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 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. 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 MCMC Manual > # > # 4 Other Features of Variance Components Models . . . . . . . . . . . .45 > # > # Browne, W.J. (2009) MCMC Estimation in MLwiN, v2.13. 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="") > # 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) > > ## save current par settings > mypar <- par(no.readonly = TRUE) > > ## Read tutorial data > data(tutorial, package = "R2MLwiN") > > ## IGLS > (mymodel1 <- runMLwiN(normexam ~ 1 + standlrt + (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 : 0.08s 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 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Gibbs > (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1), data = tutorial)) MLwiN is running, please wait...... /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 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 BURNING IN... Burning in for 50 iterations out of 500 -2 * Loglike = 9206.193266 Burning in for 100 iterations out of 500 -2 * Loglike = 9216.262176 Burning in for 150 iterations out of 500 -2 * Loglike = 9241.057582 Burning in for 200 iterations out of 500 -2 * Loglike = 9214.675885 Burning in for 250 iterations out of 500 -2 * Loglike = 9198.255145 Burning in for 300 iterations out of 500 -2 * Loglike = 9227.186873 Burning in for 350 iterations out of 500 -2 * Loglike = 9222.091977 Burning in for 400 iterations out of 500 -2 * Loglike = 9214.630238 Burning in for 450 iterations out of 500 -2 * Loglike = 9216.522216 Burning in for 500 iterations out of 500 -2 * Loglike = 9201.148603 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9212.190791 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9208.377297 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9207.886882 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9195.385976 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9238.483062 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9215.621742 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9205.716499 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9207.158850 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9210.248427 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9228.495732 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9221.683303 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9202.166694 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9237.981658 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9201.878383 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9198.726654 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9214.104227 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9227.156460 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9197.279082 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9191.816267 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9219.178731 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9214.163387 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9218.308723 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9188.214048 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9188.278770 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9208.819913 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9193.939811 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9193.651680 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9215.606479 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9195.925780 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9218.422125 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9202.244183 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9204.907738 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9194.883902 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9214.140517 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9211.397609 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9207.941176 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9216.158993 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9216.821254 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9209.099646 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9205.356036 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9226.820798 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9215.889068 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9204.485567 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9239.773102 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9204.613020 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9205.832435 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9197.787494 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9202.635017 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9202.243753 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9199.686027 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9213.435702 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9215.862131 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9203.440604 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9197.917390 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9225.824248 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9222.623770 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9226.897380 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9197.383677 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9211.390320 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9207.286579 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9217.534200 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9227.872396 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9198.935844 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9203.578259 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9193.257434 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9204.815469 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9200.291358 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9219.578031 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9214.657834 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9213.144417 