R version 3.6.3 (2020-02-29) -- "Holding the Windsock" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-w64-mingw32/x64 (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ############################################################################ > # MLwiN MCMC Manual > # > # 6 Random Slopes Regression Models . . . . . . . . . . . . . . . . . . 71 > # > # Browne, W.J. (2009) MCMC Estimation in MLwiN, v2.13. Centre for > # Multilevel Modelling, University of Bristol. > ############################################################################ > # R script to replicate all analyses using R2MLwiN > # > # Zhang, Z., Charlton, C., Parker, R, Leckie, G., and Browne, W.J. > # Centre for Multilevel Modelling, 2012 > # http://www.bristol.ac.uk/cmm/software/R2MLwiN/ > ############################################################################ > > library(R2MLwiN) R2MLwiN: A package to run models implemented in MLwiN from R Copyright 2013-2017 Zhengzheng Zhang, Christopher M. J. Charlton, Richard M. A. Parker, William J. Browne and George Leckie Support provided by the Economic and Social Research Council (ESRC) (Grants RES-149-25-1084, RES-576-25-0032 and ES/K007246/1) To cite R2MLwiN in publications use: Zhengzheng Zhang, Richard M. A. Parker, Christopher M. J. Charlton, George Leckie, William J. Browne (2016). R2MLwiN: A Package to Run MLwiN from within R. Journal of Statistical Software, 72(10), 1-43. doi:10.18637/jss.v072.i10 A BibTeX entry for LaTeX users is @Article{, title = {{R2MLwiN}: A Package to Run {MLwiN} from within {R}}, author = {Zhengzheng Zhang and Richard M. A. Parker and Christopher M. J. Charlton and George Leckie and William J. Browne}, journal = {Journal of Statistical Software}, year = {2016}, volume = {72}, number = {10}, pages = {1--43}, doi = {10.18637/jss.v072.i10}, } The MLwiN_path option is currently set to C:/Program Files/MLwiN v3.05/ To change this use: options(MLwiN_path="") > # MLwiN folder > mlwin <- getOption("MLwiN_path") > while (!file.access(mlwin, mode = 1) == 0) { + cat("Please specify the root MLwiN folder or the full path to the MLwiN executable:\n") + mlwin <- scan(what = character(0), sep = "\n") + mlwin <- gsub("\\", "/", mlwin, fixed = TRUE) + } > options(MLwiN_path = mlwin) > > ## Read tutorial data > data(tutorial, package = "R2MLwiN") > > ## Choose MCMC algoritm for estimation (IGLS will be used to obtain starting values for MCMC) > (mymodel <- runMLwiN(normexam ~ 1 + standlrt + school + school:standlrt + (1 | student), estoptions = list(EstM = 1), + data = tutorial)) MLwiN is running, please wait...... /nogui option ignored ECHO 0 Echoing is ON BATC 1 Batch mode is ON MAXI 2 STAR iteration 0 iteration 1 Convergence achieved TOLE 2 MAXI 20 BATC 1 Batch mode is ON NEXT iteration 2 Convergence achieved ECHO 0 Echoing is ON MCMC 0 500 1 5.8 50 10 1 1 1 1 1 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9119.936606 Burning in for 100 iterations out of 500 -2 * Loglike = 9117.034611 Burning in for 150 iterations out of 500 -2 * Loglike = 9090.030092 Burning in for 200 iterations out of 500 -2 * Loglike = 9099.932619 Burning in for 250 iterations out of 500 -2 * Loglike = 9129.180995 Burning in for 300 iterations out of 500 -2 * Loglike = 9121.270863 Burning in for 350 iterations out of 500 -2 * Loglike = 9115.703431 Burning in for 400 iterations out of 500 -2 * Loglike = 9093.255601 Burning in for 450 iterations out of 500 -2 * Loglike = 9120.386068 Burning in for 500 iterations out of 500 -2 * Loglike = 9135.961729 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 = 9149.956713 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9129.369232 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9113.075114 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9093.729310 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9130.591824 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9131.826204 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9121.865515 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9140.230368 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9130.272725 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9085.515965 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9127.746907 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9099.687254 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9127.297936 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9133.269951 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9098.937249 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9140.213530 