R version 3.6.3 (2020-02-29) -- "Holding the Windsock"
Copyright (C) 2020 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
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Type 'license()' or 'licence()' for distribution details.

  Natural language support but running in an English locale

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> ############################################################################
> #     MLwiN User Manual
> #
> # 2   Introduction to Multilevel Modelling . . . . . . . . . . . . . . . . 9
> #
> #     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 2013-2017 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 v3.05/
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)
> 
> 
> # 2.1 The tutorial data set . . . . . . . . . . . . . . . . . . . . . . . .9
> 
> # 2.2 Opening the worksheet and looking at the data . . . . . . . . . . . 10
> 
> data(tutorial, package = "R2MLwiN")
> 
> summary(tutorial)
     school        student        normexam              cons  
 14     : 198   1      :  65   Min.   :-3.666072   Min.   :1  
 17     : 126   2      :  65   1st Qu.:-0.699505   1st Qu.:1  
 18     : 120   3      :  64   Median : 0.004322   Median :1  
 49     : 113   4      :  64   Mean   :-0.000114   Mean   :1  
 8      : 102   5      :  64   3rd Qu.: 0.678759   3rd Qu.:1  
 15     :  91   6      :  64   Max.   : 3.666091   Max.   :1  
 (Other):3309   (Other):3673                                  
    standlrt          sex           schgend         avslrt          schav     
 Min.   :-2.93495   boy :1623   mixedsch:2169   Min.   :-0.75596   low : 640  
 1st Qu.:-0.62071   girl:2436   boysch  : 513   1st Qu.:-0.14934   mid :2263  
 Median : 0.04050               girlsch :1377   Median :-0.02020   high:1156  
 Mean   : 0.00181                               Mean   : 0.00181              
 3rd Qu.: 0.61906                               3rd Qu.: 0.21052              
 Max.   : 3.01595                               Max.   : 0.63766              
                                                                              
 vrband    
 vb1:1176  
 vb2:2344  
 vb3: 539  
           
           
           
           
> 
> head(tutorial)
  school student   normexam cons   standlrt  sex  schgend    avslrt schav
1      1       1  0.2613245    1  0.6190593 girl mixedsch 0.1661745   mid
2      1       2  0.1340668    1  0.2058020 girl mixedsch 0.1661745   mid
3      1       3 -1.7238824    1 -1.3645757  boy mixedsch 0.1661745   mid
4      1       4  0.9675860    1  0.2058020 girl mixedsch 0.1661745   mid
5      1       5  0.5443409    1  0.3711049 girl mixedsch 0.1661745   mid
6      1       6  1.7348992    1  2.1894369  boy mixedsch 0.1661745   mid
  vrband
1    vb1
2    vb2
3    vb3
4    vb2
5    vb2
6    vb1
> 
> 
> 
> # 2.3 Comparing two groups . . . . . . . . . . . . . . . . . . . . . . . .13
> 
> tab <- cbind(tapply(tutorial$normexam, tutorial$sex, length), tapply(tutorial$normexam, tutorial$sex, mean), tapply(tutorial$normexam, 
+   tutorial$sex, sd))
> tab <- rbind(tab, c(length(tutorial$normexam), mean(tutorial$normexam), sd(tutorial$normexam)))
> colnames(tab) <- c("N", "Mean", "SD")
> rownames(tab)[3] <- "Total"
> 
> tab
         N          Mean        SD
boy   1623 -0.1403503443 1.0257126
girl  2436  0.0933194718 0.9697191
Total 4059 -0.0001139137 0.9989439
> 
> t.test(normexam ~ sex, data = tutorial, var.equal = TRUE)

	Two Sample t-test

data:  normexam by sex
t = -7.348, df = 4057, p-value = 2.42e-13
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.2960165 -0.1713232
sample estimates:
 mean in group boy mean in group girl 
       -0.14035034         0.09331947 