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9217.997575 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9225.109666 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9212.063094 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9226.746381 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9214.159422 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9204.966122 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9190.735716 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9206.324394 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9205.512200 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9201.017143 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9211.234780 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9211.765768 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9200.968089 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9229.231239 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9207.636298 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9197.507235 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9208.445006 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9231.667774 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9201.470719 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9208.425209 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9216.996959 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9225.405793 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9201.746288 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9212.656436 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9202.976127 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9218.846042 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9200.637551 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9219.146880 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9215.841845 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9212.109834 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9209.1 S.D. = 11.916 S.E.M. = 0.16852 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: MCMC Elapsed time : 1.43s Number of obs: 4059 (from total 4059) Number of iter.: 5000 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9209.078 9149.069 60.010 9269.088 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept 0.00318 0.04420 0.07 0.9427 -0.08330 0.09189 223 standlrt 0.56322 0.01258 44.77 0 *** 0.53844 0.58780 3821 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09742 0.01988 0.06472 0.14144 3126 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56617 0.01249 0.54212 0.59090 4751 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 4.1 Metropolis Hastings (MH) sampling for the variance components model 46 > > # 4.2 Metropolis-Hastings settings . . . . . . . . . . . . . . . . . . . .47 > > # 4.3 Running the variance components with Metropolis Hastings . . . . . .48 > > ## MH Adaptive with defaults > (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, mcmcMeth = list(fixM = 2, + residM = 2, Lev1VarM = 2)), data = tutorial)) MLwiN is running, please wait...... /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 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 2 2 2 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9216.844644 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9193.344581 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9239.110642 Adapting for 400 iterations (Maximum 5000) -2 * Loglike = 9194.362705 Adapting for 500 iterations (Maximum 5000) -2 * Loglike = 9209.835671 Adapting for 600 iterations (Maximum 5000) -2 * Loglike = 9201.870325 Adapting for 700 iterations (Maximum 5000) -2 * Loglike = 9211.666035 Adapting for 800 iterations (Maximum 5000) -2 * Loglike = 9228.713460 Adapting for 900 iterations (Maximum 5000) -2 * Loglike = 9201.487630 Adapting for 1000 iterations (Maximum 5000) -2 * Loglike = 9214.630149 Adapting finished and took 1100 iterations Adapting took 1100 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9209.666876 Burning in for 100 iterations out of 500 -2 * Loglike = 9206.912558 Burning in for 150 iterations out of 500 -2 * Loglike = 9213.749021 Burning in for 200 iterations out of 500 -2 * Loglike = 9213.324066 Burning in for 250 iterations out of 500 -2 * Loglike = 9203.170194 Burning in for 300 iterations out of 500 -2 * Loglike = 9230.452260 Burning in for 350 iterations out of 500 -2 * Loglike = 9216.213513 Burning in for 400 iterations out of 500 -2 * Loglike = 9201.829237 Burning in for 450 iterations out of 500 -2 * Loglike = 9211.087138 Burning in for 500 iterations out of 500 -2 * Loglike = 9216.124129 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9205.171241 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9222.181500 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9203.968250 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9221.229272 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9214.287113 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9199.220252 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9201.799320 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9215.784324 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9225.801241 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9203.603169 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9206.897351 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9230.695795 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9192.683892 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9212.753972 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9183.656270 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9209.531878 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9197.737628 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9214.084144 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9239.810827 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9221.785312 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9210.388620 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9228.431943 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9220.585103 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9201.348804 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9207.767122 