R version 3.6.3 (2020-02-29) -- "Holding the Windsock" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. 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 > # > # 2 Single Level Normal Response Modelling . . . . . . . . . . . . . . .21 > # > # 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 2013-2017 Zhengzheng Zhang, Christopher M. J. Charlton, Richard M. A. Parker, William J. Browne and George Leckie Support provided by the Economic and Social Research Council (ESRC) (Grants RES-149-25-1084, RES-576-25-0032 and ES/K007246/1) To cite R2MLwiN in publications use: Zhengzheng Zhang, Richard M. A. Parker, Christopher M. J. Charlton, George Leckie, William J. Browne (2016). R2MLwiN: A Package to Run MLwiN from within R. Journal of Statistical Software, 72(10), 1-43. doi:10.18637/jss.v072.i10 A BibTeX entry for LaTeX users is @Article{, title = {{R2MLwiN}: A Package to Run {MLwiN} from within {R}}, author = {Zhengzheng Zhang and Richard M. A. Parker and Christopher M. J. Charlton and George Leckie and William J. Browne}, journal = {Journal of Statistical Software}, year = {2016}, volume = {72}, number = {10}, pages = {1--43}, doi = {10.18637/jss.v072.i10}, } The MLwiN_path option is currently set to C:/Program Files/MLwiN v3.05/ To change this use: options(MLwiN_path="") > # 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") > > ## Choose IGLS algoritm for estimation > (mymodel1 <- runMLwiN(normexam ~ 1 + standlrt + (1 | student), data = tutorial)) /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence achieved TOLE 2 MAXI 20 NEXT iteration 2 Convergence achieved ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: IGLS Elapsed time : 0.04s Number of obs: 4059 (from total 4059) The model converged after 3 iterations. Log likelihood: -4880.3 Deviance statistic: 9760.5 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval] Intercept -0.00119 0.01264 -0.09 0.9249 -0.02596 0.02358 standlrt 0.59506 0.01273 46.76 0 *** 0.57011 0.62000 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. var_Intercept 0.64842 0.01439 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 2.1 Running the Gibbs Sampler . . . . . . . . . . . . . . . . . . . . . 26 > > ## Choose MCMC algoritm for estimation > (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (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 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 1 1 1 1 1 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9762.780915 Burning in for 100 iterations out of 500 -2 * Loglike = 9765.926164 Burning in for 150 iterations out of 500 -2 * Loglike = 9762.650763 Burning in for 200 iterations out of 500 -2 * Loglike = 9762.474330 Burning in for 250 iterations out of 500 -2 * Loglike = 9762.364381 Burning in for 300 iterations out of 500 -2 * Loglike = 9762.893942 Burning in for 350 iterations out of 500 -2 * Loglike = 9761.839827 Burning in for 400 iterations out of 500 -2 * Loglike = 9762.773461 Burning in for 450 iterations out of 500 -2 * Loglike = 9760.764811 Burning in for 500 iterations out of 500 -2 * Loglike = 9761.625767 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 = 9761.208216 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9763.938181 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9766.747437 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9760.926238 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9761.971307 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9764.806422 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9763.361969 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9766.117223 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9762.858300 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9761.511185 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9765.472236 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9765.034947 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9768.212514 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9765.519356 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9765.560913 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9764.785420 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9761.003227 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9761.772431 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9761.556037 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9762.493673 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9762.383782 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9767.201421 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9760.887055 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9763.444657 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9760.785499 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9766.866985 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9763.211048 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9768.160531 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9761.045334 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9764.338007 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9765.094200 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9762.104932 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9763.047431 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9764.921262 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9767.102675 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9762.541523 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9767.662756 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9767.958850 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9762.089646 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9762.406151 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9764.488231 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9761.746909 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9761.907127 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9767.057694 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9764.234759 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9761.181638 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9762.189244 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9762.374576 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9761.224826 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9761.930640 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9766.324759 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9761.152178 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9766.013155 