Efficient Montecarlo simulation over a grid in R - r

Question

I am running a Montecarlo simulation of a multinomial logit. Therefore I have a function that generates the data and estimates the model. Additionally, I want to generate different datasets over a grid of values. In particular, changing both the number of individuals (n.indiv) and the number of answers by each individual (n.choices).
So far, I have managed to solve it, but at some point, I incurred into a nested for-loop structure over a grid search of the possible values for the number of individuals (n.indiv_list) and the number of answers by each individual(n.choices_list). Finally, I am quite worried about the efficiency of the usage of my last bit of code with the double for-loop structure running on the combinations of the possible values. Probably there is a vectorized way to do it that I am missing (or maybe not?).
Finally, and this is mostly a matter of style, I managed to arrive a multiples objects that contain the models from the combinations of the grid search with informative names, but also would be great if I could collapse all of them in a list but with the current structure, I am not sure how to do it. Thank you in advance!
1) Function that generates data and estimates the model.
library(dplyr)
library(VGAM)
library(mlogit)
#function that generates the data and estimates the model.
mlogit_sim_data <- function(...){
# generating number of (n.alter) X (n.choices)
df <- data.frame(id= rep(seq(1,n.choices ),n.alter ))
# id per individual
df <- df %>%
group_by(id) %>%
mutate(altern = sequence(n()))%>%
arrange(id)
#Repeated scheme for each individual + id_ind
df <- cbind(df[rep(1:nrow(df), n.indiv), ], id_ind = rep(1:n.indiv, each = nrow(df)))
## creating attributes
df<- df %>%
mutate(
x1=rlnorm(n.indiv*n.alter),
x2=rlnorm(n.indiv*n.alter),
)%>%
group_by(altern) %>%
mutate(
id_choice = sequence(n()))%>%
group_by(id_ind) %>%
mutate(
z1 = rpois(1,lambda = 25),
z2 = rlnorm(1,meanlog = 5, sdlog = 0.5),
z3 = ifelse(runif(1, min = 0 , max = 1) > 0.5 , 1 , 0)
)
# Observed utility
df$V1 <- with(df, b1 * x1 + b2 * x2 )
#### Generate Response Variable ####
fn_choice_generator <- function(V){
U <- V + rgumbel(length(V), 0, 1)
1L * (U == max(U))
}
# Using fn_choice_generator to generate 'choice' columns
df <- df %>%
group_by(id_choice) %>%
mutate(across(starts_with("V"),
fn_choice_generator, .names = "choice_{.col}")) %>% # generating choice(s)
select(-starts_with("V")) %>% ##drop V variables.
select(-c(id,id_ind))
tryCatch(
{
model_result <- mlogit(choice_V1 ~ 0 + x1 + x2 |1 ,
data = df,
idx = c("id_choice", "altern"))
return(model_result)
},
error = function(e){
return(NA)
}
)
}
2) Grid search over possible combinations of the data
#List with the values that varies in the simulation
#number of individuals
n.indiv_list <- c(1, 15, 100, 500 )
#number of choice situations
n.choices_list <- c(1, 2, 4, 8, 10)
# Values that remains constant across simulations
#set number of alternatives
n.alter <- 3
## Real parameters
b1 <- 1
b2 <- 2
#Number of reps
nreps <- 10
#Set seed
set.seed(777)
#iteration over different values in the simulation
for(i in n.indiv_list) {
for(j in n.choices_list) {
n.indiv <- i
n.choices <- j
assign(paste0("m_ind_", i, "_choices_", j), lapply(X = 1:nreps, FUN = mlogit_sim_data))
}
}

Answer 1

You can vectorize using the map2 function of the purrr package:
library(tidyverse)
n.indiv_list <- c(1, 15, 100, 500 )
#number of choice situations
n.choices_list <- c(1, 2, 4, 8, 10)
l1 <- length(n.indiv_list)
l2 <- length(n.choices_list)
v1 <- rep(n.indiv_list, each = l2)
v2 <- rep(n.choices_list, l1) #v1, v2 generate all pairs
> v1
[1] 1 1 1 1 1 15 15 15 15 15 100 100 100 100 100 500 500 500 500 500
> v2
[1] 1 2 4 8 10 1 2 4 8 10 1 2 4 8 10 1 2 4 8 10
result <- map2(v1, v2, function(v1, v2) assign(paste0("m_ind_", v1, "_choices_", v2), lapply(X = 1:nreps, FUN = mlogit_sim_data)))
result will be a list of your function outputs.