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> ############################################################################
> #     MLwiN User Manual
> #
> # 12  Modelling Count Data . . . . . . . . . . . . . . . . . . . . . . . 181
> #
> #     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 2013-2024 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 v3.13/
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)
> 
> 
> # 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .181
> 
> data(mmmec, package = "R2MLwiN")
> summary(mmmec)
       nation       region          county            obs        
 Italy    :95   Min.   : 1.00   Min.   :  1.00   Min.   :  0.00  
 France   :94   1st Qu.:27.00   1st Qu.: 90.25   1st Qu.:  8.00  
 UK       :70   Median :44.00   Median :178.50   Median : 14.50  
 W_Germany:30   Mean   :42.86   Mean   :178.25   Mean   : 27.83  
 Ireland  :26   3rd Qu.:60.00   3rd Qu.:266.75   3rd Qu.: 31.00  
 Denmark  :14   Max.   :79.00   Max.   :355.00   Max.   :313.00  
 (Other)  :25                                                    
      exp              cons        uvbi          
 Min.   :  0.69   Min.   :1   Min.   :-8.900200  
 1st Qu.: 11.02   1st Qu.:1   1st Qu.:-4.158400  
 Median : 18.76   Median :1   Median :-0.886400  
 Mean   : 27.80   Mean   :1   Mean   : 0.000204  
 3rd Qu.: 34.39   3rd Qu.:1   3rd Qu.: 3.275525  
 Max.   :258.86   Max.   :1   Max.   :13.359000  
                                                 
> 
> # 12.2 Fitting a simple Poisson model . . . . . . . . . . . . . . . . . .182
> 
> (mymodel1 <- runMLwiN(log(obs) ~ 1 + uvbi + offset(log(exp)), D = "Poisson", data = mmmec))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.13)  multilevel model (Poisson) 
Estimation algorithm:  IGLS MQL1        Elapsed time : 0.21s 
Number of obs:  354 (from total 354)        The model converged after 4 iterations.
Log likelihood:      NA 
Deviance statistic:  NA 
--------------------------------------------------------------------------------------------------- 
The model formula:
log(obs) ~ 1 + uvbi + offset(log(exp))
Level 1: l1id      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.        z     Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.07011     0.01105    -6.35    2.195e-10   ***     -0.09175    -0.04846 
uvbi        -0.05719     0.00268   -21.37   2.796e-101   ***     -0.06244    -0.05194 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the l1id level: 
                Coef.   Std. Err. 
var_bcons_1   1.00000     0.00000 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 12.3 A three-level analysis . . . . . . . . . . . . . . . . . . . . . .184
> 
> (mymodel2 <- runMLwiN(log(obs) ~ 1 + offset(log(exp)) + (1 | nation) + (1 | region), D = "Poisson", estoptions = list(Meth = 0), 
+   data = mmmec))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.13)  multilevel model (Poisson) 
        N min      mean max N_complete min_complete mean_complete max_complete
nation  9   3 39.333333  95          9            3     39.333333           95
region 78   1  4.538462  13         78            1      4.538462           13
Estimation algorithm:  RIGLS MQL1        Elapsed time : 0.25s 
Number of obs:  354 (from total 354)        The model converged after 5 iterations.
Log likelihood:      NA 
Deviance statistic:  NA 
--------------------------------------------------------------------------------------------------- 
The model formula:
log(obs) ~ 1 + offset(log(exp)) + (1 | nation) + (1 | region)
Level 3: nation     Level 2: region     Level 1: l1id      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
              Coef.   Std. Err.      z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   0.11032     0.16045   0.69     0.4917           -0.20415     0.42480 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the nation level: 
                  Coef.   Std. Err. 
var_Intercept   0.21450     0.10894 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the region level: 
                  Coef.   Std. Err. 
var_Intercept   0.04537     0.00965 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the l1id level: 
                Coef.   Std. Err. 
var_bcons_1   1.00000     0.00000 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> (mymodel3 <- runMLwiN(log(obs) ~ 1 + offset(log(exp)) + (1 | nation) + (1 | region), D = "Poisson", estoptions = list(Meth = 0, 
+   nonlinear = c(N = 1, M = 2)), data = mmmec))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.13)  multilevel model (Poisson) 
        N min      mean max N_complete min_complete mean_complete max_complete
nation  9   3 39.333333  95          9            3     39.333333           95
region 78   1  4.538462  13         78            1      4.538462           13
Estimation algorithm:  RIGLS PQL2        Elapsed time : 0.44s 
Number of obs:  354 (from total 354)        The model converged after 7 iterations.
