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 > # > # 9 Modelling Complex Variance at Level 1 / Heteroscedasticity. . . . .111 > # > # 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) > > # User's input if necessary > > ## Read tutorial data > data(tutorial, package = "R2MLwiN") > > boy.normexam <- tutorial$normexam[which(tutorial$sex == "boy")] > girl.normexam <- tutorial$normexam[which(tutorial$sex == "girl")] > tab1 <- cbind(c(length(boy.normexam), mean(boy.normexam), sd(boy.normexam)), c(length(girl.normexam), mean(girl.normexam), + sd(girl.normexam)), c(length(tutorial$normexam), mean(tutorial$normexam), sd(tutorial$normexam))) > colnames(tab1) <- c("0", "1", "TOTAL") > rownames(tab1) <- c("N", "MEANS", "SDs") > formatC(round(tab1, 6)) 0 1 TOTAL N "1623" "2436" "4059" MEANS "-0.1404" "0.09332" "-0.000114" SDs "1.026" "0.9697" "0.9989" > > c5 <- tutorial$standlrt > intakecat <- rep(0, length(c5)) > intakecat[which(c5 > -1)] <- 1 > intakecat[which(c5 > -0.5)] <- 2 > intakecat[which(c5 > -0.1)] <- 3 > intakecat[which(c5 > 0.3)] <- 4 > intakecat[which(c5 > 0.7)] <- 5 > intakecat[which(c5 > 1.1)] <- 6 > normexam <- tutorial$normexam > tab2 <- cbind(c(sum(intakecat == 0), mean(normexam[intakecat == 0]), sd(normexam[intakecat == 0])), c(sum(intakecat == + 1), mean(normexam[intakecat == 1]), sd(normexam[intakecat == 1])), c(sum(intakecat == 2), mean(normexam[intakecat == + 2]), sd(normexam[intakecat == 2])), c(sum(intakecat == 3), mean(normexam[intakecat == 3]), sd(normexam[intakecat == + 3])), c(sum(intakecat == 4), mean(normexam[intakecat == 4]), sd(normexam[intakecat == 4])), c(sum(intakecat == + 5), mean(normexam[intakecat == 5]), sd(normexam[intakecat == 5])), c(sum(intakecat == 6), mean(normexam[intakecat == + 6]), sd(normexam[intakecat == 6])), c(length(intakecat), mean(normexam), sd(normexam))) > colnames(tab2) <- c("0", "1", "2", "3", "4", "5", "6", "TOTAL") > rownames(tab2) <- c("N", "MEANS", "SDs") > formatC(round(tab2, 6)) 0 1 2 3 4 5 6 N "612" "594" "619" "710" "547" "428" "549" MEANS "-0.887" "-0.4988" "-0.1908" "0.04392" "0.2785" "0.571" "0.9633" SDs "0.8548" "0.7743" "0.8065" "0.8112" "0.8118" "0.8235" "0.8382" TOTAL N "4059" MEANS "-0.000114" SDs "0.9989" > > # 9.1 MCMC algorithm for a 1 level Normal model with complex variation . 113 > > # 9.2 Setting up the model in MLwiN . . . . . . . . . . . . . . . . . . .115 > > ## The highest level comes first, then the second highest and so on > ## Fit the model > (mymodel1 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | student), estoptions = list(EstM = 1), data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 1 1 1 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9766.499969 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9760.691193 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9763.396134 Adapting finished and took 400 iterations Adapting took 400 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9762.204676 Burning in for 100 iterations out of 500 -2 * Loglike = 9766.695431 Burning in for 150 iterations out of 500 -2 * Loglike = 9764.610102 Burning in for 200 iterations out of 500 -2 * Loglike = 9764.749995 Burning in for 250 iterations out of 500 -2 * Loglike = 9762.418763 Burning in for 300 iterations out of 500 -2 * Loglike = 9769.068382 Burning in for 350 iterations out of 500 -2 * Loglike = 9766.374447 Burning in for 400 iterations out of 500 -2 * Loglike = 9763.134076 Burning in for 450 iterations out of 500 -2 * Loglike = 9763.584333 Burning in for 500 iterations out of 500 -2 * Loglike = 9767.212546 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 = 9762.079610 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9762.533507 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9766.943996 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9768.609816 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9769.493465 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9778.315751 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9765.810385 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9760.652864 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9761.044100 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9763.215978 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9760.352547 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9767.501440 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9760.517234 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9763.011238 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9762.939873 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9760.749485 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9765.009841 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9768.532779 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9767.420925 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9771.098732 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9769.264123 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9761.175337 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9760.614338 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9765.007348 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9766.603156 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9763.289638 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9766.744080 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9760.835772 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9763.521102 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9764.441843 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9769.415393 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9768.271667 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9762.616886 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9763.365448 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9767.008996 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9762.729040 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9765.427403 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9761.214979 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9765.582994 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9763.211991 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9770.349020 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9761.793153 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9762.590922 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9762.525152 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9760.414653 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9765.083295 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9765.397386 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9764.511084 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9764.280025 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9768.763982 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9767.165864 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9761.929896 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9761.228934 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9764.362783 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9760.888619 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9761.164369 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9766.137012 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9764.110567 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9763.492263 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9766.714804 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9767.451871 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9763.164055 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9765.553907 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9765.219323 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9762.061486 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9762.844864 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9762.489898 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9761.647777 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9770.629363 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9765.865037 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9760.625037 