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9115.936825 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9108.530531 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9143.538081 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9103.883578 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9106.689478 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9091.585002 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9099.063402 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9110.317621 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9118.644144 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9114.615441 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9108.980209 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9085.708240 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9122.033880 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9129.011690 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9117.401243 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9120.657070 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9125.517977 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9128.403907 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9130.673651 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9118.082719 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9137.537707 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9121.852444 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9103.000083 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9106.253041 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9124.491183 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9106.709070 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9125.531869 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9109.270763 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9093.640548 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9099.296228 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9132.833067 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9096.835676 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9135.892218 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9088.525756 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9147.148815 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9123.080111 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9100.404135 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9114.959150 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9093.551174 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9139.411542 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9108.750747 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9107.604239 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9117.700537 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9141.081862 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9139.752056 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9130.035537 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9091.414396 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9095.645972 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9105.192749 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9109.954920 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9104.549680 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9106.613572 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9133.390207 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9118.490399 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9110.100075 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9109.108827 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9118.322471 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9098.440260 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9120.673916 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9114.666679 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9115.259856 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9120.634712 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9111.770336 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9116.366252 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9127.717255 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9116.466304 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9111.464332 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9128.903631 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9133.619252 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9106.662535 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9134.390873 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9106.406774 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9099.737154 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9115.093684 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9127.185960 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9126.406095 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9134.989748 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9097.564486 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9130.281318 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9133.887294 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9126.953067 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9112.897638 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9133.242546 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9110.024837 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9117.7 S.D. = 16.213 S.E.M. = 0.22928 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) Estimation algorithm: MCMC Elapsed time : 14.31s 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 9117.709 8986.955 130.754 9248.463 --------------------------------------------------------------------------------------------------- The model formula: normexam ~ 1 + standlrt + school + school:standlrt + (1 | student) Level 1: student --------------------------------------------------------------------------------------------------- The fixed part estimates: Coef. Std. Err. z Pr(>|z|) [95% Cred. Interval] ESS Intercept 0.38290 0.08828 4.34 1.442e-05 *** 0.20991 0.55408 5000 standlrt 0.70895 0.08279 8.56 1.093e-17 *** 0.54831 0.87268 4538 school2 0.10013 0.13858 0.72 0.47 -0.16773 0.37429 5000 school3 0.17342 0.14887 1.16 0.244 -0.11407 0.46519 5000 school4 -0.37976 0.12029 -3.16 0.001594 ** -0.61635 -0.14079 5000 school5 -0.12170 0.15989 -0.76 0.4466 -0.43903 0.18254 4799 school6 0.21862 0.13785 1.59 0.1128 -0.05278 0.49300 5181 school7 0.01629 0.11875 0.14 0.8909 -0.22094 0.24603 5000 school8 -0.40723 0.11463 -3.55 0.0003813 *** -0.63336 -0.18510 5482 school9 -0.61948 0.16267 -3.81 0.0001399 *** -0.94610 -0.31079 5000 school10 -0.70886 0.13817 -5.13 2.892e-07 *** -0.97603 -0.44045 4779 school11 -0.11712 0.14242 -0.82 0.4109 -0.39715 0.16062 5000 school12 -0.45475 0.14162 -3.21 0.001322 ** -0.73027 -0.17375 4832 school13 -0.53385 0.12696 -4.20 2.613e-05 *** -0.78124 -0.28619 5000 school14 -0.56613 0.10503 -5.39 7.03e-08 *** -0.76868 -0.35612 5000 school15 -0.62216 0.12237 -5.08 3.692e-07 *** -0.86359 -0.38063 5000 school16 -0.76927 0.12172 -6.32 2.616e-10 *** -1.01092 -0.52856 5000 school17 -0.57065 0.11020 -5.18 2.24e-07 *** -0.78733 -0.35864 5000 school18 -0.44192 0.11082 -3.99 6.669e-05 *** -0.65536 -0.22546 5000 school19 -0.48086 0.14566 -3.30 0.0009627 *** -0.77216 -0.20043 4782 school20 -0.11252 0.15588 -0.72 0.4704 -0.41283 0.19879 5000 school21 -0.11112 0.12399 -0.90 0.3701 -0.35100 0.13252 5000 school22 -0.84815 0.11721 -7.24 4.614e-13 *** -1.08053 -0.62337 5000 school23 -1.02076 0.16897 -6.04 1.533e-09 *** -1.35179 -0.69109 5000 school24 -0.20442 0.15976 -1.28 0.2007 -0.51829 0.10310 5268 school25 -0.64864 0.13413 -4.84 1.325e-06 *** -0.90618 -0.38797 5000 school26 -0.42008 0.13692 -3.07 0.002154 ** -0.69047 -0.15215 4753 school27 -0.34584 0.16933 -2.04 0.04111 * -0.68571 -0.02116 5000 school28 -1.15621 0.13502 -8.56 1.099e-17 *** -1.41556 -0.89382 4798 school29 -0.17815 0.12708 -1.40 0.1609 -0.43151 0.07267 4766 school30 -0.26334 0.14964 -1.76 0.07844 . -0.56106 0.02626 4616 school31 -0.42222 0.15896 -2.66 0.007903 ** -0.74809 -0.11374 5924 school32 -0.32062 0.15904 -2.02 0.04381 * -0.63047 -0.01274 5000 school33 -0.34315 0.12273 -2.80 0.005173 ** -0.58184 -0.10344 5000 school34 -0.49002 0.17480 -2.80 0.005058 ** -0.84127 -0.15147 5000 school35 -0.24970 0.15216 -1.64 0.1008 -0.55304 0.04965 5000 school36 -0.58956 0.12496 -4.72 2.381e-06 *** -0.83332 -0.34787 4764 school37 -0.86752 0.21662 -4.00 6.207e-05 *** -1.28647 -0.44226 5000 school38 -0.53894 0.13445 -4.01 6.111e-05 *** -0.79786 -0.27536 4757 school39 -0.25471 0.13931 -1.83 0.0675 . -0.52426 0.01244 5000 school40 -0.63359 0.12397 -5.11 3.209e-07 *** -0.87686 -0.39309 5000 school41 -0.16889 0.13432 -1.26 0.2086 -0.43264 0.08814 5000 school42 -0.29824 0.13341 -2.24 0.02539 * -0.55886 -0.03233 5000 school43 -0.55333 0.14362 -3.85 0.0001168 *** -0.83676 -0.27377 5000 school44 -0.73002 0.16492 -4.43 9.582e-06 *** -1.05666 -0.40743 5000 school45 -0.50476 0.13805 -3.66 0.0002557 *** -0.77549 -0.23119 5000 school46 -0.77386 0.12096 -6.40 1.578e-10 *** -1.00495 -0.53702 5000 school47 -0.41177 0.12131 -3.39 0.0006879 *** -0.65019 -0.17659 5000 school48 -3.63374 5.32415 -0.68 0.4949 -13.96691 6.93431 5000 school49 -0.33305 0.11213 -2.97 0.002975 ** -0.55237 -0.11402 5890 school50 -0.70863 0.12540 -5.65 1.597e-08 *** -0.95365 -0.46210 5387 school51 -0.52562 0.13455 -3.91 9.365e-05 *** -0.78898 -0.26243 5128 school52 0.00763 0.13335 0.06 0.9544 -0.24943 0.27087 5000 school53 0.21035 0.13154 1.60 0.1098 -0.05099 0.46567 5000 school54 -1.03856 0.38787 -2.68 0.007415 ** -1.80332 -0.27395 5592 school55 0.16765 0.13918 1.20 0.2284 -0.10929 0.44219 5000 school56 -0.34183 0.14821 -2.31 0.02109 * -0.62682 -0.05127 5000 school57 -0.34098 0.12752 -2.67 0.007496 ** -0.58704 -0.08691 5000 school58 -0.17528 0.15594 -1.12 0.261 -0.48107 0.12209 5000 school59 -1.23516 0.15274 -8.09 6.124e-16 *** -1.52863 -0.93878 5000 school60 -0.13077 0.12169 -1.07 0.2825 -0.37265 0.10175 4752 school61 -0.42049 0.12884 -3.26 0.0011 ** -0.67407 -0.17301 5000 school62 -0.43812 0.12697 -3.45 0.0005595 *** -0.68815 -0.19037 5000 school63 0.30104 0.16352 1.84 0.06563 . -0.02269 0.61808 4787 school64 -0.34755 0.14086 -2.47 0.01361 * -0.62440 -0.06432 5000 school65 -0.55777 0.12157 -4.59 4.478e-06 *** -0.79956 -0.32058 5000 standlrt:school2 0.05052 0.12186 0.41 0.6784 -0.18831 0.29096 5000 standlrt:school3 -0.12956 0.14234 -0.91 0.3627 -0.41410 0.14848 5000 standlrt:school4 0.05251 0.11609 0.45 0.651 -0.17647 0.27633 5000 standlrt:school5 -0.02686 0.19510 -0.14 0.8905 -0.41360 0.34674 5000 standlrt:school6 -0.17075 0.12779 -1.34 0.1815 -0.42077 0.07631 5000 standlrt:school7 -0.46650 0.12288 -3.80 0.0001469 *** -0.71087 -0.22597 4628 standlrt:school8 -0.14051 0.10599 -1.33 0.1849 -0.34922 0.06428 5000 standlrt:school9 -0.30826 0.13975 -2.21 0.0274 * -0.58751 -0.03468 5154 standlrt:school10 -0.41820 0.16534 -2.53 0.01143 * -0.74044 -0.09912 5243 standlrt:school11 -0.24932 0.12749 -1.96 0.05052 . -0.49982 -0.00158 5000 standlrt:school12 -0.23088 0.15411 -1.50 0.1341 -0.53234 0.06483 5000 standlrt:school13 -0.08295 0.12012 -0.69 0.4899 -0.31678 0.14937 4940 standlrt:school14 -0.10093 0.10023 -1.01 0.314 -0.29928 0.09351 5000 standlrt:school15 0.02589 0.12673 0.20 0.8381 -0.21920 0.27867 5000 standlrt:school16 -0.30162 0.12782 -2.36 0.01829 * -0.55695 -0.05350 5000 standlrt:school17 -0.21148 0.10405 -2.03 0.0421 * -0.41724 -0.00729 5099 standlrt:school18 -0.34773 0.13107 -2.65 0.007976 ** -0.60438 -0.09317 5000 standlrt:school19 0.08512 0.17372 0.49 0.6242 -0.25329 0.42954 5000 standlrt:school20 -0.18672 0.14405 -1.30 0.1949 -0.46662 0.09200 5037 standlrt:school21 -0.15792 0.12934 -1.22 0.2221 -0.41407 0.09443 5000 standlrt:school22 -0.18368 0.11129 -1.65 0.09884 . -0.40285 0.03209 5281 standlrt:school23 -0.31703 0.15726 -2.02 0.0438 * -0.62069 -0.00580 5000 standlrt:school24 -0.31047 0.15691 -1.98 0.04785 * -0.60934 -0.00086 5243 standlrt:school25 -0.17496 0.11797 -1.48 0.1381 -0.40294 0.05166 5000 standlrt:school26 -0.16512 0.12384 -1.33 0.1824 -0.40374 0.08014 4791 standlrt:school27 -0.13470 0.14795 -0.91 0.3626 -0.42987 0.15659 5000 standlrt:school28 -0.42554 0.13967 -3.05 0.002314 ** -0.69984 -0.15626 5000 standlrt:school29 -0.30873 0.12357 -2.50 0.01247 * -0.54849 -0.06607 5000 standlrt:school30 0.09628 0.13340 0.72 0.4705 -0.15670 0.36114 5264 standlrt:school31 -0.30760 0.17541 -1.75 0.0795 . -0.65078 0.03574 5433 standlrt:school32 -0.04192 0.13369 -0.31 0.7538 -0.30733 0.21295 5000 standlrt:school33 -0.20513 0.13222 -1.55 0.1208 -0.46083 0.05173 5000 standlrt:school34 0.02549 0.13920 0.18 0.8547 -0.24763 0.29987 5238 standlrt:school35 -0.31486 0.18151 -1.73 0.08279 . -0.67713 0.04395 5000 standlrt:school36 -0.26873 0.11101 -2.42 0.01548 * -0.48358 -0.05205 5000 standlrt:school37 -0.46837 0.16986 -2.76 0.005826 ** -0.80748 -0.14120 5000 standlrt:school38 -0.08534 0.12435 -0.69 0.4925 -0.32287 0.15770 5000 standlrt:school39 -0.25626 0.12807 -2.00 0.04541 * -0.51600 -0.01286 5336 standlrt:school40 0.01528 0.11757 0.13 0.8966 -0.22009 0.24264 5000 standlrt:school41 -0.22375 0.13138 -1.70 0.08855 . -0.48423 0.02724 5000 standlrt:school42 -0.29606 0.14447 -2.05 0.04043 * -0.57657 -0.00980 5000 standlrt:school43 0.02467 0.15144 0.16 0.8706 -0.27080 0.32459 5000 standlrt:school44 -0.34074 0.15656 -2.18 0.02952 * -0.65316 -0.04100 5000 standlrt:school45 -0.14284 0.13553 -1.05 0.2919 -0.41284 0.12601 5000 standlrt:school46 -0.24475 0.12433 -1.97 0.049 * -0.49090 -0.00091 5000 standlrt:school47 -0.04361 0.12670 -0.34 0.7307 -0.29106 0.20308 5000 standlrt:school48 -7.57983 12.78662 -0.59 0.5533 -32.42333 17.82283 5000 standlrt:school49 -0.22473 0.11394 -1.97 0.04857 * -0.44553 -0.00134 5000 standlrt:school50 -0.03394 0.12137 -0.28 0.7797 -0.27694 0.20120 5000 standlrt:school51 -0.36659 0.12041 -3.04 0.00233 ** -0.60629 -0.13445 5201 standlrt:school52 0.03073 0.12355 0.25 0.8036 -0.21123 0.27348 4743 standlrt:school53 0.36669 0.12567 2.92 0.003524 ** 0.11863 0.61072 5000 standlrt:school54 -0.66388 0.46941 -1.41 0.1573 -1.57854 0.26653 5000 standlrt:school55 -0.08186 0.13354 -0.61 0.5399 -0.35597 0.17465 5000 standlrt:school56 0.16477 0.16329 1.01 0.3129 -0.16021 0.48720 4783 standlrt:school57 -0.09569 0.12887 -0.74 0.4577 -0.35660 0.15325 5000 standlrt:school58 -0.35216 0.16594 -2.12 0.03381 * -0.67814 -0.03079 5259 standlrt:school59 -0.34677 0.14298 -2.43 0.01529 * -0.62354 -0.06272 5000 standlrt:school60 -0.07100 0.12619 -0.56 0.5737 -0.32061 0.17820 5000 standlrt:school61 -0.07507 0.12500 -0.60 0.5481 -0.31888 0.17332 5000 standlrt:school62 -0.16289 0.14129 -1.15 0.249 -0.44188 0.11170 4417 standlrt:school63 -0.37553 0.20144 -1.86 0.06229 . -0.76465 0.01616 5000 standlrt:school64 -0.00156 0.13119 -0.01 0.9905 -0.25853 0.24914 4761 standlrt:school65 -0.14046 0.11627 -1.21 0.227 -0.37085 0.08653 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 0.55335 0.01259 0.52932 0.57831 4659 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Define the model Choose IGLS algoritm for estimation Fit the model > (mymodel0a <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (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 not achieved TOLE 2 MAXI 20 NEXT iteration 2 iteration 3 Convergence achieved ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) 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: IGLS Elapsed time : 0.06s Number of obs: 4059 (from total 4059) The model converged after 4 iterations. Log likelihood: -4658.4 Deviance statistic: 9316.9 --------------------------------------------------------------------------------------------------- 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% Conf. Interval] Intercept -0.01151 0.03978 -0.29 0.7724 -0.08948 0.06647 standlrt 0.55673 0.01994 27.92 1.344e-171 *** 0.51765 0.59581 Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 --------------------------------------------------------------------------------------------------- The random part estimates at the school level: Coef. Std. Err. var_Intercept 0.09044 0.01792 cov_Intercept_standlrt 0.01804 0.00672 var_standlrt 0.01454 0.00441 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. var_Intercept 0.55366 0.01248 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > ## Choose MCMC algoritm for estimation (IGLS will be used to obtain starting values for MCMC) > (mymodel0 <- 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 for 50 iterations out of 500 -2 * Loglike = 9145.871584 Burning in for 100 iterations out of 500 -2 * Loglike = 9132.292720 Burning in for 150 iterations out of 500 -2 * Loglike = 9116.964735 Burning in for 200 iterations out of 500 -2 * Loglike = 9109.819138 Burning in for 250 iterations out of 500 -2 * Loglike = 9142.444254 Burning in for 300 iterations out of 500 -2 * Loglike = 9126.443022 Burning in for 350 iterations out of 500 -2 * Loglike = 9158.382599 Burning in for 400 iterations out of 500 -2 * Loglike = 9130.050027 Burning in for 450 iterations out of 500 -2 * Loglike = 9132.164613 Burning in for 500 iterations out of 500 -2 * Loglike = 9095.782185 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 = 9141.251505 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9092.112338 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9114.453660 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9130.042851 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9112.630195 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9127.189612 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9121.760133 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9095.484118 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9119.696741 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9097.278119 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9091.835441 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9147.067486 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9115.848152 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9136.364432 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9122.999236 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9125.626814 