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9203.233941 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9209.980034 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9210.065869 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9215.016175 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9210.590069 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9231.127153 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9198.362646 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9194.500793 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9206.200900 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9210.928375 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9207.926157 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9203.074990 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9196.455484 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9229.428031 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9209.802084 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9221.465246 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9219.779655 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9205.789880 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9213.135966 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9213.734512 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9208.256255 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9198.851182 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9198.211166 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9204.658451 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9204.373674 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9204.887622 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9214.430917 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9215.254256 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9214.810620 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9202.486425 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9226.249798 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9187.310147 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9185.707534 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9206.616737 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9213.142871 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9192.488140 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9219.601270 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9211.289449 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9198.502329 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9207.122808 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9204.487471 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9220.162508 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9207.944320 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9232.116201 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9203.473437 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9203.609752 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9207.835882 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9223.561270 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9217.226026 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9197.942160 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9201.726241 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9219.117464 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9206.283582 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9197.304016 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9206.002146 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9199.436587 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9204.046674 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9193.373709 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9186.480049 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9222.119987 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9198.039653 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9204.564222 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9215.307305 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9188.898150 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9201.413064 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9202.677921 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9214.486208 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9222.441606 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9243.059168 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9221.311090 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9202.431365 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9206.144576 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9235.130212 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9216.824432 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9230.171839 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9209.1 S.D. = 11.534 S.E.M. = 0.16311 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: MCMC Elapsed time : 1.5s Number of obs: 4059 (from total 4059) Number of iter.: 5000 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9209.051 9149.217 59.834 9268.885 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept 0.00057 0.04127 0.01 0.989 -0.07841 0.07812 55 standlrt 0.56334 0.01248 45.14 0 *** 0.53872 0.58814 958 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09695 0.02025 0.06387 0.14442 1935 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56635 0.01269 0.54208 0.59130 4574 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > sixway(mymodel3@chains[, "FP_standlrt", drop = FALSE], "beta_1") > > ## MH Scale Factor = 5.8 > (mymodel4 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, mcmcMeth = list(fixM = 2, + residM = 2, Lev1VarM = 2, adaption = 0)), data = tutorial)) MLwiN is running, please wait...... /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 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 0 5.8 50 10 G30[1] G30[2] 2 2 2 1 1 1 BURNING IN... Burning in for 50 iterations out of 500 -2 * Loglike = 9171.220787 Burning in for 100 iterations out of 500 -2 * Loglike = 9219.355848 Burning in for 150 iterations out of 500 -2 * Loglike = 