> 
> (mymodel1 <- runMLwiN(normexam ~ 1 + sex + (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: 3.05)  multilevel model (Normal) 
Estimation algorithm:  IGLS        Elapsed time : 0.05s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -5727.9 
Deviance statistic:  11455.7 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + sex + (1 | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z    Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.14035     0.02463   -5.70   1.209e-08   ***     -0.18862    -0.09208 
sexgirl      0.23367     0.03179    7.35   1.985e-13   ***      0.17136     0.29598 
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   0.98454     0.02185 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> # 2.4 Comparing more than two groups: Fixed effects models . . . . . . . .20
> 
> mean_normexam <- aggregate(normexam ~ school, mean, data = tutorial)$normexam
> 
> hist(mean_normexam)
> 
> mymodel2 <- runMLwiN(normexam ~ 1 + (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

> 
> tutorial$school <- relevel(tutorial$school, 65)
> 
> (mymodel3 <- runMLwiN(normexam ~ 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 achieved
TOLE 2
MAXI 20
NEXT
iteration 2

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.05)  multilevel model (Normal) 
Estimation algorithm:  IGLS        Elapsed time : 0.78s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -5391.5 
Deviance statistic:  10782.9 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + school + (1 | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z    Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.30869     0.10211   -3.02    0.002503   **      -0.50882    -0.10855 
school1      0.80990     0.14783    5.48   4.288e-08   ***      0.52015     1.09964 
school2      1.09179     0.15998    6.82    8.82e-12   ***      0.77823     1.40534 
school3      1.16413     0.16269    7.16    8.34e-13   ***      0.84526     1.48300 
school4      0.38232     0.14487    2.64    0.008312   **       0.09838     0.66625 
school5      0.71230     0.18509    3.85    0.000119   ***      0.34952     1.07508 
school6      1.25327     0.14441    8.68   4.007e-18   ***      0.97023     1.53630 
school7      0.70019     0.14109    4.96   6.951e-07   ***      0.42366     0.97672 
school8      0.26049     0.13640    1.91     0.05616   .       -0.00684     0.52783 
school9     -0.12700     0.18698   -0.68       0.497           -0.49347     0.23948 
school10     0.03930     0.16465    0.24      0.8114           -0.28341     0.36201 
school11     0.86591     0.15454    5.60   2.103e-08   ***      0.56303     1.16879 
school12     0.23621     0.16785    1.41      0.1594           -0.09278     0.56520 
school13     0.06294     0.15317    0.41      0.6811           -0.23727     0.36314 
school14     0.32426     0.12100    2.68    0.007364   **       0.08711     0.56140 
school15     0.26808     0.13998    1.92     0.05547   .       -0.00627     0.54243 
school16     0.05457     0.14109    0.39      0.6989           -0.22196     0.33110 
school17     0.06326     0.13057    0.48       0.628           -0.19264     0.31917 
school18     0.30254     0.13183    2.29     0.02174   *        0.04416     0.56091 
school19     0.51497     0.15998    3.22    0.001286   **       0.20142     0.82853 
school20     0.80778     0.17837    4.53   5.935e-06   ***      0.45818     1.15738 
school21     0.68901     0.14783    4.66   3.149e-06   ***      0.39927     0.97875 
school22    -0.18951     0.14034   -1.35      0.1769           -0.46458     0.08555 
school23    -0.42895     0.20055   -2.14     0.03244   *       -0.82201    -0.03588 
school24     0.32133     0.18158    1.77     0.07679   .       -0.03456     0.67722 
school25    -0.30442     0.14783   -2.06     0.03947   *       -0.59416    -0.01468 
school26    -0.08333     0.14680   -0.57      0.5703           -0.37105     0.20438 
school27    -0.02021     0.17837   -0.11      0.9098           -0.36981     0.32939 
school28    -0.56402     0.15831   -3.56   0.0003669   ***     -0.87430    -0.25375 
school29     0.37220     0.14487    2.57     0.01019   *        0.08826     0.65613 
school30     0.64414     0.17403    3.70   0.0002145   ***      0.30304     0.98524 
school31     0.07201     0.16568    0.43      0.6638           -0.25272     0.39674 
school32    -0.06264     0.17403   -0.36      0.7189           -0.40375     0.27846 
school33     0.38580     0.14581    2.65    0.008147   **       0.10002     0.67158 
school34    -0.06221     0.20618   -0.30      0.7629           -0.46631     0.34190 
school35     0.39264     0.17994    2.18     0.02911   *        0.03996     0.74532 
school36     0.05948     0.14948    0.40      0.6907           -0.23349     0.35245 
school37    -0.35666     0.21987   -1.62      0.1048           -0.78760     0.07428 
school38     0.02114     0.16086    0.13      0.8954           -0.29413     0.33641 
school39     0.34701     0.16675    2.08     0.03743   *        0.02019     0.67384 
school40     0.04901     0.14892    0.33      0.7421           -0.24286     0.34088 
school41     0.38161     0.15598    2.45     0.01442   *        0.07589     0.68732 
school42     0.33137     0.15751    2.10     0.03539   *        0.02266     0.64008 
school43     0.45628     0.15525    2.94    0.003292   **       0.15200     0.76056 
school44    -0.12504     0.19797   -0.63      0.5276           -0.51305     0.26297 
school45     0.08318     0.16176    0.51      0.6071           -0.23386     0.40022 
school46    -0.14872     0.14310   -1.04      0.2987           -0.42918     0.13175 
school47     0.18643     0.14353    1.30       0.194           -0.09488     0.46773 
school48    -0.10561     0.65384   -0.16      0.8717           -1.38711     1.17590 
school49     0.35558     0.13345    2.66     0.00771   **       0.09402     0.61714 
school50    -0.01309     0.14783   -0.09      0.9294           -0.30284     0.27665 
school51     0.03062     0.15751    0.19      0.8459           -0.27809     0.33933 
school52     0.84205     0.15525    5.42    5.83e-08   ***      0.53777     1.14633 
school53     1.31224     0.14948    8.78   1.652e-18   ***      1.01926     1.60521 
school54    -0.32494     0.33867   -0.96      0.3373           -0.98872     0.33884 
school55     1.02581     0.16366    6.27   3.654e-10   ***      0.70505     1.34657 
school56     0.27441     0.17994    1.52      0.1273           -0.07827     0.62708 
school57     0.30977     0.15384    2.01     0.04406   *        0.00824     0.61129 
school58     0.59057     0.18158    3.25    0.001144   **       0.23468     0.94647 
school59    -0.74040     0.16785   -4.41   1.029e-05   ***     -1.06939    -0.41141 
school60     0.50412     0.14441    3.49   0.0004814   ***      0.22108     0.78715 
school61     0.25635     0.15317    1.67      0.0942   .       -0.04385     0.55656 
school62     0.34668     0.14892    2.33     0.01991   *        0.05481     0.63855 
school63     1.04437     0.19553    5.34   9.234e-08   ***      0.66113     1.42760 
school64     0.65248     0.15673    4.16   3.141e-05   ***      0.34529     0.95967 
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   0.83416     0.01852 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> aov(normexam ~ school, data = tutorial)
Call:
   aov(formula = normexam ~ school, data = tutorial)