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9764.485725 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9760.495316 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9760.768488 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9767.501945 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9765.275615 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9760.689301 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9761.229924 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9765.990761 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9762.714872 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9761.061858 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9762.234497 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9769.859004 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9762.003690 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9761.347557 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9762.959081 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9762.557707 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9762.620705 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9762.953659 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9761.743284 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9763.010072 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9762.496540 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9765.461805 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9760.736841 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9760.336194 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9767.376729 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9763.680613 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9762.504236 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9761.593670 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9771.679148 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9764.4 S.D. = 3.1553 S.E.M. = 0.044623 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 3.26s 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 9764.430 9759.606 4.824 9769.254 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 + standlrt | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.00185 0.01245 -0.15 0.8817 -0.02598 0.02212 4741 standlrt 0.59572 0.01306 45.63 0 *** 0.57049 0.62155 4727 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 0.63855 0.01758 0.60523 0.67506 462 cov_Intercept_standlrt 0.00273 0.00734 -0.01144 0.01689 896 var_standlrt 0.01204 0.01087 -0.00764 0.03429 489 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > trajectories(mymodel1, Range = c(4501, 5000)) > > l1varfn <- mymodel1@RP["RP1_var_Intercept"] + 2 * mymodel1@RP["RP1_cov_Intercept_standlrt"] * tutorial$standlrt + + mymodel1@RP["RP1_var_standlrt"] * tutorial$standlrt^2 > plot(sort(tutorial$standlrt), l1varfn[order(tutorial$standlrt)], xlab = "standlrt", ylab = "l1varfn", type = "l") > abline(v = 0, lty = "dotted") > > # 9.3 Complex variance functions in multilevel models . . . . . . . . . .119 > > ## The highest level comes first, then the second highest and so on Choose option(s) for inference Fit the model > (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1), + data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 BURNING IN... Burning in for 50 iterations out of 500 -2 * Loglike = 9136.615416 Burning in for 100 iterations out of 500 -2 * Loglike = 9129.472590 Burning in for 150 iterations out of 500 -2 * Loglike = 9137.752388 Burning in for 200 iterations out of 500 -2 * Loglike = 9149.641457 Burning in for 250 iterations out of 500 -2 * Loglike = 9113.737768 Burning in for 300 iterations out of 500 -2 * Loglike = 9127.854908 Burning in for 350 iterations out of 500 -2 * Loglike = 9099.670195 Burning in for 400 iterations out of 500 -2 * Loglike = 9107.133017 Burning in for 450 iterations out of 500 -2 * Loglike = 9108.686421 Burning in for 500 iterations out of 500 -2 * Loglike = 9142.796685 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9114.789855 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9128.936360 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9120.626663 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9140.221260 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9133.366931 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9112.633267 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9110.267312 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9134.271816 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9146.903828 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9118.578020 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9132.630258 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9105.115711 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9126.654041 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9138.820724 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9119.239813 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9145.879653 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9132.483550 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9094.657080 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9118.502105 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9094.902922 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9135.645832 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9128.926707 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9104.509733 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9108.989181 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9111.759420 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9103.538840 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9120.142978 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9117.533977 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9114.717113 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9118.929584 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9146.845851 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9126.654978 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9127.854549 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9114.945398 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9156.130168 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9134.732656 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9142.867734 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9137.471434 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9127.702153 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9133.939751 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9107.640871 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9137.519015 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9147.472132 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9104.767457 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9118.396071 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9143.494727 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9130.468641 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9137.527730 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9106.747459 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9154.348069 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9142.340919 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9100.831693 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9131.653716 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9151.916582 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9165.855130 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9125.508254 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9146.519009 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9122.524343 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9128.808395 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9125.880481 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9130.006670 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9116.446060 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9105.444348 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9141.749060 