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 > # > # 21 Using Structured MCMC . . . . . . . . . . . . . . . . . . . . . . .327 > # > # 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/ > ############################################################################ > > # 21.1 SMCMC Theory . . . . . . . . . . . . . . . . . . . . . . . . . . .327 > > # 21.2 Fitting the model using MLwiN . . . . . . . . . . . . . . . . . . 330 > > 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) > > # User's input if necessary > > ## Read tutorial data > data(tutorial, package = "R2MLwiN") > > ## Define the model > > (mymodel <- runMLwiN(normexam ~ 1 + (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 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 = 10847.820210 Burning in for 100 iterations out of 500 -2 * Loglike = 10860.697492 Burning in for 150 iterations out of 500 -2 * Loglike = 10849.534312 Burning in for 200 iterations out of 500 -2 * Loglike = 10850.669980 Burning in for 250 iterations out of 500 -2 * Loglike = 10830.922783 Burning in for 300 iterations out of 500 -2 * Loglike = 10851.202075 Burning in for 350 iterations out of 500 -2 * Loglike = 10831.185996 Burning in for 400 iterations out of 500 -2 * Loglike = 10838.507253 Burning in for 450 iterations out of 500 -2 * Loglike = 10841.701141 Burning in for 500 iterations out of 500 -2 * Loglike = 10848.918036 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 = 10822.788554 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 10865.181453 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 10837.691010 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 10880.285801 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 10833.110370 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 10844.265285 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 10858.607291 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 10831.891735 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 10856.861189 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 10824.758702 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 10845.858482 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 10844.826770 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 10862.143583 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 10842.581776 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 10834.259783 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 10851.536606 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 10852.274846 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 10859.691303 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 10833.246510 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 10833.952872 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 10857.442801 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 10860.614963 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 10852.796622 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 10867.313931 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 10846.393808 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 10863.772380 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 10851.851077 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 10849.505973 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 10865.054208 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 10841.492988 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 10837.389713 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 10842.953827 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 10844.488117 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 10844.711929 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 10844.804653 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 10839.594052 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 10849.154512 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 10860.437188 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 10868.448153 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 10835.531519 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 10854.971210 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 10864.444840 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 10850.386020 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 10837.019413 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 10838.210205 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 10890.708596 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 10835.721417 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 10860.325900 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 10882.421282 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 10873.131139 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 10832.176646 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 10858.781415 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 10842.603391 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 10845.443157 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 10846.696377 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 10852.980508 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 10870.685540 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 10865.558879 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 10839.289690 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 10856.742990 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 10846.803219 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 10845.939902 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 10859.518226 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 10844.083604 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 10853.951361 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 10827.939196 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 10855.188273 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 10848.802236 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 10857.682890 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 10847.743677 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 10854.692582 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 10845.608539 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 10853.097860 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 10846.784628 