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 > # > # 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 2013-2024 Zhengzheng Zhang, Christopher M. J. Charlton, Richard M. A. Parker, William J. Browne and George Leckie Support provided by the Economic and Social Research Council (ESRC) (Grants RES-149-25-1084, RES-576-25-0032 and ES/K007246/1) To cite R2MLwiN in publications use: Zhengzheng Zhang, Richard M. A. Parker, Christopher M. J. Charlton, George Leckie, William J. Browne (2016). R2MLwiN: A Package to Run MLwiN from within R. Journal of Statistical Software, 72(10), 1-43. doi:10.18637/jss.v072.i10 A BibTeX entry for LaTeX users is @Article{, title = {{R2MLwiN}: A Package to Run {MLwiN} from within {R}}, author = {Zhengzheng Zhang and Richard M. A. Parker and Christopher M. J. Charlton and George Leckie and William J. Browne}, journal = {Journal of Statistical Software}, year = {2016}, volume = {72}, number = {10}, pages = {1--43}, doi = {10.18637/jss.v072.i10}, } The MLwiN_path option is currently set to C:/Program Files/MLwiN v3.11/ To change this use: options(MLwiN_path="") > # MLwiN folder > mlwin <- getOption("MLwiN_path") > while (!file.access(mlwin, mode = 1) == 0) { + cat("Please specify the root MLwiN folder or the full path to the MLwiN executable:\n") + mlwin <- scan(what = character(0), sep = "\n") + mlwin <- gsub("\\", "/", mlwin, fixed = TRUE) + } > options(MLwiN_path = mlwin) > > ## save current par settings > mypar <- par(no.readonly = TRUE) > > ## Read tutorial data > data(tutorial, package = "R2MLwiN") > > ## 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: 3.11) multilevel model (Normal) Estimation algorithm: IGLS Elapsed time : 0.08s 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... Burning in for 50 iterations out of 500 -2 * Loglike = 9763.570966 Burning in for 100 iterations out of 500 -2 * Loglike = 9761.304038 Burning in for 150 iterations out of 500 -2 * Loglike = 9761.684811 Burning in for 200 iterations out of 500 -2 * Loglike = 9762.194785 Burning in for 250 iterations out of 500 -2 * Loglike = 9763.214515 Burning in for 300 iterations out of 500 -2 * Loglike = 9761.477040 Burning in for 350 iterations out of 500 -2 * Loglike = 9763.231302 Burning in for 400 iterations out of 500 -2 * Loglike = 9764.099819 Burning in for 450 iterations out of 500 -2 * Loglike = 9764.279429 Burning in for 500 iterations out of 500 -2 * Loglike = 9761.841886 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 = 9761.330720 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9760.728263 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9761.501773 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9764.041048 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9762.501203 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9761.520463 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9765.411405 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9762.408577 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9766.733453 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9766.441604 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9764.149440 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9775.927318 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9767.717424 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9761.336433 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9762.313216 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9761.645878 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9762.455422 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9765.569837 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9761.783134 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9763.434908 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9765.435462 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9766.211262 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9763.247073 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9760.668486 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9766.106738 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9764.744948 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9761.707514 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9763.405136 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9762.614196 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9762.943139 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9761.308622 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9764.927379 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9761.641891 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9766.067628 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9761.820783 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9760.867091 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9766.082493 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9762.710906 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9763.973195 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9760.762798 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9761.235069 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9762.219658 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9760.950718 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9761.807126 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9762.407476 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9761.966697 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9762.864864 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9761.753503 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9762.321459 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9761.829923 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9767.704408 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9761.286522 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9766.271900 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9762.956927 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9765.623197 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9761.657624 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9762.997568 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9762.353095 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9762.550379 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9764.277715 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9760.692173 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9760.677272 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9761.147567 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9762.733979 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9766.948165 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9762.195572 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9761.246785 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9766.259172 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9764.681188 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9760.920060 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9763.785765 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9761.152802 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9761.795409 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9765.007972 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9762.262592 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9761.381901 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9763.449596 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9779.460222 