R version 4.4.1 (2024-06-14 ucrt) -- "Race for Your Life"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

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> ############################################################################
> #     MLwiN User Manual
> #
> # 7   Modelling the Variance as a Function of Explanatory Variables . . . 89
> #
> #     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)
> 
> 
> # 7.1 A level 1 variance function for two groups . . . . . . . . . . . . .89
> 
> data(tutorial, package = "R2MLwiN")
> 
> covmatrix <- matrix(, nrow = 3, ncol = 1)
> covmatrix[1, 1] <- 1
> covmatrix[2, 1] <- "sexboy"
> covmatrix[3, 1] <- "sexgirl"
> 
> (mymodel1 <- runMLwiN(normexam ~ 0 + sex + (0 + sex | student), estoptions = list(clre = covmatrix), 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:      -5724.8 
Deviance statistic:  11449.5 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 0 + sex + (0 + sex | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
              Coef.   Std. Err.       z    Pr(>|z|)         [95% Conf.   Interval] 
sexboy     -0.14035     0.02545   -5.51   3.504e-08   ***     -0.19024    -0.09046 
sexgirl     0.09332     0.01964    4.75   2.028e-06   ***      0.05482     0.13182 
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1  
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                Coef.   Std. Err. 
var_sexboy    1.05144     0.03691 
var_sexgirl   0.93997     0.02693 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 7.2 Variance functions at level 2 . . . . . . . . . . . . . . . . . . . 95
> 
> (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | 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 : 0.07s 
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 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> l2varfn <- mymodel2@RP["RP2_var_Intercept"] + (2 * mymodel2@RP["RP2_cov_Intercept_standlrt"] * mymodel2@data$standlrt) + 
+   (mymodel2@RP["RP2_var_standlrt"] * mymodel2@data$standlrt^2)
> 
> varfndata <- as.data.frame(cbind(mymodel2@data$standlrt, l2varfn)[order(mymodel2@data$standlrt), ])
> colnames(varfndata) <- c("standlrt", "l2varfn")
> 
> plot(varfndata$standlrt, varfndata$l2varfn, type = "l")
> 
> # 7.3 Further elaborating the model for the student-level variance . . . .99
> 
> (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | 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
iteration 4
iteration 5

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 : 0.12s 
Number of obs:  4059 (from total 4059)        The model converged after 6 iterations.
Log likelihood:      -4655.8 
Deviance statistic:  9311.6 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | 
    student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z     Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.01174     0.03985   -0.29       0.7683           -0.08984     0.06636 
standlrt     0.55787     0.01982   28.14   3.092e-174   ***      0.51901     0.59672 
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            0.09082     0.01799 
cov_Intercept_standlrt   0.01863     0.00671 
var_standlrt             0.01423     0.00437 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                            Coef.   Std. Err. 
var_Intercept             0.55322     0.01521 
cov_Intercept_standlrt   -0.01474     0.00640 
var_standlrt              0.00066     0.00911 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> l2varfn <- mymodel3@RP["RP2_var_Intercept"] + (2 * mymodel3@RP["RP2_cov_Intercept_standlrt"] * mymodel3@data$standlrt) + 
+   (mymodel3@RP["RP2_var_standlrt"] * mymodel3@data$standlrt^2)
> 
> l1varfn <- mymodel3@RP["RP1_var_Intercept"] + (2 * mymodel3@RP["RP1_cov_Intercept_standlrt"] * mymodel3@data$standlrt) + 
+   (mymodel3@RP["RP1_var_standlrt"] * mymodel3@data$standlrt^2)
> 
> varfndata <- as.data.frame(cbind(mymodel3@data$standlrt, l2varfn, l1varfn)[order(mymodel3@data$standlrt), ])
> colnames(varfndata) <- c("standlrt", "l2varfn", "l1varfn")
> 
> if (!require(lattice)) {
+   warning("package lattice required to run this example")
+ } else {
+   xyplot(l2varfn + l1varfn ~ standlrt, data = varfndata, type = "l")
+ }
Loading required package: lattice
> 
> covmatrix <- matrix(, nrow = 3, ncol = 3)
> covmatrix[1, 1] <- 1
> covmatrix[2, 1] <- "standlrt"
> covmatrix[3, 1] <- "standlrt"
> covmatrix[1, 2] <- 1
> covmatrix[2, 2] <- "sexgirl"
> covmatrix[3, 2] <- "Intercept"
> covmatrix[1, 3] <- 1
> covmatrix[2, 3] <- "standlrt"
> covmatrix[3, 3] <- "sexgirl"
> 
> (mymodel4 <- runMLwiN(normexam ~ 1 + standlrt + sex + (1 + standlrt | school) + (1 + standlrt + sex | student), estoptions = list(clre = covmatrix), 
+   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 : 0.11s 
Number of obs:  4059 (from total 4059)        The model converged after 4 iterations.