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 10847.376418 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 10851.908252 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 10841.962581 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 10844.943972 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 10866.722763 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 10838.317917 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 10826.617020 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 10844.415677 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 10846.888096 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 10859.615746 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 10834.763005 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 10852.353221 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 10856.812452 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 10852.181902 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 10848.798516 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 10864.858675 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 10844.724326 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 10840.243563 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 10834.740637 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 10848.424193 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 10854.432445 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 10829.687675 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 10840.477735 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 10873.693461 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 10849.245510 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 10856.432831 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 10850. S.D. = 11.751 S.E.M. = 0.16618 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 : 1.44s 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 10849.609 10789.729 59.879 10909.488 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept -0.01474 0.05650 -0.26 0.7942 -0.12039 0.09603 172 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 0.17775 0.03642 0.11920 0.26236 3278 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.84847 0.01900 0.81147 0.88711 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > summary(mymodel@chains[, "FP_Intercept"]) Iterations = 1:5000 Thinning interval = 1 Number of chains = 1 Sample size per chain = 5000 1. Empirical mean and standard deviation for each variable, plus standard error of the mean: Mean SD Naive SE Time-series SE -0.0147387 0.0565029 0.0007991 0.0043069 2. Quantiles for each variable: 2.5% 25% 50% 75% 97.5% -0.12039 -0.05365 -0.01626 0.02304 0.09603 > sixway(mymodel@chains[, "FP_Intercept", drop = FALSE], "beta_0") > > ## Structured MCMC > > (mymodel <- runMLwiN(normexam ~ 1 + (1 | school) + (1 | student), estoptions = list(EstM = 1, mcmcOptions = list(smcm = 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 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 = 10846.295321 Burning in for 100 iterations out of 500 -2 * Loglike = 10860.379221 Burning in for 150 iterations out of 500 -2 * Loglike = 10849.588642 Burning in for 200 iterations out of 500 -2 * Loglike = 10850.464133 Burning in for 250 iterations out of 500 -2 * Loglike = 10830.858040 Burning in for 300 iterations out of 500 -2 * Loglike = 10852.885629 Burning in for 350 iterations out of 500 -2 * Loglike = 10834.859913 Burning in for 400 iterations out of 500 -2 * Loglike = 10838.352594 Burning in for 450 iterations out of 500 -2 * Loglike = 10839.875588 Burning in for 500 iterations out of 500 -2 * Loglike = 10854.191754 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 = 10822.572693 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 10865.497519 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 10838.306110 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 10883.795012 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 10833.261755 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 10843.668564 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 10855.624497 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 10831.155915 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 10854.407844 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 10825.789319 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 10844.874034 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 10844.561099 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 10860.527696 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 10842.367445 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 10833.371851 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 10851.027208 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 10851.963438 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 10862.670772 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 10830.413146 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 10834.431100 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 10857.782589 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 10861.355664 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 10857.388683 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 10866.606557 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 10846.323795 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 10863.265527 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 10850.346927 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 10847.032594 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 10865.748127 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 10841.573071 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 10836.705449 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 10844.029745 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 10844.669835 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 10843.617847 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 10844.604218 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 10839.878437 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 10849.401716 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 10858.696833 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 10860.452052 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 10836.608173 