9194.050475 Burning in for 200 iterations out of 500 -2 * Loglike = 9207.295021 Burning in for 250 iterations out of 500 -2 * Loglike = 9206.250556 Burning in for 300 iterations out of 500 -2 * Loglike = 9203.850907 Burning in for 350 iterations out of 500 -2 * Loglike = 9211.711232 Burning in for 400 iterations out of 500 -2 * Loglike = 9206.743358 Burning in for 450 iterations out of 500 -2 * Loglike = 9179.907652 Burning in for 500 iterations out of 500 -2 * Loglike = 9199.459747 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9208.353075 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9243.794865 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9212.610569 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9214.551254 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9208.896627 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9208.969436 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9203.531102 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9218.277218 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9197.125796 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9207.690768 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9187.296121 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9239.212546 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9218.480930 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9221.498839 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9208.793315 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9210.317744 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9210.793970 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9206.222693 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9229.883357 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9198.911074 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9200.735320 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9214.938217 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9213.526119 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9195.253089 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9213.417205 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9219.643481 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9192.423865 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9231.831345 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9222.083748 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9200.165033 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9212.516585 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9192.610205 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9222.047905 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9217.310765 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9217.683192 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9199.318229 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9204.668658 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9194.445587 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9208.505037 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9210.942651 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9200.816243 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9193.853331 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9206.930750 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9201.434960 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9193.744321 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9202.603645 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9205.232375 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9211.387810 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9224.213815 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9210.423544 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9208.686017 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9203.383342 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9215.573024 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9206.700612 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9202.771284 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9197.962133 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9203.464372 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9195.759459 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9199.886484 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9201.194762 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9197.503318 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9199.027410 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9204.989987 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9200.091843 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9208.458222 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9199.437838 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9186.950279 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9201.671521 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9211.268056 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9204.500114 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9203.497082 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9199.916901 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9191.372612 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9210.796556 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9211.011955 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9210.647308 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9219.869552 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9183.195197 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9196.037683 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9193.855707 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9203.304721 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9230.341889 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9197.360632 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9195.892610 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9218.477416 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9216.109422 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9207.208041 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9212.217772 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9205.367041 