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9124.942111 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9123.715072 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9139.162535 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9093.087478 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9103.780217 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9125.714840 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9117.856745 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9104.224610 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9136.726333 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9115.553162 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9135.082659 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9106.260473 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9113.023248 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9128.720286 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9128.243265 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9112.524919 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9116.163849 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9100.141526 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9112.566069 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9129.956343 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9131.034399 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9121.937589 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9094.252149 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9117.545274 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9099.416940 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9132.162100 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9135.159139 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9110.982424 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9112.731006 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9129.335122 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9135.832789 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9115.598454 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9119.806787 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9106.961083 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9094.496029 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9114.022952 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9122.506561 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9108.681836 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9110.341205 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9131.645275 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9143.193063 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9096.461754 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9142.098601 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9090.543006 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9123.431925 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9100.574500 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9135.650108 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9131.254028 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9130.803281 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9137.320115 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9151.055699 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9113.381797 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9136.395805 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9119.182591 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9099.498807 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9094.669026 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9124.954760 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9113.843599 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9122.879346 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9138.609563 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9106.548693 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9104.254128 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9117.331443 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9094.789350 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9135.693654 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9101.392385 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9114.650394 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9113.173542 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9126.374967 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9142.771045 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9133.755790 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9146.895681 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9130.279064 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9126.639139 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9112.546091 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9130.121874 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9102.731900 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9101.131722 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9081.592796 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9107.770592 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9129.044185 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9118.474018 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9118.583370 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9132.471942 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9122.7 S.D. = 16.894 S.E.M. = 0.23892 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 1.96s 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 9122.672 9031.177 91.496 9214.168 --------------------------------------------------------------------------------------------------- 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 -0.01325 0.03984 -0.33 0.7395 -0.08901 0.07336 225 standlrt 0.55687 0.02033 27.39 4.031e-165 *** 0.51599 0.59630 563 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 0.09706 0.02004 0.06544 0.14260 3136 cov_Intercept_standlrt 0.01955 0.00737 0.00647 0.03595 1644 var_standlrt 0.01549 0.00484 0.00804 0.02681 930 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55432 0.01247 0.53027 0.57958 4575 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 6.1 Prediction intervals for a random slopes regression model . . . . . 75 > > ## Save level 2 residual chains > (mymodel <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1, + mcmcMeth = list(iterations = 5001), resi.store.levs = 2), 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 for 50 iterations out of 500 -2 * Loglike = 9145.871584 Burning in for 100 iterations out of 500 -2 * Loglike = 9132.292720 Burning in for 150 iterations out of 500 -2 * Loglike = 9116.964735 Burning in for 200 iterations out of 500 -2 * Loglike = 9109.819138 Burning in for 250 iterations out of 500 -2 * Loglike = 9142.444254 Burning in for 300 iterations out of 500 -2 * Loglike = 9126.443022 Burning in for 350 iterations out of 500 -2 * Loglike = 9158.382599 Burning in for 400 iterations out of 500 -2 * Loglike = 9130.050027 Burning in for 450 iterations out of 500 -2 * Loglike = 9132.164613 Burning in for 500 iterations out of 500 -2 * Loglike = 9095.782185 ERAS G30 LINK 0 G30 ERAS c1090 c1091 MCMC 1 5001 1 c1090 c1091 c1003 c1004 1 1 Actual update 50 of 5001, Stored update 50 of 5001 -2 * Loglike = 9141.251505 Actual update 100 of 5001, Stored update 100 of 5001 -2 * Loglike = 9092.112338 Actual update 150 of 5001, Stored update 150 of 5001 -2 * Loglike = 9114.453660 Actual update 200 of 5001, Stored update 200 of 5001 -2 * Loglike = 9130.042851 Actual update 250 of 5001, Stored update 250 of 5001 -2 * Loglike = 9112.630195 Actual update 300 of 5001, Stored update 300 of 5001 -2 * Loglike = 9127.189612 Actual update 350 of 5001, Stored update 350 of 5001 -2 * Loglike = 9121.760133 Actual update 400 of 5001, Stored update 400 of 5001 -2 * Loglike = 9095.484118 Actual update 450 of 5001, Stored update 450 of 5001 -2 * Loglike = 9119.696741 Actual update 500 of 5001, Stored update 500 of 5001 -2 * Loglike = 9097.278119 Actual update 550 of 5001, Stored update 550 of 5001 -2 * Loglike = 9091.835441 Actual update 600 of 5001, Stored update 600 of 5001 -2 * Loglike = 9147.067486 Actual update 650 of 5001, Stored update 650 of 5001 -2 * Loglike = 9115.848152 Actual update 700 of 5001, Stored update 700 of 5001 -2 * Loglike = 9136.364432 Actual update 750 of 5001, Stored update 750 of 5001 -2 * Loglike = 9122.999236 Actual update 800 of 5001, Stored update 800 of 5001 -2 * Loglike = 9125.626814 Actual update 850 of 5001, Stored update 850 of 5001 -2 * Loglike = 9124.942111 Actual update 900 of 5001, Stored update 900 of 5001 -2 * Loglike = 9123.715072 Actual update 950 of 5001, Stored update 950 of 5001 -2 * Loglike = 9139.162535 Actual update 1000 of 5001, Stored update 1000 of 5001 -2 * Loglike = 9093.087478 Actual update 1050 of 5001, Stored update 1050 of 5001 -2 * Loglike = 9103.780217 Actual update 1100 of 5001, Stored update 1100 of 5001 -2 * Loglike = 