R version 4.3.2 (2023-10-31 ucrt) -- "Eye Holes" Copyright (C) 2023 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 (64-bit) 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. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ############################################################################ > # MLwiN MCMC Manual > # > # 3 Variance Components Models . . . . . . . . . . . . . . . . . . . . .35 > # > # 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/ > ############################################################################ > > # 3.1 A 2 level variance components model for the Tutorial dataset . . . .36 > > 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 v3.09/ 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") > > ## The highest level comes first, then the second highest and so on > (mymodel1 <- 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: 3.09) 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 : 1.53s 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 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > if (!require(coda)) { + warning("package coda required to run this example") + } else { + estimates <- mymodel1@chains + par(mfrow = c(3, 2)) + plot(4501:niter(estimates), estimates[4501:niter(estimates), "deviance"], xlab = "iteration", ylab = expression(paste("Est. of deviance")), + type = "l") + plot(4501:niter(estimates), estimates[4501:niter(estimates), "FP_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + beta[0])), type = "l") + plot(4501:niter(estimates), estimates[4501:niter(estimates), "FP_standlrt"], xlab = "iteration", ylab = expression(paste("Est. of ", + beta[1])), type = "l") + plot(4501:niter(estimates), estimates[4501:niter(estimates), "RP2_var_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + sigma[u0]^2)), type = "l") + plot(4501:niter(estimates), estimates[4501:niter(estimates), "RP1_var_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", + sigma[e0]^2)), type = "l") + ## reinstate par settings + par(mypar) + } Loading required package: coda > > sixway(mymodel1@chains[, "FP_standlrt", drop = FALSE], "beta_1") > sixway(mymodel1@chains[, "RP2_var_Intercept", drop = FALSE], "sigma2u0") > > # 3.2 DIC and multilevel models . . . . . . . . . . . . . . . . . . . . . 41 > > # 3.3 Comparison between fixed and random school effects . . . . . . . . .41 > > (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + sex + (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 = 9180.759474 Burning in for 100 iterations out of 500 -2 * Loglike = 9194.936175 Burning in for 150 iterations out of 500 -2 * Loglike = 9187.579234 Burning in for 200 iterations out of 500 -2 * Loglike = 9185.806609 Burning in for 250 iterations out of 500 -2 * Loglike = 9164.048048 Burning in for 300 iterations out of 500 -2 * Loglike = 9200.472585 Burning in for 350 iterations out of 500 -2 * Loglike = 9186.465078 Burning in for 400 iterations out of 500 -2 * Loglike = 9185.695711 Burning in for 450 iterations out of 500 -2 * Loglike = 9185.352829 Burning in for 500 iterations out of 500 -2 * Loglike = 9170.684757 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 = 9176.157668 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9177.537683 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9176.378814 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9192.734381 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9178.641230 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9187.957823 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9181.903814 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9185.364941 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9199.610013 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9189.268670 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9209.801948 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9180.779542 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9173.861211 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9172.928569 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9183.393326 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9179.348545 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9172.648377 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9195.617996 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9205.457222 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9191.330991 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9180.848291 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9185.070892 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9178.832408 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9185.923629 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9194.042353 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9176.993023 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9172.469997 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9188.060318 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9174.465939 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9184.455528 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9183.920528 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9180.265754 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9166.758748 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9166.632713 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9173.641321 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9183.756578 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9190.756780 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9168.070877 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9196.328847 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9184.172946 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9194.382577 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9186.496012 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9185.988565 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9207.084202 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9164.110860 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9198.726158 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9189.079324 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9181.380599 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9174.884741 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9184.897798 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9190.049555 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9184.983257 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9214.742018 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9175.660733 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9197.831055 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9203.639129 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9174.998741 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9173.891806 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9199.362923 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9203.856872 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9185.742975 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9165.513302 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9203.342257 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9184.428113 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9174.399175 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9171.479516 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9206.142037 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9197.502331 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9183.319756 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9189.010430 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9174.162962 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9176.038065 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9180.309976 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9183.346059 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9182.923896 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9185.798041 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9175.323611 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9174.447300 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9218.371065 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9191.127280 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9181.126277 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9179.989149 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9175.175701 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9173.305779 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9173.133160 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9200.045570 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9172.694855 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9202.816875 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9179.815774 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9195.059292 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9162.811273 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9170.468640 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9174.009061 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9181.578007 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9189.562303 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9207.423630 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9190.410357 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9173.421249 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9208.411353 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9172.282289 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9185.2 S.D. = 11.919 S.E.M. = 0.16856 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.09) 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 : 1.58s 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 9185.221 9124.538 60.683 9245.904 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + sex + (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 -0.09433 0.04571 -2.06 0.03904 * -0.18102 -0.00045 266 standlrt 0.55933 0.01275 43.88 0 *** 0.53403 0.58367 3876 sexgirl 0.17237 0.03324 5.19 2.157e-07 *** 0.10698 0.23877 1977 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 0.09237 0.01919 0.06220 0.13543 2955 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56314 0.01251 0.53890 0.58844 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 43 > > > > ############################################################################ > > proc.time() user system elapsed 4.04 0.48 7.92