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9208.361324 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9198.375577 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9219.935017 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9213.341347 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9203.986620 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9215.347719 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9236.879273 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9220.357881 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9205.917920 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9182.847409 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9179.948428 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9209.1 S.D. = 11.755 S.E.M. = 0.16624 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: MCMC Elapsed time : 1.36s Number of obs: 4059 (from total 4059) Number of iter.: 5000 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9209.072 9149.406 59.666 9268.738 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept -0.00490 0.03726 -0.13 0.8953 -0.07788 0.06390 35 standlrt 0.56326 0.01230 45.78 0 *** 0.53822 0.58709 1041 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09618 0.01958 0.06419 0.13992 2097 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56630 0.01258 0.54206 0.59148 4198 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > if (!require(texreg)) { + warning("texreg package required to use screenreg() function") + } else { + screenreg(list(mymodel1, mymodel2, mymodel4, mymodel3), custom.model.names=c("IGLS", "Gibbs", "MH", "MH Adaptive"), groups = list("Fixed Part" = 1:2, "Level-2" = 3:3, "Level-1" = 4:4), + stars = numeric(0), include.nobs=FALSE, include.loglik=FALSE, include.deviance=FALSE, include.dbar=FALSE, include.dthetabar=FALSE, include.pd=FALSE, include.dic=FALSE) + } Loading required package: texreg Version: 1.39.3 Date: 2023-11-09 Author: Philip Leifeld (University of Essex) Consider submitting praise using the praise or praise_interactive functions. Please cite the JSS article in your publications -- see citation("texreg"). ========================================================================== IGLS Gibbs MH MH Adaptive -------------------------------------------------------------------------- Fixed Part FP_Intercept 0.00 0.00 -0.00 0.00 (0.04) [-0.08; 0.09] [-0.08; 0.06] [-0.08; 0.08] FP_standlrt 0.56 0.56 * 0.56 * 0.56 * (0.01) [ 0.54; 0.59] [ 0.54; 0.59] [ 0.54; 0.59] Level-2 RP2_var_Intercept 0.09 0.10 * 0.10 * 0.10 * (0.02) [ 0.06; 0.14] [ 0.06; 0.14] [ 0.06; 0.14] Level-1 RP1_var_Intercept 0.57 0.57 * 0.57 * 0.57 * (0.01) [ 0.54; 0.59] [ 0.54; 0.59] [ 0.54; 0.59] ========================================================================== * Null hypothesis value outside the confidence interval. > > rm(list = c("mymodel1", "mymodel2", "mymodel3", "mymodel4")) > # 4.4 MH cycles per Gibbs iteration . . . . . . . . . . . . . . . . . . . 49 > > # 4.5 Block updating MH sampling . . . . . . . . . . . . . . . . . . . . .49 > ## MH Adaptive with defaults > (mymodel5 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, mcmcMeth = list(fixM = 3, + residM = 2, Lev1VarM = 2, rate = 40)), data = tutorial)) MLwiN is running, please wait...... /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 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 40 10 G30[1] G30[2] 3 2 2 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9198.961206 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9211.260898 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9197.934205 Adapting for 400 iterations (Maximum 5000) -2 * Loglike = 9224.568968 Adapting for 500 iterations (Maximum 5000) -2 * Loglike = 9219.065991 Adapting for 600 iterations (Maximum 5000) -2 * Loglike = 9225.524935 Adapting for 700 iterations (Maximum 5000) -2 * Loglike = 9211.854417 Adapting for 800 iterations (Maximum 5000) -2 * Loglike = 9197.669421 Adapting for 900 iterations (Maximum 5000) -2 * Loglike = 9187.839441 Adapting finished and took 1000 iterations Adapting took 1000 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9231.985999 Burning in for 100 iterations out of 500 -2 * Loglike = 9189.557102 Burning in for 150 iterations out of 500 -2 * Loglike = 9202.522610 Burning in for 200 iterations out of 500 -2 * Loglike = 9204.067911 Burning in for 250 iterations out of 500 -2 * Loglike = 9199.629954 Burning in for 300 iterations out of 500 -2 * Loglike = 9210.286034 Burning in for 350 iterations out of 500 -2 * Loglike = 9226.510859 Burning in for 400 iterations out of 500 -2 * Loglike = 9215.654132 Burning in for 450 iterations out of 500 -2 * Loglike = 9220.238612 Burning in for 500 iterations out of 500 -2 * Loglike = 9207.944286 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9212.699283 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9227.233102 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9197.934686 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9191.464069 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9199.850038 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9203.130586 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9201.374689 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9221.155461 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9205.536330 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9199.331945 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9216.044493 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9196.403602 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9203.412759 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9225.453247 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9211.571409 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9203.192002 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9193.882992 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9220.468683 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9201.071592 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9199.597539 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9198.222323 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9205.299797 