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      name:  <unnamed>
       log:  Q:\C-modelling\runmlwin\website\logfiles\2020-03-27\16\16_An_Intro
> duction_to_Simulation_Methods_of_Estimation.smcl
  log type:  smcl
 opened on:  27 Mar 2020, 17:43:16

. ****************************************************************************
. *     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.
. ****************************************************************************
. *     Stata do-file to replicate all analyses using runmlwin
. *
. *     George Leckie and Chris Charlton, 
. *     Centre for Multilevel Modelling, 2012
. *     http://www.bristol.ac.uk/cmm/software/runmlwin/
. ****************************************************************************
. 
. * 16.1 An illustration of parameter estimation with Normally distributed . . 
. * . . .data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .242
. 
. use "http://www.bristol.ac.uk/cmm/media/runmlwin/height.dta", clear

. 
. summarize height

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
      height |        100      175.35     10.0024        154        204

. 
. histogram height
(bin=10, start=154, width=5)

. 
. quietly summarize height

. 
. display 1 - normal((200 - r(mean))/r(sd))
.00686197

. 
. capture program drop heightsim1

. 
. program define heightsim1, rclass
  1. 
.         drop _all
  2. 
.         set obs 100
  3. 
.         generate heightsim = 175.35 + 10.002*invnorm(uniform())
  4. 
.         summarize heightsim
  5. 
.         return scalar pmean = r(mean)
  6. 
.         return scalar pvar  = r(Var)
  7. end

. 
. simulate, reps(1000) seed(12345): heightsim1

      command:  heightsim1
         pvar:  r(pvar)
        pmean:  r(pmean)

Simulations (1000)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100
..................................................   150
..................................................   200
..................................................   250
..................................................   300
..................................................   350
..................................................   400
..................................................   450
..................................................   500
..................................................   550
..................................................   600
..................................................   650
..................................................   700
..................................................   750
..................................................   800
..................................................   850
..................................................   900
..................................................   950
..................................................  1000

. // Note: To obtain estimates as close as possible to the manual, ncrease the
. // number of reps to 10000.
. 
. generate iteration = _n

. 
. line pmean iteration

. 
. kdensity pmean

. 
. centile pmean, centile(2.5 97.5)

                                                       -- Binom. Interp. --
    Variable |       Obs  Percentile    Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
       pmean |     1,000        2.5    173.2063        173.0833    173.4998
             |                 97.5    177.2738        177.1252    177.4803

. 
. line pvar iteration

. 
. kdensity pvar

. 
. centile pvar, centile(2.5 97.5)

                                                       -- Binom. Interp. --
    Variable |       Obs  Percentile    Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
        pvar |     1,000        2.5     72.8153        70.54017    74.12077
             |                 97.5    128.0812        126.7303    132.4153

. 
. 
. 
. use "http://www.bristol.ac.uk/cmm/media/runmlwin/height.dta", clear

. 
. save "height.dta", replace
(note: file height.dta not found)
file height.dta saved

. 
. capture program drop heightsim2

. 
. program define heightsim2, rclass
  1. 
.         use "height.dta", clear
  2. 
.         bsample
  3. 
.         summarize height
  4. 
.         return scalar npmean = r(mean)
  5. 
.         return scalar npvar  = r(Var)
  6. end

. 
. simulate, reps(1000) seed(12345): heightsim2

      command:  heightsim2
        npvar:  r(npvar)
       npmean:  r(npmean)

Simulations (1000)
----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 
..................................................    50
..................................................   100
..................................................   150
..................................................   200
..................................................   250
..................................................   300
..................................................   350
..................................................   400
..................................................   450
..................................................   500
..................................................   550
..................................................   600
..................................................   650
..................................................   700
..................................................   750
..................................................   800
..................................................   850
..................................................   900
..................................................   950
..................................................  1000

. // Note: To obtain estimates as close as possible to the manual, increase the
. // number of reps to 10000.
. 
. erase "height.dta"

. 
. generate iteration = _n

. 
. line npmean iteration

. 
. kdensity npmean

. 
. centile npmean, centile(2.5 97.5)

                                                       -- Binom. Interp. --
    Variable |       Obs  Percentile    Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
      npmean |     1,000        2.5     173.391        173.2132      173.59
             |                 97.5      177.29        177.1536    177.4074

. 
. line npvar iteration

. 
. kdensity npvar

. 
. centile npvar, centile(2.5 97.5)

                                                       -- Binom. Interp. --
    Variable |       Obs  Percentile    Centile        [95% Conf. Interval]
-------------+-------------------------------------------------------------
       npvar |     1,000        2.5    73.62636        70.95973    76.35469
             |                 97.5    127.5858         124.643    129.8879

. 
. 
. 
. * 16.2 Generating random numbers in MLwiN . . . . . . . . . . . . . . . .249
. 
. clear

. 
. set obs 100
number of observations (_N) was 0, now 100

. 
. generate female = (uniform()<=0.6)

. 
. generate height2 = (1 - female)*(175 + 10*invnorm(uniform())) + female*(160 +
>  8*invnorm(uniform()))

. 
. histogram height2, by(female)

. 
. 
. 
. * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .253
. 
. 
. 
. ****************************************************************************
. exit

end of do-file