Log likelihood:      NA 
Deviance statistic:  NA 
--------------------------------------------------------------------------------------------------- 
The model formula:
log(obs) ~ 1 + offset(log(exp)) + (1 | nation) + (1 | region)
Level 3: nation     Level 2: region     Level 1: l1id      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.02451     0.15169   -0.16     0.8716           -0.32182     0.27280 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the nation level: 
                  Coef.   Std. Err. 
var_Intercept   0.18545     0.09705 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the region level: 
                  Coef.   Std. Err. 
var_Intercept   0.05763     0.01246 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the l1id level: 
                Coef.   Std. Err. 
var_bcons_1   1.00000     0.00000 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> (mymodel4 <- runMLwiN(log(obs) ~ 1 + uvbi + offset(log(exp)) + (1 | nation) + (1 | region), D = "Poisson", estoptions = list(Meth = 0, 
+   nonlinear = c(N = 1, M = 2)), data = mmmec))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.13)  multilevel model (Poisson) 
        N min      mean max N_complete min_complete mean_complete max_complete
nation  9   3 39.333333  95          9            3     39.333333           95
region 78   1  4.538462  13         78            1      4.538462           13
Estimation algorithm:  RIGLS PQL2        Elapsed time : 0.39s 
Number of obs:  354 (from total 354)        The model converged after 6 iterations.
Log likelihood:      NA 
Deviance statistic:  NA 
--------------------------------------------------------------------------------------------------- 
The model formula:
log(obs) ~ 1 + uvbi + offset(log(exp)) + (1 | nation) + (1 | 
    region)
Level 3: nation     Level 2: region     Level 1: l1id      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.08220     0.14226   -0.58     0.5634           -0.36101     0.19662 
uvbi        -0.02772     0.01132   -2.45    0.01435   *       -0.04991    -0.00553 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the nation level: 
                  Coef.   Std. Err. 
var_Intercept   0.15728     0.08281 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the region level: 
                  Coef.   Std. Err. 
var_Intercept   0.04922     0.01095 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the l1id level: 
                Coef.   Std. Err. 
var_bcons_1   1.00000     0.00000 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 12.4 A two-level model using separate country terms . . . . . . . . . .186
> 
> addmargins(with(mmmec, table(nation)))
nation
    Belgium   W_Germany     Denmark      France          UK       Italy 
         11          30          14          94          70          95 
    Ireland  Luxembourg Netherlands         Sum 
         26           3          11         354 
> 
> (mymodel5 <- runMLwiN(log(obs) ~ 0 + nation + nation:uvbi + offset(log(exp)) + (1 | region), D = "Poisson", estoptions = list(Meth = 0, 
+   nonlinear = c(N = 1, M = 2)), data = mmmec))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.13)  multilevel model (Poisson) 
        N min     mean max N_complete min_complete mean_complete max_complete
region 78   1 4.538462  13         78            1      4.538462           13
Estimation algorithm:  RIGLS PQL2        Elapsed time : 0.48s 
Number of obs:  354 (from total 354)        The model converged after 7 iterations.