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9122.819747 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9140.592905 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9119.521430 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9137.983211 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9128.855413 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9130.638160 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9119.619021 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9124.980114 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9135.552922 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9127.477138 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9114.227379 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9110.953194 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9118.839082 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9118.763419 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9117.590737 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9106.053640 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9112.274103 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9115.311806 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9122.276612 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9120.226668 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9140.403968 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9153.535294 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9117.253885 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9116.415887 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9136.007855 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9119.650550 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9108.406619 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9104.027872 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9104.517145 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9102.506754 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9125.791725 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9121.949129 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9123.201133 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9116.574595 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9120.080554 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9120.628553 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9123.2 S.D. = 16.792 S.E.M. = 0.23747 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 2.33s Number of obs: 4059 (from total 4059) Number of iter.: 5000 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9123.206 9031.714 91.492 9214.698 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.01257 0.04089 -0.31 0.7585 -0.09055 0.06865 209 standlrt 0.55645 0.02084 26.70 4.362e-157 *** 0.51501 0.59701 596 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09711 0.02001 0.06465 0.14261 2549 cov_Intercept_standlrt 0.01933 0.00739 0.00660 0.03537 1740 var_standlrt 0.01526 0.00485 0.00772 0.02662 846 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55440 0.01242 0.53052 0.57904 4750 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > l2varfn <- mymodel2@RP["RP2_var_Intercept"] + 2 * mymodel2@RP["RP2_cov_Intercept_standlrt"] * tutorial$standlrt + + mymodel2@RP["RP2_var_standlrt"] * tutorial$standlrt^2 > l1varfn <- mymodel2@RP["RP1_var_Intercept"] > plot(sort(tutorial$standlrt), l2varfn[order(tutorial$standlrt)], xlab = "standlrt", ylab = "varfns", ylim = c(0, 0.6), + type = "l") > abline(h = l1varfn) > abline(v = 0, lty = "dotted") > > ## Fit the model > (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | student), estoptions = list(EstM = 1), + data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 iteration 4 iteration 5 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9099.632934 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9095.234121 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9108.040574 Adapting for 400 iterations (Maximum 5000) -2 * Loglike = 9125.246080 Adapting finished and took 500 iterations Adapting took 500 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9105.739182 Burning in for 100 iterations out of 500 -2 * Loglike = 9113.485562 Burning in for 150 iterations out of 500 -2 * Loglike = 9092.874934 Burning in for 200 iterations out of 500 -2 * Loglike = 9109.755154 Burning in for 250 iterations out of 500 -2 * Loglike = 9119.910247 Burning in for 300 iterations out of 500 -2 * Loglike = 9086.997679 Burning in for 350 iterations out of 500 -2 * Loglike = 9107.980832 Burning in for 400 iterations out of 500 -2 * Loglike = 9133.947281 Burning in for 450 iterations out of 500 -2 * Loglike = 9106.969321 Burning in for 500 iterations out of 500 -2 * Loglike = 9103.596289 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9127.616499 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9100.808560 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9124.332854 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9140.096016 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9171.123648 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9141.850163 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9118.271170 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9140.173895 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9110.659839 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9125.076865 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9136.596904 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9132.968316 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9127.312966 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9139.073098 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9108.130448 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9120.083361 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9121.172264 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9118.406431 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9144.695696 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9116.176756 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9146.287322 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9102.292531 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9136.648477 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9098.317507 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9104.528163 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9139.208287 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9136.234359 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9105.588858 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9109.132080 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9108.510277 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9131.558765 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9121.293185 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9108.148543 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9128.067069 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9129.750022 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9136.442452 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9135.198710 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9140.086758 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9128.330397 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9142.069765 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9112.930534 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9125.532425 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9116.841342 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9117.998366 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9133.844159 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9135.382316 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9115.577983 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9088.626800 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9139.488496 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9173.677234 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9113.240980 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9111.222010 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9121.141361 