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9765.289873 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9760.545581 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9762.542624 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9767.151551 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9761.084773 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9766.020024 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9764.329436 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9763.506974 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9761.337698 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9760.986906 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9761.683531 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9763.071357 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9768.071216 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9766.729144 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9769.528786 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9760.558165 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9760.681342 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9766.932408 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9764.879704 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9769.212110 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9761.759135 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9760.566148 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9764.583560 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9768.371789 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9765.072699 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9764.329964 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9761.795540 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9764.074681 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9764.127839 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9762.897511 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9761.688179 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9767.774712 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9762.166833 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9762.936829 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9761.198401 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9763.027719 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9761.029382 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9761.143399 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9765.431275 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9762.770100 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9762.418131 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9761.279815 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9762.511766 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9764.389418 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9761.540116 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9762.783558 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9765.672313 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9763.5 S.D. = 2.4441 S.E.M. = 0.034565 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.57s 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 9763.518 9760.511 3.007 9766.525 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.00124 0.01265 -0.10 0.9221 -0.02623 0.02313 5000 standlrt 0.59522 0.01261 47.19 0 *** 0.57110 0.62004 5000 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.64887 0.01462 0.62136 0.67856 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > > if (!require(coda)) { + warning("package coda required to run this example") + } else { + par(mfrow = c(2, 2)) + estimates <- mymodel2@chains + plot(1:niter(estimates), estimates[, "deviance"], xlab = "iteration", ylab = expression(paste("Est. of deviance")), + type = "l") + plot(1:niter(estimates), estimates[, "FP_Intercept"], xlab = "iteration", ylab = expression(paste("Est. of ", beta[0])), + type = "l") + plot(1:niter(estimates), estimates[, "FP_standlrt"], xlab = "iteration", ylab = expression(paste("Est. of ", beta[1])), + type = "l") + plot(1:niter(estimates), 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 > > # 2.2 Deviance statistic and the DIC diagnostic . . . . . . . . . . . . . 28 > > # 2.3 Adding more predictors . . . . . . . . . . . . . . . . . . . . . . .29 > > ## Choose IGLS algoritm for estimation > (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + sex + schgend + (1 | student), data = tutorial)) /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence achieved TOLE 2 MAXI 20 NEXT iteration 2 Convergence achieved ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: IGLS Elapsed time : 0.05s Number of obs: 4059 (from total 4059) The model converged after 3 iterations. Log likelihood: -4836.1 Deviance statistic: 9672.2 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + sex + schgend + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval] Intercept -0.16086 0.02394 -6.72 1.816e-11 *** -0.20777 -0.11394 standlrt 0.59105 0.01262 46.84 0 *** 0.56632 0.61578 sexgirl 0.13264 0.03429 3.87 0.0001098 *** 0.06543 0.19986 schgendboysch 0.18255 0.04254 4.29 1.778e-05 *** 0.09917 0.26594 schgendgirlsch 0.16801 0.03257 5.16 2.492e-07 *** 0.10417 0.23185 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. var_Intercept 0.63446 0.01408 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Choose MCMC algoritm for estimation > (mymodel4 <- runMLwiN(normexam ~ 1 + standlrt + sex + schgend + (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 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 1 1 1 1 1 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9681.903317 Burning in for 100 iterations out of 500 -2 * Loglike = 9680.687052 Burning in for 150 iterations out of 500 -2 * Loglike = 9678.024599 Burning in for 200 iterations out of 500 -2 * Loglike = 9679.627905 Burning in for 250 iterations out of 500 -2 * Loglike = 9674.624112 Burning in for 300 iterations out of 500 -2 * Loglike = 9677.754584 Burning in for 350 iterations out of 500 -2 * Loglike = 9675.906199 Burning in for 400 iterations out of 500 -2 * Loglike = 9674.954614 Burning in for 450 iterations out of 500 -2 * Loglike = 9677.274038 Burning in for 500 iterations out of 500 -2 * Loglike = 9673.463036 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 = 9677.299307 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9677.926441 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9681.403933 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9677.431681 