Log likelihood:      NA 
Deviance statistic:  NA 
--------------------------------------------------------------------------------------------------- 
The model formula:
log(obs) ~ 0 + nation + nation:uvbi + offset(log(exp)) + (1 | 
    region)
Level 2: region     Level 1: l1id      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
                            Coef.   Std. Err.        z    Pr(>|z|)         [95% Conf.   Interval] 
nationBelgium             0.69790     0.74658     0.93      0.3499           -0.76538     2.16118 
nationW_Germany           0.47761     0.12022     3.97   7.106e-05   ***      0.24198     0.71324 
nationDenmark             0.31911     0.87941     0.36      0.7167           -1.40450     2.04273 
nationFrance             -0.59411     0.05433   -10.94   7.808e-28   ***     -0.70059    -0.48762 
nationUK                  0.61400     0.20697     2.97    0.003011   **       0.20835     1.01966 
nationItaly               0.28151     0.10455     2.69     0.00709   **       0.07660     0.48643 
nationIreland            -0.52867     1.30284    -0.41      0.6849           -3.08219     2.02485 
nationLuxembourg         14.71263    15.53246     0.95      0.3435          -15.73042    45.15569 
nationNetherlands        -0.34752     0.92301    -0.38      0.7065           -2.15660     1.46155 
nationBelgium:uvbi        0.26472     0.25191     1.05      0.2933           -0.22902     0.75845 
nationW_Germany:uvbi     -0.01336     0.03211    -0.42      0.6773           -0.07630     0.04957 
nationDenmark:uvbi       -0.08136     0.15521    -0.52      0.6001           -0.38557     0.22284 
nationFrance:uvbi         0.01283     0.01797     0.71      0.4753           -0.02239     0.04804 
nationUK:uvbi             0.14230     0.04267     3.33   0.0008534   ***      0.05867     0.22592 
nationItaly:uvbi         -0.08749     0.01579    -5.54   2.987e-08   ***     -0.11842    -0.05655 
nationIreland:uvbi       -0.00096     0.26276     0.00      0.9971           -0.51595     0.51404 
nationLuxembourg:uvbi     6.40748     6.77904     0.95      0.3446           -6.87918    19.69415 
nationNetherlands:uvbi   -0.11202     0.22159    -0.51      0.6132           -0.54633     0.32230 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the region level: 
                  Coef.   Std. Err. 
var_Intercept   0.03572     0.00794 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the l1id level: 
                Coef.   Std. Err. 
var_bcons_1   1.00000     0.00000 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> xb <- predict(mymodel5)
> 
> plot(mymodel5@data$uvbi, xb, xlab = "UV B radiation", ylab = "prediction", type = "n")
> lines(mymodel5@data$uvbi[mymodel5@data$nationBelgium == 1], xb[mymodel5@data$nationBelgium == 1], col = 1)
> lines(mymodel5@data$uvbi[mymodel5@data$nationW_Germany == 1], xb[mymodel5@data$nationW_Germany == 1], col = 2)
> lines(mymodel5@data$uvbi[mymodel5@data$nationDenmark == 1], xb[mymodel5@data$nationDenmark == 1], col = 3)
> lines(mymodel5@data$uvbi[mymodel5@data$nationFrance == 1], xb[mymodel5@data$nationFrance == 1], col = 4)
> lines(mymodel5@data$uvbi[mymodel5@data$nationUK == 1], xb[mymodel5@data$nationUK == 1], col = 5)
> lines(mymodel5@data$uvbi[mymodel5@data$nationItaly == 1], xb[mymodel5@data$nationItaly == 1], col = 6)
> lines(mymodel5@data$uvbi[mymodel5@data$nationIreland == 1], xb[mymodel5@data$nationIreland == 1], col = 7)
> lines(mymodel5@data$uvbi[mymodel5@data$nationLuxembourg == 1], xb[mymodel5@data$nationLuxembourg == 1], col = 8)
> lines(mymodel5@data$uvbi[mymodel5@data$nationNetherlands == 1], xb[mymodel5@data$nationNetherlands == 1], col = 9)
> legend(7, 0.7, c("belgium", "wgermany", "denmark", "france", "uk", "italy", "ireland", "luxembourg", "netherlands"), 
+   lty = 1, col = 1:9)
> 
> # 12.5 Some issues and problems for discrete response models . . . . . . 190
> 
> # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .190
> 
> ############################################################################
> 
> proc.time()
   user  system elapsed 
  10.17    1.40   14.71