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9127.820948 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9099.945782 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9128.556103 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9128.655378 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9105.369381 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9103.756617 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9131.855493 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9125.998920 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9146.792035 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9119.719090 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9112.898974 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9112.663987 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9147.198103 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9114.181102 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9157.262076 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9125.431521 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9142.301209 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9144.172385 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9128.173175 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9120.700767 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9108.198774 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9125.692288 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9100.992755 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9110.241273 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9105.221843 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9107.465510 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9144.282125 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9137.613624 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9113.791798 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9113.441099 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9099.415205 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9119.878468 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9120.360589 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9073.038481 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9154.508347 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9122.778401 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9124.207274 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9131.881672 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9105.804092 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9108.154598 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9134.577604 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9107.856253 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9123.489794 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9115.203120 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9112.917831 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9132.513391 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9123.435109 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9121.0 S.D. = 16.890 S.E.M. = 0.23886 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 6.03s 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 9120.983 9028.659 92.323 9213.306 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.01113 0.03879 -0.29 0.7743 -0.08856 0.06789 215 standlrt 0.55863 0.01948 28.68 7.142e-181 *** 0.52010 0.59578 724 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09672 0.01988 0.06447 0.14035 3077 cov_Intercept_standlrt 0.01963 0.00741 0.00670 0.03601 1538 var_standlrt 0.01492 0.00468 0.00768 0.02559 851 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55327 0.01513 0.52425 0.58360 564 cov_Intercept_standlrt -0.01477 0.00654 -0.02761 -0.00134 1022 var_standlrt 0.00215 0.00892 -0.01438 0.02091 560 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Remove term standlrt/standlrt from the level 1 covariance matrix > clre <- matrix(, nrow = 3, ncol = 1) > clre[1, 1] <- 1 > clre[2, 1] <- "standlrt" > clre[3, 1] <- "standlrt" > > ## Fit the model > (mymodel4 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | student), estoptions = list(EstM = 1, + clre = clre), data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9103.608537 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9104.794384 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9106.587808 Adapting finished and took 400 iterations Adapting took 400 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9084.012286 Burning in for 100 iterations out of 500 -2 * Loglike = 9141.372249 Burning in for 150 iterations out of 500 -2 * Loglike = 9139.924757 Burning in for 200 iterations out of 500 -2 * Loglike = 9147.919590 Burning in for 250 iterations out of 500 -2 * Loglike = 9112.965804 Burning in for 300 iterations out of 500 -2 * Loglike = 9134.813097 Burning in for 350 iterations out of 500 -2 * Loglike = 9126.493198 Burning in for 400 iterations out of 500 -2 * Loglike = 9132.058349 Burning in for 450 iterations out of 500 -2 * Loglike = 9110.128490 Burning in for 500 iterations out of 500 -2 * Loglike = 9122.485183 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9113.827004 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9120.344774 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9131.571748 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9122.675089 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9109.400100 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9083.311268 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9099.539189 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9110.952384 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9098.254055 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9112.838223 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9119.123120 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9107.725474 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9137.566142 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9127.469372 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9133.232775 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9109.845660 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9104.634721 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9116.117349 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9131.814804 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9103.069871 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9124.351722 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9127.129672 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9119.558083 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9130.582940 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9135.941001 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9114.183876 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9103.545768 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9136.561307 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9116.921294 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9138.400180 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9100.716722 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9116.150103 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9114.982774 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9093.000974 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9101.102749 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9124.873918 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9118.299658 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9106.783387 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9130.420897 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9091.230699 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9126.291871 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9123.904320 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9130.713719 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9108.373348 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9100.333375 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9096.674412 