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 10856.052439 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 10861.403598 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 10850.120764 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 10837.219749 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 10839.251498 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 10891.662616 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 10838.551339 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 10855.290253 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 10881.943962 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 10874.286981 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 10832.260682 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 10856.219130 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 10842.149778 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 10845.720817 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 10845.539342 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 10852.966204 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 10866.425504 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 10866.899000 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 10837.449136 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 10855.378566 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 10846.571765 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 10847.298293 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 10859.741882 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 10843.632220 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 10853.809195 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 10826.622663 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 10856.034477 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 10847.483796 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 10857.910324 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 10846.251613 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 10853.350314 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 10844.732607 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 10852.691975 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 10846.689988 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 10847.806553 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 10852.167452 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 10847.223032 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 10846.164487 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 10866.779677 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 10838.259173 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 10826.983427 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 10845.639654 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 10847.402900 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 10859.970568 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 10834.765693 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 10852.678796 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 10853.283954 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 10853.292283 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 10848.998606 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 10863.897382 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 10842.826785 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 10843.171736 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 10834.370032 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 10848.742877 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 10854.111023 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 10831.637137 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 10843.526473 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 10871.263474 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 10849.493845 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 10857.388428 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 10850. S.D. = 11.786 S.E.M. = 0.16668 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 : 1.37s 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 10849.595 10789.744 59.852 10909.447 --------------------------------------------------------------------------------------------------- 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% Cred. Interval] ESS Intercept -0.01358 0.05524 -0.25 0.8057 -0.12344 0.09240 5000 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 0.17760 0.03647 0.11872 0.26161 3230 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.84847 0.01900 0.81140 0.88702 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > summary(mymodel@chains[, "FP_Intercept"]) Iterations = 1:5000 Thinning interval = 1 Number of chains = 1 Sample size per chain = 5000 1. Empirical mean and standard deviation for each variable, plus standard error of the mean: Mean SD Naive SE Time-series SE -0.0135842 0.0552376 0.0007812 0.0007812 2. Quantiles for each variable: 2.5% 25% 50% 75% 97.5% -0.12344 -0.05053 -0.01334 0.02357 0.09240 > sixway(mymodel@chains[, "FP_Intercept", drop = FALSE], "beta_0") > > # 21.3 A random intercepts model . . . . . . . . . . . . . . . . . . . . 334 > > (mymodel <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, mcmcOptions = list(smcm = 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 = 9204.819343 Burning in for 100 iterations out of 500 -2 * Loglike = 9215.929214 Burning in for 150 iterations out of 500 -2 * Loglike = 9240.880687 Burning in for 200 iterations out of 500 -2 * Loglike = 9215.087010 Burning in for 250 iterations out of 500 -2 * Loglike = 9200.144970 Burning in for 300 iterations out of 500 -2 * Loglike = 9229.011288 Burning in for 350 iterations out of 500 -2 * Loglike = 9221.762675 Burning in for 400 iterations out of 500 -2 * Loglike = 9214.135739 Burning in for 450 iterations out of 500 -2 * Loglike = 9219.335854 Burning in for 500 iterations out of 500 -2 * Loglike = 9199.853827 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 = 9215.053001 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9207.418846 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9207.892983 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9195.344750 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9237.241877 