-------------------------------------------------------------------------------
      name:  <unnamed>
       log:  Q:\C-modelling\runmlwin\website\logfiles\2024-10-11\18\10_Modellin
> g_Binary_Responses.smcl
  log type:  smcl
 opened on:  11 Oct 2024, 17:09:23

. ****************************************************************************
. *     MLwiN MCMC Manual 
. *
. * 10  Modelling Binary Responses . . . . . . . . . . . . . . . . . . . . 129
. *
. *     Browne, W. J. (2009). MCMC Estimation in 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
. *     https://www.bristol.ac.uk/cmm/software/runmlwin/
. ****************************************************************************
. 
. use "https://www.bristol.ac.uk/cmm/media/runmlwin/bang1.dta", clear

. 
. describe

Contains data from https://www.bristol.ac.uk/cmm/media/runmlwin/bang1.dta
 Observations:         1,934                  
    Variables:            13                  21 Oct 2011 12:19
-------------------------------------------------------------------------------
Variable      Storage   Display    Value
    name         type    format    label      Variable label
-------------------------------------------------------------------------------
woman           int     %9.0g                 
district        byte    %9.0g                 
use             byte    %9.0g                 
lc              byte    %9.0g      lc         
age             float   %9.0g                 
urban           byte    %9.0g                 
educ            byte    %9.0g                 
hindu           byte    %9.0g                 
d_illit         float   %9.0g                 
d_pray          float   %9.0g                 
cons            byte    %9.0g                 
bcons           byte    %9.0g                 
denomb          byte    %9.0g                 
-------------------------------------------------------------------------------
Sorted by: 

. 
. 
. 
. * 10.1 Simple logistic regression model . . . . . . . . . . . . . . . . .130
. 
. quietly runmlwin use cons age, ///
>         level2(district:) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause

. 
. runmlwin use cons age, ///
>         level2(district:) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsprevious nopause level(90)
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       11.8
Deviance (dbar)            =    2591.29
Deviance (thetabar)        =    2589.29
Effective no. of pars (pd) =       2.00
Bayesian DIC               =    2593.29
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [90% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -.4385755    .047307     1198   0.000     -.515495   -.3615458
         age |   .0068138   .0050855     1235   0.089    -.0014546    .0150039
------------------------------------------------------------------------------


. 
. mcmcsum [FP1]age, detail

                                  [FP1]age
------------------------------------------------------------------------------
                                Percentiles
Mean          .0068138     0.5%  -.0068774     Thinned Chain Length       5000
MCSE of Mean  .0001503     2.5%  -.0033339     Effective Sample Size      1235
Std. Dev.     .0050855       5%  -.0014546     Raftery Lewis (2.5%)      13099
Mode          .0066046      25%   .0034059     Raftery Lewis (97.5%)     13496
P(mean)      0.089                             Brooks Draper (mean)     173547
P(mode)      0.089          50%   .0067932     
P(median)    0.089
                            75%   .0104303     
                            95%   .0150039     
                          97.5%   .0164863     
                          99.5%     .01952     
------------------------------------------------------------------------------

. 
. mcmcsum [FP1]age, fiveway

. 
. runmlwin use cons age, ///
>         level2(district:) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(chain(15000)) initsprevious nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =      15000
Thinning                   =          1
Run time (seconds)         =         27
Deviance (dbar)            =    2591.29
Deviance (thetabar)        =    2589.29
Effective no. of pars (pd) =       2.00
Bayesian DIC               =    2593.29
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -.4394264    .045736     3686   0.000    -.5284889    -.350504
         age |    .006372   .0052533     3663   0.113    -.0040397    .0165157
------------------------------------------------------------------------------


. // Note: Here runmlwin is fitting 15000 iterations from scratch. This
. // contrasts the manual where we are fitting 10000 iterations in addition 
. // to the original 5000 giving a total of 15000..
. 
. gen onekid = (lc==1)

. 
. gen twokids = (lc==2)

. 
. gen threepluskids = (lc==3)

. 
. quietly runmlwin use cons age onekid twokids threepluskids, ///
>         level2(district:) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause