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9107.961560 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9124.296642 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9115.375578 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9107.832295 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9086.485266 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9086.334257 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9102.834515 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9087.637119 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9146.131898 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9147.761211 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9144.639618 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9101.821107 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9116.112986 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9142.605812 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9103.559125 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9100.487145 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9114.395407 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9112.983182 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9107.293014 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9117.535013 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9109.291518 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9124.974215 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9091.478123 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9121.507439 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9139.082276 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9101.265442 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9095.316154 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9129.938008 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9132.250234 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9141.292142 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9138.141800 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9098.604112 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9130.551409 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9101.352643 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9127.468174 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9124.600038 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9106.285622 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9110.730618 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9132.395836 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9112.423021 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9093.589587 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9112.306785 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9098.915403 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9122.868776 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9107.372921 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9105.571833 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9099.547815 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9106.817675 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9104.380929 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9121.932768 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9108.100616 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9129.336859 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9117.824475 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9133.520562 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9118.9 S.D. = 16.764 S.E.M. = 0.23708 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 5.05s 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 9118.930 9027.486 91.444 9210.375 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 + standlrt | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.01652 0.04238 -0.39 0.6968 -0.10004 0.06424 201 standlrt 0.55661 0.02069 26.90 2.234e-159 *** 0.51697 0.59685 665 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09740 0.02001 0.06503 0.14251 2668 cov_Intercept_standlrt 0.02026 0.00741 0.00720 0.03639 1601 var_standlrt 0.01534 0.00459 0.00810 0.02572 923 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55609 0.01235 0.53182 0.58156 1206 cov_Intercept_standlrt -0.01496 0.00635 -0.02760 -0.00301 899 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 9.4 Relationship with gender . . . . . . . . . . . . . . . . . . . . . 123 > > tutorial$girl <- as.integer(tutorial$sex) - 1 > > ## Remove term standlrt/standlrt and girl/girl from the level 1 covariance matrix > clre <- matrix(, nrow = 3, ncol = 2) > clre[1, 1] <- 1 > clre[2, 1] <- "standlrt" > clre[3, 1] <- "standlrt" > clre[1, 2] <- 1 > clre[2, 2] <- "girl" > clre[3, 2] <- "girl" > > (mymodel5 <- runMLwiN(normexam ~ 1 + standlrt + girl + (1 + standlrt | school) + (1 + standlrt + girl | student), + estoptions = list(EstM = 1, clre = clre), data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9110.921196 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9067.047034 Adapting for 300 iterations (Maximum 5000) -2 * Loglike = 9066.447766 Adapting for 400 iterations (Maximum 5000) -2 * Loglike = 9061.376957 Adapting finished and took 500 iterations Adapting took 500 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9124.001759 Burning in for 100 iterations out of 500 -2 * Loglike = 9077.859505 Burning in for 150 iterations out of 500 -2 * Loglike = 9064.900895 Burning in for 200 iterations out of 500 -2 * Loglike = 9093.705697 Burning in for 250 iterations out of 500 -2 * Loglike = 9110.246177 Burning in for 300 iterations out of 500 -2 * Loglike = 9091.414712 Burning in for 350 iterations out of 500 -2 * Loglike = 9129.468588 Burning in for 400 iterations out of 500 -2 * Loglike = 9067.771448 Burning in for 450 iterations out of 500 -2 * Loglike = 9076.249530 Burning in for 500 iterations out of 500 -2 * Loglike = 9112.539637 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9109.441602 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9090.422079 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9071.175973 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9077.353111 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9075.501213 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9081.689949 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9093.284882 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9070.820963 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9081.675736 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9075.932203 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9054.041060 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9081.479172 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9092.010277 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9113.444057 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9106.311211 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9048.691686 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9081.451283 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9088.175631 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9090.571763 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9084.208026 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9053.899192 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9105.029614 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9077.990293 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9109.843943 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9073.546170 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9104.987083 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9051.624287 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9095.823029 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9085.213635 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9097.600879 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9061.804961 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9079.527365 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9096.816295 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9120.389673 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9113.120148 