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9216.477610 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9206.680434 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9211.304947 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9208.584083 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9218.785921 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9210.925499 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9224.314673 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9208.506162 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9189.205560 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9229.921344 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9197.319711 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9209.887057 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9223.206953 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9214.126304 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9212.196439 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9208.486856 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9235.640654 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9216.911983 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9212.611939 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9212.690991 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9219.878790 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9221.700930 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9198.536834 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9207.199983 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9198.812871 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9198.285894 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9200.309140 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9208.737298 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9196.973891 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9208.810027 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9204.707518 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9198.883365 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9207.804500 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9208.367194 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9223.542168 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9229.674966 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9185.707945 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9193.426994 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9226.920766 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9216.106236 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9209.478676 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9204.931071 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9202.790601 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9217.531386 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9219.427798 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9212.351879 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9235.785490 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9198.686467 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9212.046825 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9201.474862 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9195.416401 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9196.588357 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9205.424228 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9216.739985 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9215.136709 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9202.803014 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9215.193087 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9189.486004 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9206.235485 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9203.446638 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9212.138871 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9213.709736 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9204.737559 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9210.323641 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9200.978442 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9189.480709 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9192.834023 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9207.254937 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9209.161382 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9214.433427 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9198.369232 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9205.302554 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9220.582815 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9193.388342 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9208.137706 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9207.769254 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9200.171391 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9233.787023 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9209.0 S.D. = 12.155 S.E.M. = 0.17189 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: MCMC Elapsed time : 1.42s Number of obs: 4059 (from total 4059) Number of iter.: 5000 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9208.982 9148.806 60.175 9269.157 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept -0.00035 0.04218 -0.01 0.9934 -0.08298 0.08548 41 standlrt 0.56377 0.01239 45.50 0 *** 0.53867 0.58656 201 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09795 0.02015 0.06523 0.14331 1959 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56585 0.01254 0.54188 0.59072 4663 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > estimates <- mymodel5@chains > par(mfrow = c(3, 2)) > plot(4951:nrow(estimates), estimates[4951:nrow(estimates), "deviance"], xlab = "iteration", ylab = expression(paste("Est. of deviance")), + type = "l") > plot(4951:nrow(estimates), estimates[4951:nrow(estimates), "FP_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + beta[0])), type = "l") > plot(4951:nrow(estimates), estimates[4951:nrow(estimates), "FP_standlrt"], xlab = "iteration", ylab = expression(paste("Est. of ", + beta[1])), type = "l") > plot(4951:nrow(estimates), estimates[4951:nrow(estimates), "RP2_var_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + sigma[u0]^2)), type = "l") > plot(4951:nrow(estimates), estimates[4951:nrow(estimates), "RP1_var_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + sigma[e0]^2)), type = "l") > par(mfrow = c(1, 1)) > rm(mymodel5) > > # 4.6 Residuals in MCMC . . . . . . . . . . . . . . . . . . . . . . . . . 