Terms:
                  school Residuals
Sum of Squares   663.580  3385.853
Deg. of Freedom       64      3994

Residual standard error: 0.9207252
Estimated effects may be unbalanced
> 
> if (!require(lmtest)) {
+   warning("lmtest package required to use lrtest() function")
+ } else {
+   lrtest(mymodel2, mymodel3)
+ }
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Likelihood ratio test

Model 1: normexam ~ 1 + (1 | student)
Model 2: normexam ~ 1 + school + (1 | student)
  #Df  LogLik Df  Chisq Pr(>Chisq)    
1   2 -5754.7                         
2  66 -5391.5 64 726.44  < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> (mymodel4 <- runMLwiN(normexam ~ 1 + school + 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: 3.05)  multilevel model (Normal) 
Estimation algorithm:  IGLS        Elapsed time : 0.82s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -5391.5 
Deviance statistic:  10782.9 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + school + schgend + (1 | student)
Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
                    Coef.   Std. Err.       z    Pr(>|z|)         [95% Conf.   Interval] 
Intercept        -0.30869     0.10211   -3.02    0.002503   **      -0.50882    -0.10855 
school1           0.80990     0.14783    5.48   4.288e-08   ***      0.52015     1.09964 
school2           1.09179     0.15998    6.82    8.82e-12   ***      0.77823     1.40534 
school3           1.16413     0.16269    7.16    8.34e-13   ***      0.84526     1.48300 
school4           0.38232     0.14487    2.64    0.008312   **       0.09838     0.66625 
school5           0.71230     0.18509    3.85    0.000119   ***      0.34952     1.07508 
school6           1.25327     0.14441    8.68   4.007e-18   ***      0.97023     1.53630 
school7           0.70019     0.14109    4.96   6.951e-07   ***      0.42366     0.97672 
school8           0.26049     0.13640    1.91     0.05616   .       -0.00684     0.52783 
school9          -0.12700     0.18698   -0.68       0.497           -0.49347     0.23948 
school10          0.03930     0.16465    0.24      0.8114           -0.28341     0.36201 
school11          0.86591     0.15454    5.60   2.103e-08   ***      0.56303     1.16879 
school12          0.23621     0.16785    1.41      0.1594           -0.09278     0.56520 
school13          0.06294     0.15317    0.41      0.6811           -0.23727     0.36314 
school14          0.32426     0.12100    2.68    0.007364   **       0.08711     0.56140 
school15          0.26808     0.13998    1.92     0.05547   .       -0.00627     0.54243 
school16          0.05457     0.14109    0.39      0.6989           -0.22196     0.33110 
school17          0.06326     0.13057    0.48       0.628           -0.19264     0.31917 
school18          0.30254     0.13183    2.29     0.02174   *        0.04416     0.56091 
school19          0.51497     0.15998    3.22    0.001286   **       0.20142     0.82853 
school20          0.80778     0.17837    4.53   5.935e-06   ***      0.45818     1.15738 
school21          0.68901     0.14783    4.66   3.149e-06   ***      0.39927     0.97875 
school22         -0.18951     0.14034   -1.35      0.1769           -0.46458     0.08555 
school23         -0.42895     0.20055   -2.14     0.03244   *       -0.82201    -0.03588 
school24          0.32133     0.18158    1.77     0.07679   .       -0.03456     0.67722 
school25         -0.30442     0.14783   -2.06     0.03947   *       -0.59416    -0.01468 
school26         -0.08333     0.14680   -0.57      0.5703           -0.37105     0.20438 
school27         -0.02021     0.17837   -0.11      0.9098           -0.36981     0.32939 
school28         -0.56402     0.15831   -3.56   0.0003669   ***     -0.87430    -0.25375 