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9761.912910 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9763.390877 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9766.360558 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9761.919470 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9763.191611 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9765.410558 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9764.642653 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9766.129450 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9760.749791 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9763.403276 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9760.653563 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9761.345380 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9760.640209 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9763.019714 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9766.667800 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9769.339721 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9760.795037 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9761.074376 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9762.153120 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9760.761360 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9764.689958 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9761.859670 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9763.5 S.D. = 2.4581 S.E.M. = 0.034762 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.53s 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 9763.487 9760.512 2.976 9766.463 --------------------------------------------------------------------------------------------------- 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 -0.00115 0.01259 -0.09 0.927 -0.02627 0.02346 5000 standlrt 0.59512 0.01282 46.42 0 *** 0.57029 0.61950 4533 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 0.64909 0.01423 0.62245 0.67784 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: 3.11) multilevel model (Normal) Estimation algorithm: IGLS Elapsed time : 0.08s 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... Burning in for 50 iterations out of 500 -2 * Loglike = 9679.200430 Burning in for 100 iterations out of 500 -2 * Loglike = 9683.477051 Burning in for 150 iterations out of 500 -2 * Loglike = 9680.514433 Burning in for 200 iterations out of 500 -2 * Loglike = 9690.921221 Burning in for 250 iterations out of 500 -2 * Loglike = 9675.875957 Burning in for 300 iterations out of 500 -2 * Loglike = 9679.343812 Burning in for 350 iterations out of 500 -2 * Loglike = 9674.228728 Burning in for 400 iterations out of 500 -2 * Loglike = 9674.325599 Burning in for 450 iterations out of 500 -2 * Loglike = 9673.111441 Burning in for 500 iterations out of 500 -2 * Loglike = 9675.146465 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 = 9677.113657 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9677.128086 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9674.019641 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9680.694764 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9676.654864 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9676.850069 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9678.144706 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9677.785406 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9680.982298 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9681.435060 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9676.385314 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9674.552791 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9677.726801 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9678.556041 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9674.125460 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9674.947106 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9677.433637 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9678.916643 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9684.356087 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9682.228510 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9678.513943 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9685.411208 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9683.829709 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9680.042108 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9682.449498 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9675.757972 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9676.541281 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9679.656203 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9677.021694 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9674.374964 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9679.397670 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9675.144310 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9677.909598 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9680.254025 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9674.883296 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9675.920755 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9677.646463 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9681.273848 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9677.813280 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9677.838371 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9679.096107 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9678.027750 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9673.435202 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9680.058374 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9674.650405 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9677.630358 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9677.470099 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9675.089977 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9675.614590 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9673.605404 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9675.358819 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9683.258401 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9680.619110 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9680.669807 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9675.125862 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9681.741759 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9676.833026 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9681.188820 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9682.609337 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9679.415388 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9674.282889 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9672.968691 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9674.329415 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9674.302208 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9675.925555 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9673.865496 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9676.212717 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9679.326460 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9681.706803 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9679.849582 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9677.017275 