51 > > (mymodel6 <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, resi.store = TRUE, + resi.store.levs = 2, mcmcMeth = list(iterations = 5001)), data = tutorial)) MLwiN is running, please wait...... /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 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 BURNING IN... Burning in for 50 iterations out of 500 -2 * Loglike = 9206.193266 Burning in for 100 iterations out of 500 -2 * Loglike = 9216.262176 Burning in for 150 iterations out of 500 -2 * Loglike = 9241.057582 Burning in for 200 iterations out of 500 -2 * Loglike = 9214.675885 Burning in for 250 iterations out of 500 -2 * Loglike = 9198.255145 Burning in for 300 iterations out of 500 -2 * Loglike = 9227.186873 Burning in for 350 iterations out of 500 -2 * Loglike = 9222.091977 Burning in for 400 iterations out of 500 -2 * Loglike = 9214.630238 Burning in for 450 iterations out of 500 -2 * Loglike = 9216.522216 Burning in for 500 iterations out of 500 -2 * Loglike = 9201.148603 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5001 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5001, Stored update 50 of 5001 -2 * Loglike = 9212.190791 Actual update 100 of 5001, Stored update 100 of 5001 -2 * Loglike = 9208.377297 Actual update 150 of 5001, Stored update 150 of 5001 -2 * Loglike = 9207.886882 Actual update 200 of 5001, Stored update 200 of 5001 -2 * Loglike = 9195.385976 Actual update 250 of 5001, Stored update 250 of 5001 -2 * Loglike = 9238.483062 Actual update 300 of 5001, Stored update 300 of 5001 -2 * Loglike = 9215.621742 Actual update 350 of 5001, Stored update 350 of 5001 -2 * Loglike = 9205.716499 Actual update 400 of 5001, Stored update 400 of 5001 -2 * Loglike = 9207.158850 Actual update 450 of 5001, Stored update 450 of 5001 -2 * Loglike = 9210.248427 Actual update 500 of 5001, Stored update 500 of 5001 -2 * Loglike = 9228.495732 Actual update 550 of 5001, Stored update 550 of 5001 -2 * Loglike = 9221.683303 Actual update 600 of 5001, Stored update 600 of 5001 -2 * Loglike = 9202.166694 Actual update 650 of 5001, Stored update 650 of 5001 -2 * Loglike = 9237.981658 Actual update 700 of 5001, Stored update 700 of 5001 -2 * Loglike = 9201.878383 Actual update 750 of 5001, Stored update 750 of 5001 -2 * Loglike = 9198.726654 Actual update 800 of 5001, Stored update 800 of 5001 -2 * Loglike = 9214.104227 Actual update 850 of 5001, Stored update 850 of 5001 -2 * Loglike = 9227.156460 Actual update 900 of 5001, Stored update 900 of 5001 -2 * Loglike = 9197.279082 Actual update 950 of 5001, Stored update 950 of 5001 -2 * Loglike = 9191.816267 Actual update 1000 of 5001, Stored update 1000 of 5001 -2 * Loglike = 9219.178731 Actual update 1050 of 5001, Stored update 1050 of 5001 -2 * Loglike = 9214.163387 Actual update 1100 of 5001, Stored update 1100 of 5001 -2 * Loglike = 9218.308723 Actual update 1150 of 5001, Stored update 1150 of 5001 -2 * Loglike = 9188.214048 Actual update 1200 of 5001, Stored update 1200 of 5001 -2 * Loglike = 9188.278770 Actual update 1250 of 5001, Stored update 1250 of 5001 -2 * Loglike = 9208.819913 Actual update 1300 of 5001, Stored update 1300 of 5001 -2 * Loglike = 9193.939811 Actual update 1350 of 5001, Stored update 1350 of 5001 -2 * Loglike = 9193.651680 Actual update 1400 of 5001, Stored update 1400 of 5001 -2 * Loglike = 9215.606479 Actual update 1450 of 5001, Stored update 1450 of 5001 -2 * Loglike = 9195.925780 Actual update 1500 of 5001, Stored update 1500 of 5001 -2 * Loglike = 9218.422125 Actual update 1550 of 5001, Stored update 1550 of 5001 -2 * Loglike = 9202.244183 Actual update 1600 of 5001, Stored update 1600 of 5001 -2 * Loglike = 9204.907738 Actual update 1650 of 5001, Stored update 1650 of 5001 -2 * Loglike = 9194.883902 Actual update 1700 of 5001, Stored update 1700 of 5001 -2 * Loglike = 9214.140517 Actual update 1750 of 5001, Stored update 1750 of 5001 -2 * Loglike = 9211.397609 Actual update 1800 of 5001, Stored update 1800 of 5001 -2 * Loglike = 9207.941176 Actual update 1850 of 5001, Stored update 1850 of 5001 -2 * Loglike = 9216.158993 Actual update 1900 of 5001, Stored update 1900 of 5001 -2 * Loglike = 9216.821254 Actual update 1950 of 5001, Stored update 1950 of 5001 -2 * Loglike = 9209.099646 Actual update 2000 of 5001, Stored update 2000 of 5001 -2 * Loglike = 9205.356036 Actual update 2050 of 5001, Stored update 2050 of 5001 -2 * Loglike = 9226.820798 Actual update 2100 of 5001, Stored update 2100 of 5001 -2 * Loglike = 9215.889068 Actual update 2150 of 5001, Stored update 2150 of 5001 -2 * Loglike = 9204.485567 Actual update 2200 of 5001, Stored update 2200 of 5001 -2 * Loglike = 9239.773102 Actual update 2250 of 5001, Stored update 2250 of 5001 -2 * Loglike = 9204.613020 Actual update 2300 of 5001, Stored update 2300 of 5001 -2 * Loglike = 9205.832435 Actual update 2350 of 5001, Stored update 2350 of 5001 -2 * Loglike = 9197.787494 Actual update 2400 of 5001, Stored update 2400 of 5001 -2 * Loglike = 9202.635017 Actual update 2450 of 5001, Stored update 2450 of 5001 -2 * Loglike = 9202.243753 Actual update 2500 of 5001, Stored update 2500 of 5001 -2 * Loglike = 9199.686027 Actual update 2550 of 5001, Stored update 2550 of 5001 -2 * Loglike = 9213.435702 Actual update 2600 of 5001, Stored update 2600 of 5001 -2 * Loglike = 9215.862131 Actual update 2650 of 5001, Stored update 2650 of 5001 -2 * Loglike = 9203.440604 Actual update 2700 of 5001, Stored update 2700 of 5001 -2 * Loglike = 9197.917390 Actual update 2750 of 5001, Stored update 2750 of 5001 -2 * Loglike = 9225.824248 Actual update 2800 of 5001, Stored update 2800 of 5001 -2 * Loglike = 9222.623770 Actual update 2850 of 5001, Stored update 2850 of 5001 -2 * Loglike = 9226.897380 Actual update 2900 of 5001, Stored update 2900 of 5001 -2 * Loglike = 9197.383677 