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9212.959420 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9206.768823 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9208.305697 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9210.226717 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9227.563551 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9221.677434 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9201.554490 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9240.698558 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9201.888360 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9205.299616 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9213.540135 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9226.162043 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9197.191623 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9188.967136 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9221.158009 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9215.374325 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9212.308688 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9188.095863 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9187.357905 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9205.502792 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9194.510537 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9191.230641 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9214.792811 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9193.897434 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9215.890352 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9203.979844 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9206.107714 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9194.561955 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9218.290864 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9212.337310 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9207.822603 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9214.504311 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9219.289206 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9208.169647 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9206.581718 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9229.293564 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9216.656842 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9206.921298 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9239.847062 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9202.931462 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9206.190786 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9200.412806 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9204.521730 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9205.833107 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9200.467965 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9212.759563 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9213.235164 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9201.261485 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9197.980073 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9224.924066 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9221.766988 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9228.977500 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9198.894289 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9212.170523 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9205.314507 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9219.004588 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9227.886567 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9198.939036 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9205.154008 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9191.719281 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9203.249538 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9206.230987 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9219.216064 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9214.342006 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9213.938460 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9217.957717 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9224.831542 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9211.965247 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9228.784992 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9215.152268 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9204.731936 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9191.901860 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9204.385270 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9205.165691 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9195.282462 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9210.926728 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9212.213805 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9200.747242 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9223.742589 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9207.001007 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9197.283292 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9207.752775 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9233.339087 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9203.351501 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9212.950072 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9217.619530 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9224.858375 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9201.336371 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9210.620397 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9203.418573 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9218.744669 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9197.902249 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9219.156737 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9215.985241 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9218.578744 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9209.1 S.D. = 11.911 S.E.M. = 0.16844 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 : 1.65s 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 9209.124 9149.119 60.005 9269.129 --------------------------------------------------------------------------------------------------- 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 0.00232 0.04035 0.06 0.9541 -0.07769 0.08336 5000 standlrt 0.56324 0.01258 44.79 0 *** 0.53857 0.58783 5000 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 0.09707 0.01982 0.06484 0.14169 3140 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56618 0.01248 0.54208 0.59093 4748 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > trajectories(mymodel, Range = c(1, 500)) > > # 21.4 Examining the residual chains . . . . . . . . . . . . . . . . . . 