school29          0.37220     0.14487    2.57     0.01019   *        0.08826     0.65613 
school30          0.64414     0.17403    3.70   0.0002145   ***      0.30304     0.98524 
school31          0.07201     0.16568    0.43      0.6638           -0.25272     0.39674 
school32         -0.06264     0.17403   -0.36      0.7189           -0.40375     0.27846 
school33          0.38580     0.14581    2.65    0.008147   **       0.10002     0.67158 
school34         -0.06221     0.20618   -0.30      0.7629           -0.46631     0.34190 
school35          0.39264     0.17994    2.18     0.02911   *        0.03996     0.74532 
school36          0.05948     0.14948    0.40      0.6907           -0.23349     0.35245 
school37         -0.35666     0.21987   -1.62      0.1048           -0.78760     0.07428 
school38          0.02114     0.16086    0.13      0.8954           -0.29413     0.33641 
school39          0.34701     0.16675    2.08     0.03743   *        0.02019     0.67384 
school40          0.04901     0.14892    0.33      0.7421           -0.24286     0.34088 
school41          0.38161     0.15598    2.45     0.01442   *        0.07589     0.68732 
school42          0.33137     0.15751    2.10     0.03539   *        0.02266     0.64008 
school43          0.45628     0.15525    2.94    0.003292   **       0.15200     0.76056 
school44         -0.12504     0.19797   -0.63      0.5276           -0.51305     0.26297 
school45          0.08318     0.16176    0.51      0.6071           -0.23386     0.40022 
school46         -0.14872     0.14310   -1.04      0.2987           -0.42918     0.13175 
school47          0.18643     0.14353    1.30       0.194           -0.09488     0.46773 
school48         -0.10561     0.65384   -0.16      0.8717           -1.38711     1.17590 
school49          0.35558     0.13345    2.66     0.00771   **       0.09402     0.61714 
school50         -0.01309     0.14783   -0.09      0.9294           -0.30284     0.27665 
school51          0.03062     0.15751    0.19      0.8459           -0.27809     0.33933 
school52          0.84205     0.15525    5.42    5.83e-08   ***      0.53777     1.14633 
school53          1.31224     0.14948    8.78   1.652e-18   ***      1.01926     1.60521 
school54         -0.32494     0.33867   -0.96      0.3373           -0.98872     0.33884 
school55          1.02581     0.16366    6.27   3.654e-10   ***      0.70505     1.34657 
school56          0.27441     0.17994    1.52      0.1273           -0.07827     0.62708 
school57          0.30977     0.15384    2.01     0.04406   *        0.00824     0.61129 
school58          0.59057     0.18158    3.25    0.001144   **       0.23468     0.94647 
school59         -0.74040     0.16785   -4.41   1.029e-05   ***     -1.06939    -0.41141 
school60          0.50412     0.14441    3.49   0.0004814   ***      0.22108     0.78715 
school61          0.25635     0.15317    1.67      0.0942   .       -0.04385     0.55656 
school62          0.34668     0.14892    2.33     0.01991   *        0.05481     0.63855 
school63          1.04437     0.19553    5.34   9.234e-08   ***      0.66113     1.42760 
school64          0.65248     0.15673    4.16   3.141e-05   ***      0.34529     0.95967 
schgendboysch     0.00000     0.00000     NaN         NaN   N/A      0.00000     0.00000 
schgendgirlsch    0.00000     0.00000     NaN         NaN   N/A      0.00000     0.00000 
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   0.83416     0.01852 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> 
> 
> # 2.5 Comparing means: Random effects or multilevel model . . .  . . . . .28
> 
> tutorial$school <- as.numeric(levels(tutorial$school))[tutorial$school]
> 
> (mymodel5 <- runMLwiN(normexam ~ 1 + (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