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9078.905991 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9103.846688 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9105.149997 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9070.717474 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9091.035945 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9074.052266 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9067.193953 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9082.591146 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9081.899722 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9101.348857 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9076.064207 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9056.630332 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9096.711090 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9091.716613 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9116.488536 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9056.518589 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9092.519940 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9114.347284 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9067.723578 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9064.182703 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9094.947224 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9106.551782 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9123.947813 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9070.667462 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9092.636405 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9080.711677 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9093.806902 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9048.962438 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9076.323723 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9071.930033 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9056.644116 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9118.885631 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9063.212911 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9089.217762 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9102.912147 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9122.683629 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9079.149034 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9115.194344 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9089.251553 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9092.762311 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9092.979223 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9082.110834 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9073.710397 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9046.340427 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9080.561444 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9077.465145 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9076.748862 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9080.497809 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9084.648608 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9086.241051 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9078.416276 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9061.218142 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9078.185988 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9073.149276 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9089.791408 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9102.255345 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9062.224030 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9071.012282 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9082.055753 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9087.572831 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9093.210045 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9112.740200 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9103.127892 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9069.234890 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9052.042819 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9084.8 S.D. = 17.343 S.E.M. = 0.24527 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 7.68s 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 9084.784 8991.147 93.638 9178.422 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + girl + (1 + standlrt | school) + (1 + standlrt + girl | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.10748 0.04345 -2.47 0.01337 * -0.18925 -0.01782 230 standlrt 0.55535 0.02041 27.21 4.552e-163 *** 0.51455 0.59535 467 girl 0.17549 0.03235 5.43 5.785e-08 *** 0.11132 0.23867 1794 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09217 0.01903 0.06117 0.13576 3143 cov_Intercept_standlrt 0.02078 0.00723 0.00827 0.03659 1643 var_standlrt 0.01551 0.00475 0.00806 0.02631 893 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.58687 0.02009 0.55016 0.62641 260 cov_Intercept_standlrt -0.03377 0.00974 -0.05235 -0.01430 263 cov_Intercept_girl -0.02973 0.01279 -0.05668 -0.00572 269 cov_standlrt_girl 0.03226 0.01247 0.00791 0.05657 273 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > l2varfn <- mymodel5@RP["RP2_var_Intercept"] + 2 * mymodel5@RP["RP2_cov_Intercept_standlrt"] * tutorial$standlrt + + mymodel5@RP["RP2_var_standlrt"] * tutorial$standlrt^2 > l1varfnboys <- mymodel5@RP["RP1_var_Intercept"] + 2 * mymodel5@RP["RP1_cov_Intercept_standlrt"] * tutorial$standlrt > l1varfngirls <- mymodel5@RP["RP1_var_Intercept"] + 2 * mymodel5@RP["RP1_cov_Intercept_standlrt"] * tutorial$standlrt + + 2 * mymodel5@RP["RP1_cov_Intercept_girl"] + 2 * mymodel5@RP["RP1_cov_standlrt_girl"] * tutorial$standlrt > plot(sort(tutorial$standlrt), l2varfn[order(tutorial$standlrt)], xlab = "standlrt", ylab = "varfns", ylim = c(0, 0.8), + type = "l") > lines(sort(tutorial$standlrt), l1varfnboys[order(tutorial$standlrt)]) > lines(sort(tutorial$standlrt), l1varfngirls[order(tutorial$standlrt)]) > abline(v = 0, lty = "dotted") > > # 9.5 Alternative log precision formulation . . . . . . . . . . . . . . .126 > > (mymodel6 <- runMLwiN(normexam ~ 1 + standlrt + girl + (1 + standlrt | school) + (1 + standlrt + girl | student), + estoptions = list(EstM = 1, clre = clre, mcmcMeth = list(lclo = 1)), data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence not achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 G30[1] G30[2] 1 1 1 1 1 1 RUNNING ADAPTIVE PROCEDURE AND BURNING IN... Adapting for 100 iterations (Maximum 5000) -2 * Loglike = 9071.607665 Adapting for 200 iterations (Maximum 5000) -2 * Loglike = 9057.435736 Adapting finished and took 300 iterations Adapting took 300 iterations Burning in for 50 iterations out of 500 -2 * Loglike = 9081.145444 Burning in for 100 iterations out of 500 -2 * Loglike = 9095.321762 Burning in for 150 iterations out of 500 -2 * Loglike = 9081.767979 Burning in for 200 iterations out of 500 -2 * Loglike = 9084.489028 Burning in for 250 iterations out of 500 -2 * Loglike = 9117.683002 Burning in for 300 iterations out of 500 -2 * Loglike = 9076.173678 Burning in for 350 iterations out of 500 -2 * Loglike = 9086.357099 Burning in for 400 iterations out of 500 -2 * Loglike = 9071.482363 Burning in for 450 iterations out of 500 -2 * Loglike = 9101.989220 Burning in for 500 iterations out of 500 -2 * Loglike = 9090.600550 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5000 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5000, Stored update 50 of 5000 -2 * Loglike = 9038.877398 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9089.530247 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9130.096619 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9091.853893 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9102.319059 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9087.969842 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9082.357312 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9081.005283 