335 > > (mymodel <- runMLwiN(normexam ~ 1 + standlrt + (1 | school) + (1 | student), estoptions = list(EstM = 1, resi.store = TRUE, + resi.store.levs = 2, mcmcMeth = list(iterations = 5001), mcmcOptions = list(smcm = 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 = 9204.819343 Burning in for 100 iterations out of 500 -2 * Loglike = 9215.929214 Burning in for 150 iterations out of 500 -2 * Loglike = 9240.880687 Burning in for 200 iterations out of 500 -2 * Loglike = 9215.087010 Burning in for 250 iterations out of 500 -2 * Loglike = 9200.144970 Burning in for 300 iterations out of 500 -2 * Loglike = 9229.011288 Burning in for 350 iterations out of 500 -2 * Loglike = 9221.762675 Burning in for 400 iterations out of 500 -2 * Loglike = 9214.135739 Burning in for 450 iterations out of 500 -2 * Loglike = 9219.335854 Burning in for 500 iterations out of 500 -2 * Loglike = 9199.853827 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 = 9215.053001 Actual update 100 of 5001, Stored update 100 of 5001 -2 * Loglike = 9207.418846 Actual update 150 of 5001, Stored update 150 of 5001 -2 * Loglike = 9207.892983 Actual update 200 of 5001, Stored update 200 of 5001 -2 * Loglike = 9195.344750 Actual update 250 of 5001, Stored update 250 of 5001 -2 * Loglike = 9237.241877 Actual update 300 of 5001, Stored update 300 of 5001 -2 * Loglike = 9212.959420 Actual update 350 of 5001, Stored update 350 of 5001 -2 * Loglike = 9206.768823 Actual update 400 of 5001, Stored update 400 of 5001 -2 * Loglike = 9208.305697 Actual update 450 of 5001, Stored update 450 of 5001 -2 * Loglike = 9210.226717 Actual update 500 of 5001, Stored update 500 of 5001 -2 * Loglike = 9227.563551 Actual update 550 of 5001, Stored update 550 of 5001 -2 * Loglike = 9221.677434 Actual update 600 of 5001, Stored update 600 of 5001 -2 * Loglike = 9201.554490 Actual update 650 of 5001, Stored update 650 of 5001 -2 * Loglike = 9240.698558 Actual update 700 of 5001, Stored update 700 of 5001 -2 * Loglike = 9201.888360 Actual update 750 of 5001, Stored update 750 of 5001 -2 * Loglike = 9205.299616 Actual update 800 of 5001, Stored update 800 of 5001 -2 * Loglike = 9213.540135 Actual update 850 of 5001, Stored update 850 of 5001 -2 * Loglike = 9226.162043 Actual update 900 of 5001, Stored update 900 of 5001 -2 * Loglike = 9197.191623 Actual update 950 of 5001, Stored update 950 of 5001 -2 * Loglike = 9188.967136 Actual update 1000 of 5001, Stored update 1000 of 5001 -2 * Loglike = 9221.158009 Actual update 1050 of 5001, Stored update 1050 of 5001 -2 * Loglike = 9215.374325 Actual update 1100 of 5001, Stored update 1100 of 5001 -2 * Loglike = 9212.308688 Actual update 1150 of 5001, Stored update 1150 of 5001 -2 * Loglike = 9188.095863 Actual update 1200 of 5001, Stored update 1200 of 5001 -2 * Loglike = 9187.357905 Actual update 1250 of 5001, Stored update 1250 of 5001 -2 * Loglike = 9205.502792 Actual update 1300 of 5001, Stored update 1300 of 5001 -2 * Loglike = 9194.510537 Actual update 1350 of 5001, Stored update 1350 of 5001 -2 * Loglike = 9191.230641 Actual update 1400 of 5001, Stored update 1400 of 5001 -2 * Loglike = 9214.792811 Actual update 1450 of 5001, Stored update 1450 of 5001 -2 * Loglike = 9193.897434 Actual update 1500 of 5001, Stored update 1500 of 5001 -2 * Loglike = 9215.890352 Actual update 1550 of 5001, Stored update 1550 of 5001 -2 * Loglike = 9203.979844 Actual update 1600 of 5001, Stored update 1600 of 5001 -2 * Loglike = 9206.107714 Actual update 1650 of 5001, Stored update 1650 of 5001 -2 * Loglike = 9194.561955 Actual update 1700 of 5001, Stored update 1700 of 5001 -2 * Loglike = 9218.290864 Actual update 1750 of 5001, Stored update 1750 of 5001 -2 * Loglike = 9212.337310 Actual update 1800 of 5001, Stored update 1800 of 5001 -2 * Loglike = 9207.822603 Actual update 1850 of 5001, Stored update 1850 of 5001 -2 * Loglike = 9214.504311 Actual update 1900 of 5001, Stored update 1900 of 5001 -2 * Loglike = 9219.289206 Actual update 1950 of 5001, Stored update 1950 of 5001 -2 * Loglike = 9208.169647 Actual update 2000 of 5001, Stored update 2000 of 5001 -2 * Loglike = 9206.581718 Actual update 2050 of 5001, Stored update 2050 of 5001 -2 * Loglike = 9229.293564 Actual update 2100 of 5001, Stored update 2100 of 5001 -2 * Loglike = 9216.656842 Actual update 2150 of 5001, Stored update 2150 of 5001 -2 * Loglike = 9206.921298 Actual update 2200 of 5001, Stored update 2200 of 5001 -2 * Loglike = 9239.847062 Actual update 2250 of 5001, Stored update 2250 of 5001 -2 * Loglike = 9202.931462 Actual update 2300 of 5001, Stored update 2300 of 5001 -2 * Loglike = 9206.190786 Actual update 2350 of 5001, Stored update 2350 of 5001 -2 * Loglike = 9200.412806 Actual update 2400 of 5001, Stored update 2400 of 5001 -2 * Loglike = 9204.521730 Actual update 2450 of 5001, Stored update 2450 of 5001 -2 * Loglike = 9205.833107 Actual update 2500 of 5001, Stored update 2500 of 5001 -2 * Loglike = 9200.467965 Actual update 2550 of 5001, Stored update 2550 of 5001 -2 * Loglike = 9212.759563 Actual update 2600 of 5001, Stored update 2600 of 5001 -2 * Loglike = 9213.235164 Actual update 2650 of 5001, Stored update 2650 of 5001 -2 * Loglike = 9201.261485 Actual update 2700 of 5001, Stored update 2700 of 5001 -2 * Loglike = 9197.980073 Actual update 2750 of 5001, Stored update 2750 of 5001 -2 * Loglike = 9224.924066 Actual update 2800 of 5001, Stored update 2800 of 5001 -2 * Loglike = 9221.766988 Actual update 2850 of 5001, Stored update 2850 of 5001 -2 * Loglike = 9228.977500 Actual update 2900 of 5001, Stored update 2900 of 5001 -2 * Loglike = 9198.894289 Actual update 2950 of 5001, Stored update 2950 of 5001 -2 * Loglike = 9212.170523 Actual update 