Actual update 2950 of 5001, Stored update 2950 of 5001 -2 * Loglike = 9211.390320 Actual update 3000 of 5001, Stored update 3000 of 5001 -2 * Loglike = 9207.286579 Actual update 3050 of 5001, Stored update 3050 of 5001 -2 * Loglike = 9217.534200 Actual update 3100 of 5001, Stored update 3100 of 5001 -2 * Loglike = 9227.872396 Actual update 3150 of 5001, Stored update 3150 of 5001 -2 * Loglike = 9198.935844 Actual update 3200 of 5001, Stored update 3200 of 5001 -2 * Loglike = 9203.578259 Actual update 3250 of 5001, Stored update 3250 of 5001 -2 * Loglike = 9193.257434 Actual update 3300 of 5001, Stored update 3300 of 5001 -2 * Loglike = 9204.815469 Actual update 3350 of 5001, Stored update 3350 of 5001 -2 * Loglike = 9200.291358 Actual update 3400 of 5001, Stored update 3400 of 5001 -2 * Loglike = 9219.578031 Actual update 3450 of 5001, Stored update 3450 of 5001 -2 * Loglike = 9214.657834 Actual update 3500 of 5001, Stored update 3500 of 5001 -2 * Loglike = 9213.144417 Actual update 3550 of 5001, Stored update 3550 of 5001 -2 * Loglike = 9217.997575 Actual update 3600 of 5001, Stored update 3600 of 5001 -2 * Loglike = 9225.109666 Actual update 3650 of 5001, Stored update 3650 of 5001 -2 * Loglike = 9212.063094 Actual update 3700 of 5001, Stored update 3700 of 5001 -2 * Loglike = 9226.746381 Actual update 3750 of 5001, Stored update 3750 of 5001 -2 * Loglike = 9214.159422 Actual update 3800 of 5001, Stored update 3800 of 5001 -2 * Loglike = 9204.966122 Actual update 3850 of 5001, Stored update 3850 of 5001 -2 * Loglike = 9190.735716 Actual update 3900 of 5001, Stored update 3900 of 5001 -2 * Loglike = 9206.324394 Actual update 3950 of 5001, Stored update 3950 of 5001 -2 * Loglike = 9205.512200 Actual update 4000 of 5001, Stored update 4000 of 5001 -2 * Loglike = 9201.017143 Actual update 4050 of 5001, Stored update 4050 of 5001 -2 * Loglike = 9211.234780 Actual update 4100 of 5001, Stored update 4100 of 5001 -2 * Loglike = 9211.765768 Actual update 4150 of 5001, Stored update 4150 of 5001 -2 * Loglike = 9200.968089 Actual update 4200 of 5001, Stored update 4200 of 5001 -2 * Loglike = 9229.231239 Actual update 4250 of 5001, Stored update 4250 of 5001 -2 * Loglike = 9207.636298 Actual update 4300 of 5001, Stored update 4300 of 5001 -2 * Loglike = 9197.507235 Actual update 4350 of 5001, Stored update 4350 of 5001 -2 * Loglike = 9208.445006 Actual update 4400 of 5001, Stored update 4400 of 5001 -2 * Loglike = 9231.667774 Actual update 4450 of 5001, Stored update 4450 of 5001 -2 * Loglike = 9201.470719 Actual update 4500 of 5001, Stored update 4500 of 5001 -2 * Loglike = 9208.425209 Actual update 4550 of 5001, Stored update 4550 of 5001 -2 * Loglike = 9216.996959 Actual update 4600 of 5001, Stored update 4600 of 5001 -2 * Loglike = 9225.405793 Actual update 4650 of 5001, Stored update 4650 of 5001 -2 * Loglike = 9201.746288 Actual update 4700 of 5001, Stored update 4700 of 5001 -2 * Loglike = 9212.656436 Actual update 4750 of 5001, Stored update 4750 of 5001 -2 * Loglike = 9202.976127 Actual update 4800 of 5001, Stored update 4800 of 5001 -2 * Loglike = 9218.846042 Actual update 4850 of 5001, Stored update 4850 of 5001 -2 * Loglike = 9200.637551 Actual update 4900 of 5001, Stored update 4900 of 5001 -2 * Loglike = 9219.146880 Actual update 4950 of 5001, Stored update 4950 of 5001 -2 * Loglike = 9215.841845 Actual update 5000 of 5001, Stored update 5000 of 5001 -2 * Loglike = 9212.109834 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5001 Average = 9209.1 S.D. = 11.915 S.E.M. = 0.16849 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: MCMC Elapsed time : 1.64s Number of obs: 4059 (from total 4059) Number of iter.: 5001 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9209.079 9149.068 60.011 9269.090 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept 0.00316 0.04422 0.07 0.9431 -0.08335 0.09189 223 standlrt 0.56322 0.01258 44.77 0 *** 0.53844 0.58780 3822 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09742 0.01988 0.06472 0.14144 3127 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56618 0.01249 0.54212 0.59090 4753 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > resi.chain2 <- mymodel6@resi.chains$resi_lev2 > sixway(resi.chain2[, 1, drop = FALSE], name = "u0_1") > > # 4.7 Comparing two schools . . . . . . . . . . . . . . . . . . . . . . . 54 > > dif <- resi.chain2[, 1] - resi.chain2[, 2] > sixway(dif, name = "dif") > prop <- (dif > 0) > mean(prop) [1] 0.1587682 > > # 4.8 Calculating ranks of schools . . . . . . . . . . . . . . . . . . . .55 > > u0rank <- apply(resi.chain2, 1, rank) > u0rankmn <- apply(u0rank, 1, mean) > u0ranklo <- apply(u0rank, 1, function(x) quantile(x, 0.025)) > u0rankmd <- apply(u0rank, 1, median) > u0rankhi <- apply(u0rank, 1, function(x) quantile(x, 0.975)) > > plot(1:65, u0rankmd, ylim = c(0.5, 65.5), pch = 15, xlab = "School", ylab = "Rank") > points(1:65, u0ranklo, pch = 24, bg = "grey") > points(1:65, u0rankhi, pch = 25, bg = "grey") > for (i in 1:65) lines(rep(i, 2), c(u0ranklo[i], u0rankhi[i])) > > ## common caterpillar plot > > rankno <- order(u0rankmn) > plot(1:65, u0rankmn[rankno], ylim = c(0.5, 65.5), pch = 15, xlab = "School", ylab = "Rank") > points(1:65, u0ranklo[rankno], pch = 24, bg = "grey") > points(1:65, u0rankhi[rankno], pch = 25, bg = "grey") > for (i in 1:65) lines(rep(i, 2), c(u0ranklo[rankno[i]], u0rankhi[rankno[i]])) > > # 4.9 Estimating a function of parameters . . . . . . . . . . . . . . . . 58 > estimates <- mymodel6@chains > isc <- estimates[, "RP2_var_Intercept"]/(estimates[, "RP2_var_Intercept"] + estimates[, "RP1_var_Intercept"]) > summary(isc) Iterations = 1:5001 Thinning interval = 1 Number of chains = 1 Sample size per chain = 5001 1. Empirical mean and standard deviation for each variable, plus standard error of the mean: Mean SD Naive SE Time-series SE 0.1461230 0.0253555 0.0003585 0.0004551 2. Quantiles for each variable: 2.5% 25% 50% 75% 97.5% 0.1024 0.1285 0.1443 0.1615 0.2002 > sixway(isc, "isc") > rm(mymodel6) > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 60 > > ## reinstate par settings > par(mypar) > > > ############################################################################ > > proc.time() user system elapsed 6.18 0.92 15.40