Log likelihood:      -4638.7 
Deviance statistic:  9277.4 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + sex + (1 + standlrt | school) + (1 + 
    standlrt + sex | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z     Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.11200     0.04331   -2.59     0.009706   **      -0.19689    -0.02712 
standlrt     0.55417     0.01994   27.79   5.388e-170   ***      0.51509     0.59325 
sexgirl      0.17580     0.03236    5.43    5.545e-08   ***      0.11238     0.23923 
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            0.08653     0.01722 
cov_Intercept_standlrt   0.01957     0.00665 
var_standlrt             0.01456     0.00441 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                            Coef.   Std. Err. 
var_Intercept             0.58261     0.02082 
cov_Intercept_standlrt   -0.01281     0.00635 
var_sexgirl              -0.05412     0.02589 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> covmatrix <- matrix(, nrow = 3, ncol = 2)
> covmatrix[1, 1] <- 1
> covmatrix[2, 1] <- "standlrt"
> covmatrix[3, 1] <- "standlrt"
> covmatrix[1, 2] <- 1
> covmatrix[2, 2] <- "sexgirl"
> covmatrix[3, 2] <- "Intercept"
> 
> (mymodel5 <- runMLwiN(normexam ~ 1 + standlrt + sex + (1 + standlrt | school) + (1 + standlrt + sex | student), estoptions = list(clre = covmatrix), 
+   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 : 0.11s 
Number of obs:  4059 (from total 4059)        The model converged after 4 iterations.
Log likelihood:      -4635.8 
Deviance statistic:  9271.6 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + standlrt + sex + (1 + standlrt | school) + (1 + 
    standlrt + sex | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z     Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.11206     0.04329   -2.59     0.009633   **      -0.19689    -0.02722 
standlrt     0.55390     0.02003   27.66   2.237e-168   ***      0.51465     0.59315 
sexgirl      0.17532     0.03229    5.43    5.647e-08   ***      0.11203     0.23860 
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            0.08643     0.01720 
cov_Intercept_standlrt   0.01957     0.00668 
var_standlrt             0.01479     0.00445 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                            Coef.   Std. Err. 
var_Intercept             0.58371     0.02090 
cov_Intercept_standlrt   -0.03368     0.00996 
cov_standlrt_sexgirl      0.03209     0.01290 
var_sexgirl              -0.05827     0.02593 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> l2varfn <- mymodel5@RP["RP2_var_Intercept"] + (2 * mymodel5@RP["RP2_cov_Intercept_standlrt"] * mymodel5@data$standlrt) + 
+   (mymodel5@RP["RP2_var_standlrt"] * mymodel5@data$standlrt^2)
> 
> l1varfnboys <- mymodel5@RP["RP1_var_Intercept"] + (2 * mymodel5@RP["RP1_cov_Intercept_standlrt"] * mymodel5@data$standlrt)
> 
> l1varfngirls <- mymodel5@RP["RP1_var_Intercept"] + (2 * mymodel5@RP["RP1_cov_Intercept_standlrt"] * mymodel5@data$standlrt) + 
+   (2 * mymodel5@RP["RP1_cov_standlrt_sexgirl"] * mymodel5@data$standlrt) + mymodel5@RP["RP1_var_sexgirl"]
> 
> varfndata <- as.data.frame(cbind(mymodel5@data$standlrt, l2varfn, l1varfnboys, l1varfngirls)[order(mymodel5@data$standlrt), 
+   ])
> colnames(varfndata) <- c("standlrt", "l2varfn", "l1varfnboys", "l1varfngirls")
> 
> if (!require(lattice)) {
+   warning("package lattice required to run this example")
+ } else {
+   xyplot(l2varfn + l1varfnboys + l1varfngirls ~ standlrt, data = varfndata, type = "l")
+ }
> 
> #     Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . .106
> 
> ############################################################################
> 
> proc.time()
   user  system elapsed 
   4.12    0.35    5.81