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9102.545164 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9082.449441 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9079.699415 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9112.255740 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9074.152343 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9066.515330 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9070.486740 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9073.502814 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9084.108359 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9072.075290 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9063.883258 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9069.678222 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9085.038716 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9065.067694 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9070.473029 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9099.935038 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9085.441751 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9080.501962 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9075.678308 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9070.491287 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9068.604256 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9093.037544 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9083.115979 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9086.563486 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9099.717911 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9080.093201 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9118.474318 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9087.668810 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9089.845693 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9079.390599 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9078.541589 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9060.052507 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9074.099706 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9095.174384 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9067.108592 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9089.900970 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9100.632668 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9093.757378 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9083.762573 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9090.360921 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9116.536864 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9076.415490 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9096.960905 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9070.411601 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9074.555075 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9075.215433 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9080.850771 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9062.190956 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9098.711168 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9114.355793 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9063.171673 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9082.151592 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9055.118453 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9079.305726 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9076.177301 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9085.017116 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9079.686487 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9115.303961 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9101.767043 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9103.755484 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9062.894988 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9094.214127 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9060.678721 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9061.683134 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9099.394638 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9086.181211 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9063.805610 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9064.333526 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9067.335725 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9065.833301 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9094.501616 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9120.973075 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9100.812824 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9079.303021 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9105.741798 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9089.288527 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9073.236320 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9095.297416 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9089.099875 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9114.863946 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9086.506897 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9107.759461 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9095.931245 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9099.030241 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9107.259082 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9112.847385 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9089.495614 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9075.627534 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9088.741093 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9078.614947 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9086.408920 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9076.916867 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9084.8 S.D. = 16.891 S.E.M. = 0.23888 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.11) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 9.61s 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 9084.850 8991.299 93.551 9178.401 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + girl + (1 + standlrt | school) + (1 + standlrt + girl | student) Level 2: school Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept -0.11328 0.04646 -2.44 0.01477 * -0.20356 -0.02398 197 standlrt 0.55263 0.02077 26.61 5.463e-156 *** 0.51190 0.59357 478 girl 0.17578 0.03139 5.60 2.154e-08 *** 0.11402 0.23831 1959 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.09311 0.01928 0.06243 0.13820 2688 cov_Intercept_standlrt 0.02101 0.00712 0.00887 0.03665 1763 var_standlrt 0.01568 0.00465 0.00818 0.02626 827 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.54296 0.03417 0.47895 0.61279 331 cov_Intercept_standlrt 0.05343 0.01795 0.01877 0.08898 328 cov_Intercept_girl 0.04945 0.02167 0.00661 0.09159 319 cov_standlrt_girl -0.04945 0.02325 -0.09629 -0.00448 300 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > l2varfn <- mymodel6@RP["RP2_var_Intercept"] + 2 * mymodel6@RP["RP2_cov_Intercept_standlrt"] * tutorial$standlrt + + mymodel6@RP["RP2_var_standlrt"] * tutorial$standlrt^2 > l1varfnboys <- 1/exp(mymodel6@RP["RP1_var_Intercept"] + 2 * mymodel6@RP["RP1_cov_Intercept_standlrt"] * tutorial$standlrt) > l1varfngirls <- 1/exp(mymodel6@RP["RP1_var_Intercept"] + 2 * mymodel6@RP["RP1_cov_Intercept_standlrt"] * tutorial$standlrt + + 2 * mymodel6@RP["RP1_cov_Intercept_girl"] + 2 * mymodel6@RP["RP1_cov_standlrt_girl"] * tutorial$standlrt) > plot(sort(tutorial$standlrt), l2varfn[order(tutorial$standlrt)], xlab = "standlrt", ylab = "varfns", ylim = c(0, 0.8), + type = "l") > lines(sort(tutorial$standlrt), l1varfnboys[order(tutorial$standlrt)]) > lines(sort(tutorial$standlrt), l1varfngirls[order(tutorial$standlrt)]) > abline(v = 0, lty = "dotted") > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .128 > > > > > > ############################################################################ > > proc.time() user system elapsed 5.46 0.93 41.78