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9675.712400 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9677.542719 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9678.132294 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9673.777984 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9678.243439 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9682.360529 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9676.074651 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9677.546067 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9677.906382 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9677.749593 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9678.108019 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9678.733799 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9680.035060 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9683.514037 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9676.537449 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9676.134408 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9674.913880 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9677.832154 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9676.352016 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9677.817453 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9673.753933 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9677.206020 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9682.669435 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9675.978616 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9676.218962 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9676.689038 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9686.230575 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9680.835177 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9678.334266 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9672.787139 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9679.815606 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9675.389353 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9675.543714 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9677.444587 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9673.378126 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9675.750714 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9677.237830 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9676.628082 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9678.704686 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9676.086599 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9680.856352 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9682.688899 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9688.488136 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9673.929212 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9676.995079 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9679.377123 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9688.073715 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9678.859466 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9673.964754 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9678.237879 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9680.098150 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9684.648424 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9678.953555 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9683.809060 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9675.638198 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9679.672287 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9673.349528 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9687.367968 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9679.198291 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9674.134322 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9682.046963 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9678.259628 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9674.956077 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9678.077458 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9674.939786 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9676.624811 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9680.825682 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9677.059185 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9676.883577 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9685.677692 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9674.465674 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9677.922623 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9676.825972 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9676.289931 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9679.960793 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9675.534237 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9677.914785 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9680.802701 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9682.313440 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9675.573504 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9680.323667 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9674.939205 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9675.969802 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9676.444166 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9676.448911 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9682.777957 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9684.071874 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9678.729369 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9679.849807 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9676.498440 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9675.255670 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9677.382990 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9679.816214 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9674.545996 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9676.278283 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9680.968370 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9678.2 S.D. = 3.4365 S.E.M. = 0.048599 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.72s 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 9678.214 9672.203 6.011 9684.225 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + sex + schgend + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.16095 0.02395 -6.72 1.812e-11 *** -0.20769 -0.11509 5580 standlrt 0.59102 0.01266 46.70 0 *** 0.56625 0.61567 5000 sexgirl 0.13208 0.03456 3.82 0.0001324 *** 0.06274 0.19960 5203 schgendboysch 0.18237 0.04279 4.26 2.026e-05 *** 0.09978 0.26589 5000 schgendgirlsch 0.16846 0.03214 5.24 1.592e-07 *** 0.10727 0.23027 5000 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.63564 0.01428 0.60868 0.66487 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 2.4 Fitting school effects as fixed parameters . . . . . . . . . . . . .32 > > tutorial$school <- as.factor(tutorial$school) > > ## Choose MCMC algoritm for estimation (IGLS will be used to obtain starting values for MCMC) > (mymodel5 <- runMLwiN(normexam ~ 1 + standlrt + sex + 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 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 1 1 1 1 1 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9194.560582 Burning in for 100 iterations out of 500 -2 * Loglike = 9177.040435 Burning in for 150 iterations out of 500 -2 * Loglike = 9204.368667 Burning in for 200 iterations out of 500 -2 * Loglike = 9174.393223 Burning in for 250 iterations out of 500 -2 * Loglike = 9163.143420 Burning in for 300 iterations out of 500 -2 * Loglike = 9171.437773 Burning in for 350 iterations out of 500 -2 * Loglike = 9202.090295 Burning in for 400 iterations out of 500 -2 * Loglike = 9201.237132 Burning in for 450 iterations out of 500 -2 * Loglike = 9182.344297 Burning in for 500 iterations out of 500 -2 * Loglike = 9189.432715 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 = 9197.072247 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9189.240150 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9184.343403 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9169.866369 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9195.853107 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9200.305719 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9207.361394 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9182.380615 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9187.047463 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9169.888237 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9183.268750 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9197.897470 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9187.742903 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9179.970835 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9181.353930 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9189.858566 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9178.950079 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9174.907728 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9172.093995 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9183.186036 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9172.692397 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9187.850608 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9183.460456 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9176.517945 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9186.187455 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9192.884942 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9166.335305 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9175.562253 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9175.263868 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9192.706229 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9180.088034 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9166.689515 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9165.818433 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9180.492582 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9192.678394 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9185.322787 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9192.729093 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9182.137470 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9187.431666 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9185.796900 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9199.149536 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9198.758014 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9211.720671 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9192.136490 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9188.879907 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9185.443205 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9194.757434 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9181.421324 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9174.094284 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9194.085707 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9171.081293 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9175.419822 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9195.823782 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9196.988999 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9187.412814 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9171.704001 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9163.277607 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9172.968326 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9193.184114 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9180.387650 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9168.788552 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9173.421471 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9206.708543 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9171.196000 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9179.879973 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9202.402523 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9173.265807 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9177.560039 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9190.955257 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9190.758945 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9168.472577 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9189.131564 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9170.778938 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9176.355818 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9177.656499 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9188.419805 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9181.997647 