3000 of 5001, Stored update 3000 of 5001 -2 * Loglike = 9205.314507 Actual update 3050 of 5001, Stored update 3050 of 5001 -2 * Loglike = 9219.004588 Actual update 3100 of 5001, Stored update 3100 of 5001 -2 * Loglike = 9227.886567 Actual update 3150 of 5001, Stored update 3150 of 5001 -2 * Loglike = 9198.939036 Actual update 3200 of 5001, Stored update 3200 of 5001 -2 * Loglike = 9205.154008 Actual update 3250 of 5001, Stored update 3250 of 5001 -2 * Loglike = 9191.719281 Actual update 3300 of 5001, Stored update 3300 of 5001 -2 * Loglike = 9203.249538 Actual update 3350 of 5001, Stored update 3350 of 5001 -2 * Loglike = 9206.230987 Actual update 3400 of 5001, Stored update 3400 of 5001 -2 * Loglike = 9219.216064 Actual update 3450 of 5001, Stored update 3450 of 5001 -2 * Loglike = 9214.342006 Actual update 3500 of 5001, Stored update 3500 of 5001 -2 * Loglike = 9213.938460 Actual update 3550 of 5001, Stored update 3550 of 5001 -2 * Loglike = 9217.957717 Actual update 3600 of 5001, Stored update 3600 of 5001 -2 * Loglike = 9224.831542 Actual update 3650 of 5001, Stored update 3650 of 5001 -2 * Loglike = 9211.965247 Actual update 3700 of 5001, Stored update 3700 of 5001 -2 * Loglike = 9228.784992 Actual update 3750 of 5001, Stored update 3750 of 5001 -2 * Loglike = 9215.152268 Actual update 3800 of 5001, Stored update 3800 of 5001 -2 * Loglike = 9204.731936 Actual update 3850 of 5001, Stored update 3850 of 5001 -2 * Loglike = 9191.901860 Actual update 3900 of 5001, Stored update 3900 of 5001 -2 * Loglike = 9204.385270 Actual update 3950 of 5001, Stored update 3950 of 5001 -2 * Loglike = 9205.165691 Actual update 4000 of 5001, Stored update 4000 of 5001 -2 * Loglike = 9195.282462 Actual update 4050 of 5001, Stored update 4050 of 5001 -2 * Loglike = 9210.926728 Actual update 4100 of 5001, Stored update 4100 of 5001 -2 * Loglike = 9212.213805 Actual update 4150 of 5001, Stored update 4150 of 5001 -2 * Loglike = 9200.747242 Actual update 4200 of 5001, Stored update 4200 of 5001 -2 * Loglike = 9223.742589 Actual update 4250 of 5001, Stored update 4250 of 5001 -2 * Loglike = 9207.001007 Actual update 4300 of 5001, Stored update 4300 of 5001 -2 * Loglike = 9197.283292 Actual update 4350 of 5001, Stored update 4350 of 5001 -2 * Loglike = 9207.752775 Actual update 4400 of 5001, Stored update 4400 of 5001 -2 * Loglike = 9233.339087 Actual update 4450 of 5001, Stored update 4450 of 5001 -2 * Loglike = 9203.351501 Actual update 4500 of 5001, Stored update 4500 of 5001 -2 * Loglike = 9212.950072 Actual update 4550 of 5001, Stored update 4550 of 5001 -2 * Loglike = 9217.619530 Actual update 4600 of 5001, Stored update 4600 of 5001 -2 * Loglike = 9224.858375 Actual update 4650 of 5001, Stored update 4650 of 5001 -2 * Loglike = 9201.336371 Actual update 4700 of 5001, Stored update 4700 of 5001 -2 * Loglike = 9210.620397 Actual update 4750 of 5001, Stored update 4750 of 5001 -2 * Loglike = 9203.418573 Actual update 4800 of 5001, Stored update 4800 of 5001 -2 * Loglike = 9218.744669 Actual update 4850 of 5001, Stored update 4850 of 5001 -2 * Loglike = 9197.902249 Actual update 4900 of 5001, Stored update 4900 of 5001 -2 * Loglike = 9219.156737 Actual update 4950 of 5001, Stored update 4950 of 5001 -2 * Loglike = 9215.985241 Actual update 5000 of 5001, Stored update 5000 of 5001 -2 * Loglike = 9218.578744 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5001 Average = 9209.1 S.D. = 11.910 S.E.M. = 0.16841 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 : 1.67s 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 9209.124 9149.119 60.005 9269.130 --------------------------------------------------------------------------------------------------- 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 0.00231 0.04036 0.06 0.9544 -0.07769 0.08336 5001 standlrt 0.56324 0.01257 44.79 0 *** 0.53857 0.58782 5001 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 0.09707 0.01982 0.06485 0.14169 3140 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56618 0.01248 0.54208 0.59093 4750 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Each row represents each iteration > sixway(mymodel@resi.chains$resi_lev2[, 1, drop = FALSE], name = "school1") > > # 21.5 Random slopes model theory . . . . . . . . . . . . . . . . . . . .336 > > # 21.6 Random Slopes model practice . . . . . . . . . . . . . . . . . . .338 > > (mymodel <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1, + mcmcOptions = list(smcm = 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 = 9132.680377 Burning in for 100 iterations out of 500 -2 * Loglike = 9130.529343 Burning in for 150 iterations out of 500 -2 * Loglike = 9134.882851 Burning in for 200 iterations out of 500 -2 * Loglike = 9147.099708 Burning in for 250 iterations out of 500 -2 * Loglike = 9112.794139 Burning in for 300 iterations out of 500 -2 * Loglike = 9140.267154 Burning in for 350 iterations out of 500 -2 * Loglike = 9101.930503 Burning in for 400 iterations out of 500 -2 * Loglike = 9106.338280 Burning in for 450 iterations out of 500 -2 * Loglike = 9111.183719 Burning in for 500 iterations out of 500 -2 * Loglike = 9149.933574 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 = 9129.275682 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9127.957557 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9120.230173 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9140.628755 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9127.075452 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9111.138797 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9119.600356 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9133.632816 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9148.318155 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9115.717333 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9137.002682 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9106.095041 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9115.727728 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9139.576951 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9117.995914 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9146.868428 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9135.478916 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9095.315140 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9121.863861 