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9683.342589 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9678.503972 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9676.145455 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9681.403040 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9678.075411 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9673.426420 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9683.121966 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9676.135811 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9675.434640 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9681.663240 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9675.668802 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9679.362186 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9676.915146 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9675.975415 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9678.230121 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9675.948058 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9677.333314 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9676.371385 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9678.654487 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9673.224289 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9678.313632 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9674.488482 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9673.465631 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9677.227775 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9678.804004 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9679.875954 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9675.024836 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9676.874481 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9680.389275 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9678.2 S.D. = 3.4643 S.E.M. = 0.048992 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.73s 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 9678.169 9672.200 5.970 9684.139 --------------------------------------------------------------------------------------------------- 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 -0.16137 0.02390 -6.75 1.456e-11 *** -0.20891 -0.11569 5000 standlrt 0.59093 0.01259 46.92 0 *** 0.56621 0.61553 4807 sexgirl 0.13328 0.03427 3.89 0.0001007 *** 0.06727 0.20074 5000 schgendboysch 0.18304 0.04324 4.23 2.31e-05 *** 0.09959 0.26845 5000 schgendgirlsch 0.16837 0.03208 5.25 1.535e-07 *** 0.10511 0.23056 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 0.63530 0.01405 0.60872 0.66383 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... Burning in for 50 iterations out of 500 -2 * Loglike = 9175.879176 Burning in for 100 iterations out of 500 -2 * Loglike = 9184.171148 Burning in for 150 iterations out of 500 -2 * Loglike = 9181.645088 Burning in for 200 iterations out of 500 -2 * Loglike = 9166.662736 Burning in for 250 iterations out of 500 -2 * Loglike = 9194.440785 Burning in for 300 iterations out of 500 -2 * Loglike = 9185.838607 Burning in for 350 iterations out of 500 -2 * Loglike = 9192.785108 Burning in for 400 iterations out of 500 -2 * Loglike = 9181.969070 Burning in for 450 iterations out of 500 -2 * Loglike = 9189.119443 Burning in for 500 iterations out of 500 -2 * Loglike = 9176.527531 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 = 9185.893582 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9195.876011 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9208.851000 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9191.922289 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9171.588853 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9181.038339 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9205.725566 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9190.270909 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9180.866832 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9195.846063 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9178.174074 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9203.894041 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9181.054405 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9158.663706 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9183.239124 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9173.045381 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9179.426197 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9178.422484 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9186.959805 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9178.200070 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9167.542636 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9190.796450 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9176.005578 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9192.885388 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9183.157266 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9188.178170 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9176.702381 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9185.355338 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9164.306507 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9178.135502 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9182.603557 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9188.186643 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9158.729615 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9183.604483 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9166.987169 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9181.968238 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9161.442922 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9193.134563 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9185.416282 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9170.039921 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9177.420982 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9200.399332 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9166.904590 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9178.896212 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9190.293919 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9187.858788 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9176.286359 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9169.923545 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9190.667251 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9175.260713 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9181.356409 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9161.657129 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9169.679619 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9188.873850 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9175.161400 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9191.721320 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9178.563796 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9195.025642 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9198.198688 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9192.799337 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9179.598695 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9193.180395 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9181.460386 