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9192.758749 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9171.763070 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9203.131998 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9198.074095 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9205.231181 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9179.242252 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9182.856677 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9199.676353 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9187.072280 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9182.076320 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9176.123137 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9177.028692 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9199.353117 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9188.225474 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9180.488725 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9195.742975 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9175.259537 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9175.294750 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9194.803694 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9169.611976 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9194.332495 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9185.945791 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9172.413548 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9183.2 S.D. = 11.735 S.E.M. = 0.16596 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 5.63s 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 9183.164 9115.376 67.789 9250.953 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + sex + school + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept 0.34476 0.08753 3.94 8.188e-05 *** 0.17057 0.51728 5000 standlrt 0.55577 0.01236 44.96 0 *** 0.53125 0.57996 5000 sexgirl 0.16985 0.03430 4.95 7.37e-07 *** 0.10200 0.23897 5000 school2 0.04946 0.13405 0.37 0.7121 -0.20818 0.31514 5000 school3 0.14972 0.13502 1.11 0.2675 -0.11342 0.40845 5000 school4 -0.39372 0.12035 -3.27 0.00107 ** -0.62913 -0.15345 5000 school5 -0.15472 0.15273 -1.01 0.3111 -0.44966 0.14210 5000 school6 0.07567 0.12272 0.62 0.5375 -0.16437 0.32238 5000 school7 -0.10551 0.11905 -0.89 0.3755 -0.33847 0.12953 5000 school8 -0.54129 0.11614 -4.66 3.152e-06 *** -0.77059 -0.31009 5000 school9 -0.57034 0.15546 -3.67 0.0002437 *** -0.88138 -0.27087 5000 school10 -0.78349 0.13833 -5.66 1.48e-08 *** -1.05715 -0.51430 5000 school11 -0.14077 0.13014 -1.08 0.2794 -0.39275 0.11108 5215 school12 -0.50144 0.14077 -3.56 0.0003678 *** -0.77111 -0.22523 5000 school13 -0.60902 0.12629 -4.82 1.419e-06 *** -0.85756 -0.36814 5000 school14 -0.60258 0.10154 -5.93 2.952e-09 *** -0.79792 -0.40074 5000 school15 -0.61906 0.11671 -5.30 1.13e-07 *** -0.84854 -0.38842 5000 school16 -0.94863 0.11986 -7.91 2.479e-15 *** -1.18179 -0.71671 5000 school17 -0.65390 0.11144 -5.87 4.411e-09 *** -0.86848 -0.43524 5000 school18 -0.60217 0.11263 -5.35 8.961e-08 *** -0.82145 -0.38145 5206 school19 -0.42052 0.13243 -3.18 0.001496 ** -0.68215 -0.15940 5000 school20 -0.16984 0.14675 -1.16 0.2471 -0.45887 0.10931 5000 school21 -0.24590 0.12480 -1.97 0.04879 * -0.49009 -0.00231 5000 school22 -0.88821 0.11963 -7.42 1.131e-13 *** -1.12328 -0.65302 5445 school23 -1.05124 0.16615 -6.33 2.499e-10 *** -1.36844 -0.72346 5000 school24 -0.10290 0.15235 -0.68 0.4994 -0.40615 0.18605 5000 school25 -0.76753 0.12575 -6.10 1.036e-09 *** -1.01313 -0.51368 5000 school26 -0.44273 0.12358 -3.58 0.0003401 *** -0.68369 -0.20499 5000 school27 -0.32029 0.14744 -2.17 0.02983 * -0.61467 -0.03980 4759 school28 -1.09872 0.13320 -8.25 1.605e-16 *** -1.36463 -0.84687 5000 school29 -0.25309 0.12309 -2.06 0.03978 * -0.49054 -0.01093 5000 school30 -0.32584 0.14425 -2.26 0.02389 * -0.61127 -0.03940 5000 school31 -0.47664 0.14009 -3.40 0.0006683 *** -0.75624 -0.19995 5000 school32 -0.41693 0.14495 -2.88 0.004023 ** -0.69936 -0.13302 5000 school33 -0.38270 0.12021 -3.18 0.001455 ** -0.62188 -0.14617 5000 school34 -0.56844 0.17023 -3.34 0.0008402 *** -0.90356 -0.23835 4790 school35 -0.36457 0.14938 -2.44 0.01467 * -0.65395 -0.06720 5000 school36 -0.54056 0.12260 -4.41 1.038e-05 *** -0.77641 -0.30298 5000 school37 -0.58917 0.18236 -3.23 0.001235 ** -0.94221 -0.22808 5000 school38 -0.58582 0.13404 -4.37 1.24e-05 *** -0.85313 -0.31615 5000 school39 -0.36844 0.14056 -2.62 0.008762 ** -0.63601 -0.08731 5000 school40 -0.59599 0.12518 -4.76 1.926e-06 *** -0.83618 -0.35132 5000 school41 -0.28031 0.13114 -2.14 0.03256 * -0.53465 -0.02536 5000 school42 -0.30863 0.13162 -2.34 0.01904 * -0.56678 -0.05399 5698 school43 -0.60155 0.12949 -4.65 3.392e-06 *** -0.85459 -0.34797 5205 school44 -0.64227 0.16231 -3.96 7.586e-05 *** -0.95916 -0.32809 5000 school45 -0.62130 0.13540 -4.59 4.464e-06 *** -0.88490 -0.35080 3739 school46 -0.79631 0.11993 -6.64 3.145e-11 *** -1.03031 -0.55764 5335 school47 -0.39074 0.12048 -3.24 0.001182 ** -0.63337 -0.15820 5000 school48 -0.69728 0.54470 -1.28 0.2005 -1.74782 0.39884 5000 school49 -0.46717 0.11406 -4.10 4.208e-05 *** -0.68879 -0.24801 5000 school50 -0.75801 0.12413 -6.11 1.019e-09 *** -0.99726 -0.51473 5000 school51 -0.49824 0.13166 -3.78 0.0001541 *** -0.75141 -0.23622 4880 school52 0.08048 0.13072 0.62 0.5381 -0.16963 0.34087 5342 school53 0.27915 0.12787 2.18 0.02903 * 0.02686 0.52687 5000 school54 -1.39249 0.28101 -4.96 7.221e-07 *** -1.93452 -0.84081 5000 school55 0.14045 0.13542 1.04 0.2997 -0.12004 0.41210 5000 school56 -0.42750 0.15051 -2.84 0.004507 ** -0.72704 -0.13389 5000 school57 -0.30736 0.13033 -2.36 0.01836 * -0.55337 -0.05391 6001 school58 -0.34675 0.15183 -2.28 0.02239 * -0.63811 -0.04816 5000 school59 -1.15259 0.14013 -8.22 1.954e-16 *** -1.42721 -0.88136 5000 school60 -0.27037 0.12276 -2.20 0.02764 * -0.50862 -0.03135 5000 school61 -0.45958 0.12773 -3.60 0.0003207 *** -0.71039 -0.20959 4491 school62 -0.46446 0.12651 -3.67 0.0002412 *** -0.70783 -0.21501 5000 school63 0.20899 0.16185 1.29 0.1966 -0.10107 0.52569 5000 school64 -0.23769 0.13195 -1.80 0.07164 . -0.49991 0.02313 5000 school65 -0.69368 0.12250 -5.66 1.491e-08 *** -0.93391 -0.45212 5000 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.56282 0.01260 0.53859 0.58754 4993 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 33 > > > > > ############################################################################ > > proc.time() user system elapsed 5.56 0.76 15.17