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9096.302434 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9133.382890 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9130.186537 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9105.033572 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9111.605314 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9120.348799 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9102.002041 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9114.895204 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9122.306793 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9113.524865 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9113.014106 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9148.128302 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9123.225511 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9130.521840 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9116.367260 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9155.974594 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9133.769165 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9140.461547 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9136.440216 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9123.560695 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9135.146871 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9107.310985 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9130.391893 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9154.202664 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9107.641208 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9122.254609 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9143.748828 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9130.070205 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9133.988858 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9109.099556 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9150.696141 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9140.028236 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9102.089362 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9133.050208 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9153.432952 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9170.076129 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9129.639135 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9147.847607 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9129.426363 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9132.631483 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9125.986164 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9133.321177 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9108.400647 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9102.619819 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9139.155540 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9122.349790 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9146.303835 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9119.690374 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9135.216021 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9126.618903 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9130.121961 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9119.876384 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9130.028964 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9133.586164 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9127.269893 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9111.214454 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9110.462007 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9117.625669 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9116.236788 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9127.971676 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9101.191640 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9111.509954 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9116.086723 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9123.176435 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9123.574736 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9138.870477 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9153.419131 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9122.361701 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9118.733646 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9136.337720 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9118.086113 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9110.614757 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9106.654229 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9103.405561 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9097.824094 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9131.293633 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9123.792946 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9123.659213 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9120.729616 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9126.124600 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9120.132607 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9123.2 S.D. = 16.764 S.E.M. = 0.23708 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 : 6.04s 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 9123.153 9031.727 91.426 9214.579 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.01136 0.04093 -0.28 0.7814 -0.09229 0.06937 5000 standlrt 0.55678 0.01988 28.01 1.224e-172 *** 0.51708 0.59535 5000 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 0.09713 0.02011 0.06443 0.14253 2821 cov_Intercept_standlrt 0.01927 0.00736 0.00641 0.03535 1791 var_standlrt 0.01523 0.00481 0.00773 0.02648 874 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55439 0.01242 0.53038 0.57907 4753 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > sixway(mymodel@chains[, "FP_Intercept", drop = FALSE], "beta_0") > sixway(mymodel@chains[, "FP_standlrt", drop = FALSE], "beta_1") > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .340 > > > > > > ############################################################################ > > proc.time() user system elapsed 5.28 0.84 19.12