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9173.788131 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9184.641496 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9187.053178 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9185.398709 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9191.050653 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9212.304961 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9174.119324 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9210.497560 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9184.935382 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9182.734364 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9170.580461 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9197.196813 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9169.236160 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9184.415442 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9185.555445 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9204.911744 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9181.191290 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9181.360500 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9187.470079 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9183.960303 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9177.245002 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9181.434917 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9167.527029 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9206.708220 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9190.253857 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9172.030052 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9181.718167 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9188.752165 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9171.923416 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9185.377192 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9180.558643 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9183.632232 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9184.828389 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9180.818509 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9190.432228 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9169.976601 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9176.193185 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9183.1 S.D. = 11.783 S.E.M. = 0.16663 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 6.06s 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 9183.111 9115.374 67.738 9250.849 --------------------------------------------------------------------------------------------------- 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 0.34277 0.08821 3.89 0.0001019 *** 0.17327 0.52093 5000 standlrt 0.55576 0.01262 44.05 0 *** 0.53157 0.58065 4986 sexgirl 0.17034 0.03393 5.02 5.144e-07 *** 0.10537 0.23743 5000 school2 0.05279 0.13487 0.39 0.6955 -0.21715 0.31186 5000 school3 0.15155 0.13579 1.12 0.2644 -0.11788 0.41303 4770 school4 -0.39381 0.12039 -3.27 0.001071 ** -0.62581 -0.15627 5000 school5 -0.14698 0.15205 -0.97 0.3337 -0.44402 0.15056 5000 school6 0.07805 0.12219 0.64 0.523 -0.16311 0.31910 5000 school7 -0.10462 0.11935 -0.88 0.3807 -0.33393 0.13306 5000 school8 -0.53628 0.11611 -4.62 3.863e-06 *** -0.76395 -0.30994 5000 school9 -0.56706 0.15183 -3.73 0.0001878 *** -0.86770 -0.27233 5000 school10 -0.78015 0.13682 -5.70 1.185e-08 *** -1.04467 -0.51432 5000 school11 -0.13669 0.13014 -1.05 0.2936 -0.39456 0.12138 5000 school12 -0.49694 0.13802 -3.60 0.0003178 *** -0.76777 -0.22162 4798 school13 -0.60831 0.12733 -4.78 1.777e-06 *** -0.86383 -0.35704 5000 school14 -0.59890 0.10232 -5.85 4.818e-09 *** -0.79954 -0.40188 5000 school15 -0.61727 0.11766 -5.25 1.554e-07 *** -0.84877 -0.39526 5000 school16 -0.94506 0.11902 -7.94 2.015e-15 *** -1.17418 -0.71513 5000 school17 -0.64991 0.10899 -5.96 2.478e-09 *** -0.86327 -0.43779 5000 school18 -0.59703 0.11422 -5.23 1.724e-07 *** -0.82561 -0.37371 5000 school19 -0.41353 0.13398 -3.09 0.002025 ** -0.67250 -0.15500 5000 school20 -0.16587 0.14960 -1.11 0.2675 -0.45859 0.12241 5000 school21 -0.24338 0.12728 -1.91 0.05586 . -0.49226 0.00357 4615 school22 -0.88822 0.11638 -7.63 2.314e-14 *** -1.11794 -0.66300 5172 school23 -1.04703 0.16746 -6.25 4.04e-10 *** -1.37332 -0.72178 4736 school24 -0.09998 0.15075 -0.66 0.5072 -0.39987 0.19066 5000 school25 -0.76625 0.12719 -6.02 1.695e-09 *** -1.01476 -0.51989 5000 school26 -0.44247 0.12293 -3.60 0.0003189 *** -0.68046 -0.20210 5000 school27 -0.31564 0.14958 -2.11 0.03485 * -0.61073 -0.02220 5000 school28 -1.09808 0.13196 -8.32 8.689e-17 *** -1.35909 -0.84169 4782 school29 -0.25433 0.12388 -2.05 0.04007 * -0.49844 -0.01357 5000 school30 -0.32524 0.14675 -2.22 0.02668 * -0.61056 -0.04538 5000 school31 -0.47702 0.13912 -3.43 0.0006063 *** -0.74650 -0.20469 5000 school32 -0.41322 0.14521 -2.85 0.004431 ** -0.69983 -0.12473 5000 school33 -0.38108 0.12134 -3.14 0.001686 ** -0.62455 -0.14720 5000 school34 -0.56303 0.17241 -3.27 0.001092 ** -0.92008 -0.23484 5000 school35 -0.36395 0.15143 -2.40 0.01624 * -0.67176 -0.07437 4793 school36 -0.53801 0.12456 -4.32 1.566e-05 *** -0.77466 -0.29561 5000 school37 -0.58770 0.18545 -3.17 0.001529 ** -0.94500 -0.22285 5000 school38 -0.58501 0.13318 -4.39 1.12e-05 *** -0.84442 -0.32698 5000 school39 -0.36314 0.13819 -2.63 0.008594 ** -0.64179 -0.10078 5000 school40 -0.59509 0.12546 -4.74 2.102e-06 *** -0.84498 -0.34916 4767 school41 -0.27868 0.13233 -2.11 0.03521 * -0.53438 -0.02248 5000 school42 -0.30358 0.13060 -2.32 0.0201 * -0.56070 -0.04476 5000 school43 -0.60257 0.13019 -4.63 3.688e-06 *** -0.86172 -0.34566 5187 school44 -0.64696 0.16385 -3.95 7.867e-05 *** -0.97064 -0.33148 5000 school45 -0.61923 0.13629 -4.54 5.531e-06 *** -0.89489 -0.35499 5000 school46 -0.79505 0.11992 -6.63 3.365e-11 *** -1.03403 -0.56131 5000 school47 -0.38876 0.12259 -3.17 0.001518 ** -0.62994 -0.14726 5000 school48 -0.70351 0.53567 -1.31 0.1891 -1.76493 0.34136 5000 school49 -0.46547 0.11499 -4.05 5.167e-05 *** -0.69548 -0.24752 5000 school50 -0.75914 0.12295 -6.17 6.645e-10 *** -1.00184 -0.52835 5000 school51 -0.49304 0.13332 -3.70 0.0002172 *** -0.75292 -0.23568 5000 school52 0.08045 0.13076 0.62 0.5384 -0.17737 0.33594 5000 school53 0.27814 0.12928 2.15 0.03145 * 0.02249 0.52788 5000 school54 -1.38939 0.28454 -4.88 1.045e-06 *** -1.93835 -0.83246 5000 school55 0.14161 0.13681 1.04 0.3007 -0.12420 0.40367 4343 school56 -0.43034 0.14871 -2.89 0.003805 ** -0.72218 -0.14161 5000 school57 -0.30572 0.12821 -2.38 0.0171 * -0.55498 -0.05162 5000 school58 -0.35011 0.15070 -2.32 0.02017 * -0.65009 -0.05589 4731 school59 -1.14990 0.14096 -8.16 3.421e-16 *** -1.42712 -0.87983 5000 school60 -0.26757 0.12130 -2.21 0.02739 * -0.50853 -0.03219 5209 school61 -0.46216 0.12859 -3.59 0.0003256 *** -0.71836 -0.21271 5000 school62 -0.46633 0.12318 -3.79 0.0001532 *** -0.70531 -0.22673 5000 school63 0.21091 0.16143 1.31 0.1914 -0.10413 0.52356 5000 school64 -0.23929 0.13108 -1.83 0.06793 . -0.50424 0.00927 5489 school65 -0.69068 0.12059 -5.73 1.018e-08 *** -0.93051 -0.45481 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 0.56280 0.01247 0.53949 0.58799 5000 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 33 > > > > > ############################################################################ > > proc.time() user system elapsed 5.84 0.71 15.64