.matrix(sample) # not sure whether this is necessary for one-parameter distribution.
N <- nrow(X)
logLik <- N*log(lambda) - lambda*N*mean(X)
return(loglik)
}
log_like_graph <- Vectorize(log_like_graph)
# set range of lambda
lambda_vals <- seq(-10,10,by=1)
log_vals <- outer(lambda_vals,log_like_graph)
Based on the above lambda_vals and log_vals, I expect to produce a plot like below:
However, when I excute the last command: log_vals <- outer(lambda_vals,log_like_graph), I got the error hint
Error in as.vector(x, mode) :
cannot coerce type 'closure' to vector of type 'any'
Could you please help me solve this problem? Thank you very much!
(FYI: I mainly follow the youtube video https://www.youtube.com/watch?v=w3drLH-DFpE&ab_channel=CalebLikesR that teaches to draw the curve for a log-likelihood function, although it uses normal distribution for demonstration.)

Answer 1

A couple of things I see; no need to vectorise log_like_graph as you can just pass lambda values into it with sapply rather than outer, you are passing lambda_vals < 0 but the support of lambda is >= 0, and I don't think your log-likelihood function is correct (I think it should be -N * lambda - sum(lfactorial(sample)) + log(lambda) * sum(X) but it is easier/more accurate to use dpois(..., log=TRUE)).
So fixing these things
# data
set.seed(123)
samples <- rpois(50, 1.65)
# The log-likelihood becomes
log_like_graph <- function(X, lambda){
N <- NROW(X)
logLik <- -N * lambda - sum(lfactorial(X)) + log(lambda) * sum(X)
return(logLik)
}
# set lambda >= 0 and take smaller steps (0.01) for a smoother curve
lambda_vals <- seq(0,10,by=0.01)
# loop through lambda values calculating the log-likehood at each value
ll1 <- sapply(lambda_vals, function(i) log_like_graph(samples, i))
plot(lambda_vals, ll1, type="l")
This can also be done with dpois(..., log=TRUE) :
ll2 <- sapply(lambda_vals, function(i) sum(dpois(samples, lambda=i, log=TRUE)))
all.equal(ll1, ll2)
# [1] TRUE