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 > # > # 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 v3.09/ 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") > > ## 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: 3.09) multilevel model (Normal) Estimation algorithm: IGLS Elapsed time : 0.07s 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: 3.09) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.61s 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: 3.09) 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: 3.09) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 0.77s 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: 3.09) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 5.94s 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 5.35 0.84 14.87