. 
. runmlwin use cons age onekid twokids threepluskids, ///
>         level2(district:) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsprevious nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       16.5
Deviance (dbar)            =    2519.98
Deviance (thetabar)        =    2515.10
Effective no. of pars (pd) =       4.88
Bayesian DIC               =    2524.87
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.257306   .1172414       74   0.000     -1.50365   -1.044943
         age |  -.0216689   .0072982      154   0.000    -.0368835   -.0075772
      onekid |   1.023307   .1556602      145   0.000     .7301328    1.345265
     twokids |   1.178552    .162634      120   0.000     .8654791     1.49371
threeplusk~s |   1.104576   .1711481       84   0.000     .7886095    1.455924
------------------------------------------------------------------------------


. 
. 
. 
. * 10.2 Random effects logistic regression model . . . . . . . . . . . . .136
. 
. runmlwin use cons age onekid twokids threepluskids, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Run time (seconds)   =       3.02
Number of iterations =          5
------------------------------------------------------------------------------
         use |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.368827   .1387225   -9.87    0.000    -1.640718   -1.096935
         age |  -.0235103    .007618   -3.09    0.002    -.0384414   -.0085793
      onekid |   1.020336   .1534657    6.65    0.000     .7195486    1.321123
     twokids |   1.218038   .1687095    7.22    0.000     .8873739    1.548703
threeplusk~s |   1.194597   .1734567    6.89    0.000     .8546283    1.534566
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |   .2463276   .0747691      .0997829    .3928723
------------------------------------------------------------------------------

. 
. runmlwin use cons age onekid twokids threepluskids, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsprevious nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       20.3
Deviance (dbar)            =    2396.32
Deviance (thetabar)        =    2355.12
Effective no. of pars (pd) =      41.20
Bayesian DIC               =    2437.53
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.489344   .1376958       59   0.000    -1.767119   -1.228622
         age |  -.0260354   .0077301      216   0.000    -.0411373    -.011358
      onekid |   1.110088   .1524513      259   0.000      .813606    1.417751
     twokids |   1.329594   .1689007      149   0.000     1.006129    1.666637
threeplusk~s |   1.305332   .1687296       80   0.000     .9843593    1.623929
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .3022512  .0979855    474   .1503189  .5334598
------------------------------------------------------------------------------

. 
. mcmcsum [RP2]var(cons), detail

                               [RP2]var(cons)
------------------------------------------------------------------------------
                                Percentiles
Mean          .3022512     0.5%   .1230625     Thinned Chain Length       5000
MCSE of Mean  .0029601     2.5%   .1503189     Effective Sample Size       474
Std. Dev.     .0979855       5%   .1665779     Raftery Lewis (2.5%)      12836
Mode          .2711853      25%   .2307661     Raftery Lewis (97.5%)     10430
P(mean)      0.000                             Brooks Draper (mean)       6732
P(mode)      0.000          50%   .2893552     
P(median)    0.000
                            75%   .3595042     
                            95%   .4803195     
                          97.5%   .5334598     
                          99.5%   .6343197     
------------------------------------------------------------------------------

. 
. mcmcsum [RP2]var(cons), fiveway

. 
. 
. 
. * 10.3 Random coefficients for area type . . . . . . . . . . . . . . . . 139
. 
. quietly runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause

. 
. runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsprevious nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       21.9
Deviance (dbar)            =    2370.45
Deviance (thetabar)        =    2331.27
Effective no. of pars (pd) =      39.18
Bayesian DIC               =    2409.63
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.722633   .1564096       85   0.000    -2.040373   -1.434551
         age |  -.0273354   .0084955      199   0.000    -.0450483   -.0112923
      onekid |   1.128914   .1646927      173   0.000     .8040234     1.44924
     twokids |   1.386754   .1807106      135   0.000     1.058083    1.759067
threeplusk~s |   1.374087   .1998872       95   0.000     1.008914    1.789485
       urban |   .7392214   .1167651      502   0.000     .5070931    .9664549
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .2344319  .0851539    292   .0985325  .4319376
------------------------------------------------------------------------------

. 
. quietly runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons urban) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause

