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Platform: x86_64-w64-mingw32/x64

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> ############################################################################
> #     MLwiN User Manual
> #
> # 4   Random Intercept and Random Slope Models . . . . . . . . . . . . . .47
> #
> #     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 v3.11/
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)
> 
> 
> # 4.1 Random intercept models . . . . . . . . . . . . . . . . . . . . . . 47
> 
> data(tutorial, package = "R2MLwiN")
> 
> plot(tutorial$standlrt, tutorial$normexam, asp = 1)
> 
> (mymodel1 <- runMLwiN(normexam ~ 1 + standlrt + (1 | student), data = tutorial))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.11)  multilevel model (Normal) 
Estimation algorithm:  IGLS        Elapsed time : 0.08s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -4880.3 
Deviance statistic:  9760.5 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + (1 | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.00119     0.01264   -0.09     0.9249           -0.02596     0.02358 
standlrt     0.59506     0.01273   46.76          0   ***      0.57011     0.62000 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.64842     0.01439 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(resi.store = TRUE), 
+   data = tutorial))
/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: 3.11)  multilevel model (Normal) 
        N min     mean max N_complete min_complete mean_complete max_complete
school 65   2 62.44615 198         65            2      62.44615          198
Estimation algorithm:  IGLS        Elapsed time : 0.14s 
Number of obs:  4059 (from total 4059)        The model converged after 4 iterations.
Log likelihood:      -4678.6 
Deviance statistic:  9357.2 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + (1 | school) + (1 | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
              Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   0.00239     0.04002    0.06     0.9524           -0.07605     0.08083 
standlrt    0.56337     0.01247   45.19          0   ***      0.53894     0.58780 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the school level: 
                  Coef.   Std. Err. 
var_Intercept   0.09213     0.01815 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.56573     0.01266 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 4.2 Graphing predicted school lines from a random intercept model . . . 51
> 
> xb <- predict(mymodel2)
> 
> plot(tutorial$standlrt, xb, type = "l")
> 
> u0 <- mymodel2@residual$lev_2_resi_est_Intercept
> 
> xbu <- xb + u0[mymodel2@data$school]
> 
> head(u0)
[1] 0.37376013 0.50204279 0.50388852 0.01813113 0.24043062 0.54139498
> 
> plot(tutorial$standlrt, xbu, type = "l")
> 
> pred <- as.data.frame(cbind(mymodel2@data$school, mymodel2@data$standlrt, xbu)[order(mymodel2@data$school, mymodel2@data$standlrt), 
+   ])
> 
> colnames(pred) <- c("school", "standlrt", "xbu")
> 
> if (!require(lattice)) {
+   warning("package lattice required to run this example")
+ } else {
+   xyplot(xbu ~ standlrt, type = "l", group = school, data = pred)
+ }
Loading required package: lattice
> 
> # 4.3 The effect of clustering on the standard errors of coeficients . . .58
> 
> (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + schgend + (1 | school) + (1 | student), data = tutorial))
/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: 3.11)  multilevel model (Normal) 
        N min     mean max N_complete min_complete mean_complete max_complete
school 65   2 62.44615 198         65            2      62.44615          198
Estimation algorithm:  IGLS        Elapsed time : 0.09s 
Number of obs:  4059 (from total 4059)        The model converged after 4 iterations.
Log likelihood:      -4674.7 
Deviance statistic:  9349.4 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + schgend + (1 | school) + (1 | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
                    Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept        -0.08704     0.05112   -1.70    0.08863   .       -0.18723     0.01315 
standlrt          0.56379     0.01246   45.26          0   ***      0.53938     0.58821 
schgendboysch     0.09688     0.10891    0.89     0.3737           -0.11658     0.31034 
schgendgirlsch    0.24511     0.08497    2.88   0.003919   **       0.07857     0.41165 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the school level: 
                  Coef.   Std. Err. 
var_Intercept   0.07999     0.01599 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.56576     0.01266 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> (mymodel4 <- runMLwiN(normexam ~ 1 + standlrt + schgend + (1 | student), data = tutorial))
/nogui option ignored
ECHO    0


Echoing is ON
BATC 1

Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1

Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.11)  multilevel model (Normal) 
Estimation algorithm:  IGLS        Elapsed time : 0.06s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -4843.6 
Deviance statistic:  9687.1 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + schgend + (1 | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
                    Coef.   Std. Err.       z    Pr(>|z|)         [95% Conf.   Interval] 
Intercept        -0.09608     0.01713   -5.61   2.052e-08   ***     -0.12967    -0.06250 
standlrt          0.59433     0.01261   47.12           0   ***      0.56961     0.61905 
schgendboysch     0.11777     0.03918    3.01    0.002647   **       0.04098     0.19456 
schgendgirlsch    0.23584     0.02750    8.58   9.732e-18   ***      0.18195     0.28974 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.63680     0.01414 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 4.4 Does the coeficient of standlrt vary across schools? Introducing a random slope . . . . . . . . . . . . . .
> # . . . . . . . . . . . . . .59
> 
> (mymodel5 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(resi.store = TRUE), 
+   data = tutorial))
/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: 3.11)  multilevel model (Normal) 
        N min     mean max N_complete min_complete mean_complete max_complete
school 65   2 62.44615 198         65            2      62.44615          198
Estimation algorithm:  IGLS        Elapsed time : 0.14s 
Number of obs:  4059 (from total 4059)        The model converged after 4 iterations.
Log likelihood:      -4658.4 
Deviance statistic:  9316.9 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z     Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.01151     0.03978   -0.29       0.7724           -0.08948     0.06647 
standlrt     0.55673     0.01994   27.92   1.344e-171   ***      0.51765     0.59581 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the school level: 
                           Coef.   Std. Err. 
var_Intercept            0.09044     0.01792 
cov_Intercept_standlrt   0.01804     0.00672 
var_standlrt             0.01454     0.00441 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.55366     0.01248 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 4.5 Graphing predicted school lines from a random slope model . . . . . 62
> 
> xb <- predict(mymodel5)
> 
> u <- cbind(mymodel5@residual$lev_2_resi_est_Intercept, mymodel5@residual$lev_2_resi_est_standlrt)
> 
> rphat <- rowSums(as.matrix(mymodel5@data[, c("Intercept", "standlrt")]) * as.matrix(u[tutorial$school, ]))
> 
> xbu <- xb + rphat
> 
> pred <- as.data.frame(cbind(mymodel5@data$school, mymodel5@data$standlrt, xbu)[order(mymodel5@data$school, mymodel5@data$standlrt), 
+   ])
> 
> colnames(pred) <- c("school", "standlrt", "xbu")
> 
> if (!require(lattice)) {
+   warning("package lattice required to run this example")
+ } else {
+   xyplot(xbu ~ standlrt, type = "l", group = school, data = pred)
+ }
> 
> 
> #     Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . 64
> 
> ############################################################################
> 
> proc.time()
   user  system elapsed 
   4.57    0.59    6.42