dimanche 22 novembre 2020

Equivalent of Stata command `simulate` in R for Montecarlo Simulation

I am searching for an equivalent function in R of the extremely convenient Stata command simulate. The command basically allows you to declare a program (reg_simulation in the example below) and then invoke such a program from simulate and store desired outputs.

Below is a Stata illustration of the usage of the simulate program, together with my attempt to replicate it using R.

Finally, my main question is: is this how R users will run a Montecarlo simulation? or am I missing something in terms of structure or speed bottlenecks? Thank you a lot in advance.

Stata example

  1. Defining reg_simulation program.
clear all
*Define "reg_simulation" to be used later on by "simulate" command 
program reg_simulation, rclass
    *Declaring Stata version
    version 13
    *Droping all variables on memory
    drop _all
    *Set sample size (n=100)
    set obs 100
    *Simulate model
    gen x1 = rnormal()
    gen x2 = rnormal()
    gen y = 1 + 0.5 * x1 + 1.5 *x2 + rnormal()
    *Estimate OLS
    reg y x1 x2 
    *Store coefficients
    matrix B = e(b)
    return matrix betas = B 
end
  1. Calling reg_simulation from simulate command:
*Seet seed
set seed 1234
*Run the actual simulation 10 times using "reg_simulation"
simulate , reps(10) nodots: reg_simulation
  1. Obtained result (stored data on memory)
_b_x1   _b_x2   _b_cons
.4470155    1.50748     1.043514
.4235979    1.60144     1.048863
.5006762    1.362679    .8828927
.5319981    1.494726    1.103693
.4926634    1.476443    .8611253
.5920001    1.557737    .8391003
.5893909    1.384571    1.312495
.4721891    1.37305     1.017576
.7109139    1.47294     1.055216
.4197589    1.442816    .9404677

R replication of the Stata program above.

Using R I have managed to get the following (not an R expert tho). However, the part that worries me the most is the for-loop structure that loops over each the number of repetitions nreps.

  1. Defining reg_simulation function.
#Defining a function 
reg_simulation<- function(obs = 1000){
    data <- data.frame(
    #Generate data
    x1 <-rnorm(obs, 0 , 1) ,
    x2 <-rnorm(obs, 0 , 1) ,
    y <- 1 + 0.5* x1 + 1.5 * x2 + rnorm(obs, 0 , 1) )
  #Estimate OLS
  ols <- lm(y ~ x1 + x2, data=data)  
  return(ols$coefficients)  
}
  1. Calling reg_simulation 10 times using a for-loop structure:
#Generate list to store results from simulation
results_list <- list()
# N repetitions
nreps <- 10
for (i in 1:nreps) {
  #Set seed internally (to get different values in each run)
  set.seed(i)
  #Save results into list
  results_list[i]  <- list(reg_simulation(obs=1000))  
}
#unlist results
df_results<- data.frame(t(sapply(results_list, 
                       function(x) x[1:max(lengths(results_list))])))
  1. Obtained result: df_results.
#final results
df_results
#   X.Intercept.  x1        x2
# 1     1.0162384 0.5490488 1.522017
# 2     1.0663263 0.4989537 1.496758
# 3     0.9862365 0.5144083 1.462388
# 4     1.0137042 0.4767466 1.551139
# 5     0.9996164 0.5020535 1.489724
# 6     1.0351182 0.4372447 1.444495
# 7     0.9975050 0.4809259 1.525741
# 8     1.0286192 0.5253288 1.491966
# 9     1.0107962 0.4659812 1.505793
# 10    0.9765663 0.5317318 1.501162



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