. 
. runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons urban) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsprevious nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       25.4
Deviance (dbar)            =    2328.81
Deviance (thetabar)        =    2271.29
Effective no. of pars (pd) =      57.53
Bayesian DIC               =    2386.34
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.724727   .1608096       78   0.000    -2.057061   -1.436916
         age |  -.0269958   .0077822      213   0.000    -.0424352   -.0116732
      onekid |   1.140499   .1610437      246   0.000     .8443593    1.464803
     twokids |   1.371608   .1713673      187   0.000     1.037695    1.698188
threeplusk~s |   1.366217   .1767875      118   0.000     1.023669    1.720137
       urban |   .8306543   .1920122       96   0.000     .4591159    1.215496
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .4339787   .149603    185   .2080162  .7832098
             cov(cons,urban) | -.4587883  .1958078    104  -.9070693 -.1595674
                  var(urban) |  .7720941  .3588608     98   .2745705  1.659193
------------------------------------------------------------------------------

. 
. 
. 
. * 10.4 Probit regression . . . . . . . . . . . . . . . . . . . . . . . . 141
. 
. * 10.5 Running a probit regression in MLwiN . . . . . . . . . . . . . . .142
. 
. quietly runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons urban) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(probit) denom(cons)) nopause

. 
. matrix b = e(b)

. 
. matrix V = e(V)

. 
. runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons urban) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(probit) denom(cons)) ///
>         mcmc(on) initsb(b) initsv(V) nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial probit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       33.7
Deviance (dbar)            =    2327.26
Deviance (thetabar)        =    2270.55
Effective no. of pars (pd) =      56.72
Bayesian DIC               =    2383.98
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -1.055831   .0928036       84   0.000    -1.253128   -.8847331
         age |  -.0161719   .0049991      178   0.001    -.0262923   -.0068061
      onekid |   .6917918   .0970108      137   0.000     .4978677    .8724751
     twokids |   .8289826   .1063514      139   0.000     .5996459    1.030021
threeplusk~s |    .826828   .1137056       56   0.000     .5961093    1.062812
       urban |   .5145897   .1073405      130   0.000     .3057807    .7200971
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .1596531  .0525276    234   .0811271   .281848
             cov(cons,urban) | -.1699949  .0693228    132  -.3381742 -.0668061
                  var(urban) |   .286465  .1180859    134   .1208212  .5769592
------------------------------------------------------------------------------

. 
. estimates store mh

. 
. matrix mh_ess = e(ess)

. 
. runmlwin use cons age onekid twokids threepluskids urban, ///
>         level2(district: cons urban) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(probit) denom(cons)) ///
>         mcmc(femethod(gibbs) remethod(gibbs)) ///
>         initsb(b) initsv(V) nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial probit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       17.5
Deviance (dbar)            =    2327.59
Deviance (thetabar)        =    2271.08
Effective no. of pars (pd) =      56.51
Bayesian DIC               =    2384.10
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |   -1.04158   .0977987      782   0.000    -1.232331   -.8516307
         age |  -.0162636   .0048217     1899   0.001    -.0259902   -.0067695
      onekid |   .6877396   .0969737     1766   0.000     .4947631    .8745657
     twokids |   .8237693   .1063055     1788   0.000     .6172041    1.033748
threeplusk~s |   .8264746   .1084864     1691   0.000     .6152342    1.041743
       urban |   .4956297   .1056626      711   0.000     .2884581    .6974879
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .1580596  .0504436    875   .0792161  .2720135
             cov(cons,urban) | -.1641594  .0673555    597    -.31634 -.0552599
                  var(urban) |  .2726501  .1165671    504   .1019579  .5562358
------------------------------------------------------------------------------

. 
. estimates store gibbs

. 
. matrix gibbs_ess = e(ess)

. 
. estimates table gibbs mh, b(%3.2f)

----------------------------------
    Variable |  gibbs      mh     
-------------+--------------------
FP1          |
        cons |   -1.04     -1.06  
         age |   -0.02     -0.02  
      onekid |    0.69      0.69  
     twokids |    0.82      0.83  
threeplusk~s |    0.83      0.83  
       urban |    0.50      0.51  
-------------+--------------------
RP2          |
   var(cons) |    0.16      0.16  
cov(cons\u~) |   -0.16     -0.17  
  var(urban) |    0.27      0.29  
-------------+--------------------
OD           |
     bcons_1 |    1.00      1.00  
----------------------------------

. 
. matrix ess = (gibbs_ess', mh_ess')

