R version 3.6.3 (2020-02-29) -- "Holding the Windsock"
Copyright (C) 2020 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)

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> ############################################################################
> #     MLwiN User Manual
> #
> # 16  An Introduction to Simulation Methods of Estimation . . . . . . . .241
> #
> #     Rasbash, J., Steele, F., Browne, W. J. and Goldstein, H. (2012).
> #     A User's Guide to MLwiN, v2.26. Centre for Multilevel Modelling,
> #     University of Bristol.
> ############################################################################
> #     R script to replicate all analyses using R2MLwiN
> #
> #     Zhang, Z., Charlton, C., Parker, R, Leckie, G., and Browne, W.J.
> #     Centre for Multilevel Modelling, 2012
> #     http://www.bristol.ac.uk/cmm/software/R2MLwiN/
> ############################################################################
> 
> library(R2MLwiN)

R2MLwiN: A package to run models implemented in MLwiN from R
Copyright 2013-2017 Zhengzheng Zhang, Christopher M. J. Charlton, Richard M. A. Parker, William J. Browne and George Leckie

Support provided by the Economic and Social Research Council (ESRC)
(Grants RES-149-25-1084, RES-576-25-0032 and ES/K007246/1)

To cite R2MLwiN in publications use:

  Zhengzheng Zhang, Richard M. A. Parker, Christopher M. J. Charlton,
  George Leckie, William J. Browne (2016). R2MLwiN: A Package to Run
  MLwiN from within R. Journal of Statistical Software, 72(10), 1-43.
  doi:10.18637/jss.v072.i10

A BibTeX entry for LaTeX users is

  @Article{,
    title = {{R2MLwiN}: A Package to Run {MLwiN} from within {R}},
    author = {Zhengzheng Zhang and Richard M. A. Parker and Christopher M. J. Charlton and George Leckie and William J. Browne},
    journal = {Journal of Statistical Software},
    year = {2016},
    volume = {72},
    number = {10},
    pages = {1--43},
    doi = {10.18637/jss.v072.i10},
  }

The MLwiN_path option is currently set to C:/Program Files/MLwiN v3.05/
To change this use: options(MLwiN_path="<path to MLwiN>")
> # MLwiN folder
> mlwin <- getOption("MLwiN_path")
> while (!file.access(mlwin, mode = 1) == 0) {
+   cat("Please specify the root MLwiN folder or the full path to the MLwiN executable:\n")
+   mlwin <- scan(what = character(0), sep = "\n")
+   mlwin <- gsub("\\", "/", mlwin, fixed = TRUE)
+ }
> options(MLwiN_path = mlwin)
> 
> 
> # 16.1 An illustration of parameter estimation with Normally distributed . .
> # . . .data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .242
> 
> data(height, package = "R2MLwiN")
> summary(height)
     height     
 Min.   :154.0  
 1st Qu.:168.0  
 Median :175.0  
 Mean   :175.3  
 3rd Qu.:181.0  
 Max.   :204.0  
> 
> hist(height$height)
> 
> 1 - pnorm((200 - mean(height$height))/sd(height$height))
[1] 0.006861973
> 
> heightsim1 <- function() {
+   heightsim <- 175.35 + 10.002 * qnorm(runif(100))
+   c(pmean = mean(heightsim), pvar = var(heightsim))
+ }
> 
> set.seed(1)
> 
> # Note: To obtain estimates as close as possible to the manual, increase the
> # number of reps to 10000.
> 
> simdata1 <- as.data.frame(t(replicate(1000, heightsim1())))
> simdata1$iteration <- 1:nrow(simdata1)
> 
> plot(simdata1$iteration, simdata1$pmean, type = "l")
> 
> plot(density(simdata1$pmean))
> 
> quantile(simdata1$pmean, c(0.025, 0.975))
    2.5%    97.5% 
173.3495 177.1498 
> 
> plot(simdata1$iteration, simdata1$pvar, type = "l")
> 
> plot(density(simdata1$pvar))
> 
> quantile(simdata1$pvar, c(0.025, 0.975))
     2.5%     97.5% 
 75.53613 129.95900 
> 
> heightsim2 <- function(variable) {
+   samp <- sample(variable, replace = TRUE)
+   c(npmean = mean(samp), npvar = var(samp))
+ }
> 
> simdata2 <- as.data.frame(t(replicate(1000, heightsim2(height$height))))
> simdata2$iteration <- 1:nrow(simdata2)
> 
> plot(simdata2$iteration, simdata2$npmean, type = "l")
> 
> plot(density(simdata2$npmean))
> 
> quantile(simdata2$npmean, c(0.025, 0.975))
  2.5%  97.5% 
173.53 177.38 
> 
> plot(simdata2$iteration, simdata2$npvar, type = "l")
> 
> plot(density(simdata2$npvar))
> 
> quantile(simdata2$npvar, c(0.025, 0.975))
     2.5%     97.5% 
 73.26895 128.29689 
> 
> # 16.2 Generating random numbers in MLwiN . . . . . . . . . . . . . . . .249
> 
> female <- as.integer(runif(100) <= 0.6)
> 
> height2 <- (1 - female) * (175 + 10 * qnorm(runif(100))) + female * (160 + 8 * qnorm(runif(100)))
> 
> hist(height2[female == 0])
> hist(height2[female == 1])
> 
> # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .253
> 
> ############################################################################
> 
> proc.time()
   user  system elapsed 
   3.10    0.29    3.57