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.05)  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 : 0.05s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -5505.3 
Deviance statistic:  11010.6 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + (1 | school) + (1 | student)
Level 2: school     Level 1: student      
--------------------------------------------------------------------------------------------------- 
The fixed part estimates:  
               Coef.   Std. Err.       z   Pr(>|z|)         [95% Conf.   Interval] 
Intercept   -0.01317     0.05363   -0.25      0.806           -0.11827     0.09194 
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   0.16863     0.03245 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.84776     0.01897 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> (mymodel6 <- runMLwiN(normexam ~ 1 + 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

Convergence achieved
ECHO 0
Execution completed


-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
MLwiN (version: 3.05)  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 : 0.04s 
Number of obs:  4059 (from total 4059)        The model converged after 3 iterations.
Log likelihood:      -5503 
Deviance statistic:  11005.9 
--------------------------------------------------------------------------------------------------- 
The model formula:
normexam ~ 1 + 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        -0.10140     0.07020   -1.44     0.1486           -0.23900     0.03620 
schgendboysch     0.06435     0.14941    0.43     0.6667           -0.22847     0.35718 
schgendgirlsch    0.25760     0.11682    2.21    0.02744   *        0.02865     0.48655 
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   0.15513     0.03005 
--------------------------------------------------------------------------------------------------- 
The random part estimates at the student level: 
                  Coef.   Std. Err. 
var_Intercept   0.84779     0.01897 
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- 
> 
> 
> #     Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . 35
> 
> 
> ############################################################################
> 
> proc.time()
   user  system elapsed 
   3.57    0.92    8.48