. 
. matrix list ess

ess[10,2]
                    r1    r1
        FP1:cons   782    84
         FP1:age  1899   178
      FP1:onekid  1766   137
     FP1:twokids  1788   139
FP1:threeplusk~s  1691    56
       FP1:urban   711   130
   RP2:var(cons)   875   234
RP2:cov(cons\u~)   597   132
  RP2:var(urban)   504   134
      OD:bcons_1     0     0

. 
. 
. 
. * 10.6 Comparison with WinBUGS . . . . . . . . . . . . . . . . . . . . . 144
. 
. quietly runmlwin use cons age, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) nopause

. 
. matrix b = e(b)

. 
. matrix V = e(V)

. 
. quietly runmlwin use cons age, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(savewinbugs( ///
>                 model("bang_model.txt", replace) ///
>                 inits("bang_inits.txt", replace) ///
>                 data("bang_data.txt", replace) ///
>         nofit)) ///
>         initsb(b) initsv(V) nopause

. 
. view "bang_model.txt"

. 
. /* There is a known MLwiN bug here which will be fixed in version 2.29
> wbscript , ///
>         model("`c(pwd)'\bang_model.txt") ///
>         data("`c(pwd)'\bang_data.txt") ///
>         inits("`c(pwd)'\bang_inits.txt") ///
>         coda("`c(pwd)'\out") ///
>         set(beta sigma2.u2) ///
>         burn(4000) update(5000) ///
>         saving("`c(pwd)'\script.txt", replace) ///
>         quit
> 
> wbrun, script("`c(pwd)'\script.txt") ///
>         winbugs("C:\WinBUGS14\winbugs14.exe")
> 
> wbcoda, root("`c(pwd)'\out") clear
> 
> mcmcsum beta_1, variables
> 
> mcmcsum beta_1, variables fiveway
> */
. 
. use "https://www.bristol.ac.uk/cmm/media/runmlwin/bang1.dta", clear

. 
. runmlwin use cons age, ///
>         level2(district: cons) ///
>         level1(woman:) ///
>         discrete(distribution(binomial) link(logit) denom(cons)) ///
>         mcmc(on) initsb(b) initsv(V) nopause
 
MLwiN 3.13 multilevel model                     Number of obs      =      1934
Binomial logit response model (hierarchical)
Estimation algorithm: MCMC

-----------------------------------------------------------
                |   No. of       Observations per Group
 Level Variable |   Groups    Minimum    Average    Maximum
----------------+------------------------------------------
       district |       60          2       32.2        118
-----------------------------------------------------------

Burnin                     =        500
Chain                      =       5000
Thinning                   =          1
Run time (seconds)         =       17.1
Deviance (dbar)            =    2477.18
Deviance (thetabar)        =    2440.20
Effective no. of pars (pd) =      36.98
Bayesian DIC               =    2514.16
------------------------------------------------------------------------------
         use |      Mean    Std. Dev.     ESS     P       [95% Cred. Interval]
-------------+----------------------------------------------------------------
        cons |  -.5368289   .0871881      221   0.000    -.7229493   -.3775872
         age |   .0085463   .0052379     1183   0.050    -.0012621    .0189108
------------------------------------------------------------------------------

------------------------------------------------------------------------------
   Random-effects Parameters |     Mean   Std. Dev.   ESS     [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: district            |
                   var(cons) |  .2638906  .0892931    404    .131411  .4693553
------------------------------------------------------------------------------

. 
. mcmcsum [FP1]cons, detail

                                  [FP1]cons
------------------------------------------------------------------------------
                                Percentiles
Mean         -.5368289     0.5%  -.7872517     Thinned Chain Length       5000
MCSE of Mean   .004917     2.5%  -.7229493     Effective Sample Size       221
Std. Dev.     .0871881       5%  -.6841772     Raftery Lewis (2.5%)      25734
Mode          -.539376      25%   -.590112     Raftery Lewis (97.5%)     19686
P(mean)      0.000                             Brooks Draper (mean)      18575
P(mode)      0.000          50%  -.5356112     
P(median)    0.000
                            75%  -.4778811     
                            95%  -.3994635     
                          97.5%  -.3775872     
                          99.5%  -.3221758     
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. mcmcsum [FP1]cons, fiveway

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. * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .151
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. exit

end of do-file