9125.714840 Actual update 1150 of 5001, Stored update 1150 of 5001 -2 * Loglike = 9117.856745 Actual update 1200 of 5001, Stored update 1200 of 5001 -2 * Loglike = 9104.224610 Actual update 1250 of 5001, Stored update 1250 of 5001 -2 * Loglike = 9136.726333 Actual update 1300 of 5001, Stored update 1300 of 5001 -2 * Loglike = 9115.553162 Actual update 1350 of 5001, Stored update 1350 of 5001 -2 * Loglike = 9135.082659 Actual update 1400 of 5001, Stored update 1400 of 5001 -2 * Loglike = 9106.260473 Actual update 1450 of 5001, Stored update 1450 of 5001 -2 * Loglike = 9113.023248 Actual update 1500 of 5001, Stored update 1500 of 5001 -2 * Loglike = 9128.720286 Actual update 1550 of 5001, Stored update 1550 of 5001 -2 * Loglike = 9128.243265 Actual update 1600 of 5001, Stored update 1600 of 5001 -2 * Loglike = 9112.524919 Actual update 1650 of 5001, Stored update 1650 of 5001 -2 * Loglike = 9116.163849 Actual update 1700 of 5001, Stored update 1700 of 5001 -2 * Loglike = 9100.141526 Actual update 1750 of 5001, Stored update 1750 of 5001 -2 * Loglike = 9112.566069 Actual update 1800 of 5001, Stored update 1800 of 5001 -2 * Loglike = 9129.956343 Actual update 1850 of 5001, Stored update 1850 of 5001 -2 * Loglike = 9131.034399 Actual update 1900 of 5001, Stored update 1900 of 5001 -2 * Loglike = 9121.937589 Actual update 1950 of 5001, Stored update 1950 of 5001 -2 * Loglike = 9094.252149 Actual update 2000 of 5001, Stored update 2000 of 5001 -2 * Loglike = 9117.545274 Actual update 2050 of 5001, Stored update 2050 of 5001 -2 * Loglike = 9099.416940 Actual update 2100 of 5001, Stored update 2100 of 5001 -2 * Loglike = 9132.162100 Actual update 2150 of 5001, Stored update 2150 of 5001 -2 * Loglike = 9135.159139 Actual update 2200 of 5001, Stored update 2200 of 5001 -2 * Loglike = 9110.982424 Actual update 2250 of 5001, Stored update 2250 of 5001 -2 * Loglike = 9112.731006 Actual update 2300 of 5001, Stored update 2300 of 5001 -2 * Loglike = 9129.335122 Actual update 2350 of 5001, Stored update 2350 of 5001 -2 * Loglike = 9135.832789 Actual update 2400 of 5001, Stored update 2400 of 5001 -2 * Loglike = 9115.598454 Actual update 2450 of 5001, Stored update 2450 of 5001 -2 * Loglike = 9119.806787 Actual update 2500 of 5001, Stored update 2500 of 5001 -2 * Loglike = 9106.961083 Actual update 2550 of 5001, Stored update 2550 of 5001 -2 * Loglike = 9094.496029 Actual update 2600 of 5001, Stored update 2600 of 5001 -2 * Loglike = 9114.022952 Actual update 2650 of 5001, Stored update 2650 of 5001 -2 * Loglike = 9122.506561 Actual update 2700 of 5001, Stored update 2700 of 5001 -2 * Loglike = 9108.681836 Actual update 2750 of 5001, Stored update 2750 of 5001 -2 * Loglike = 9110.341205 Actual update 2800 of 5001, Stored update 2800 of 5001 -2 * Loglike = 9131.645275 Actual update 2850 of 5001, Stored update 2850 of 5001 -2 * Loglike = 9143.193063 Actual update 2900 of 5001, Stored update 2900 of 5001 -2 * Loglike = 9096.461754 Actual update 2950 of 5001, Stored update 2950 of 5001 -2 * Loglike = 9142.098601 Actual update 3000 of 5001, Stored update 3000 of 5001 -2 * Loglike = 9090.543006 Actual update 3050 of 5001, Stored update 3050 of 5001 -2 * Loglike = 9123.431925 Actual update 3100 of 5001, Stored update 3100 of 5001 -2 * Loglike = 9100.574500 Actual update 3150 of 5001, Stored update 3150 of 5001 -2 * Loglike = 9135.650108 Actual update 3200 of 5001, Stored update 3200 of 5001 -2 * Loglike = 9131.254028 Actual update 3250 of 5001, Stored update 3250 of 5001 -2 * Loglike = 9130.803281 Actual update 3300 of 5001, Stored update 3300 of 5001 -2 * Loglike = 9137.320115 Actual update 3350 of 5001, Stored update 3350 of 5001 -2 * Loglike = 9151.055699 Actual update 3400 of 5001, Stored update 3400 of 5001 -2 * Loglike = 9113.381797 Actual update 3450 of 5001, Stored update 3450 of 5001 -2 * Loglike = 9136.395805 Actual update 3500 of 5001, Stored update 3500 of 5001 -2 * Loglike = 9119.182591 Actual update 3550 of 5001, Stored update 3550 of 5001 -2 * Loglike = 9099.498807 Actual update 3600 of 5001, Stored update 3600 of 5001 -2 * Loglike = 9094.669026 Actual update 3650 of 5001, Stored update 3650 of 5001 -2 * Loglike = 9124.954760 Actual update 3700 of 5001, Stored update 3700 of 5001 -2 * Loglike = 9113.843599 Actual update 3750 of 5001, Stored update 3750 of 5001 -2 * Loglike = 9122.879346 Actual update 3800 of 5001, Stored update 3800 of 5001 -2 * Loglike = 9138.609563 Actual update 3850 of 5001, Stored update 3850 of 5001 -2 * Loglike = 9106.548693 Actual update 3900 of 5001, Stored update 3900 of 5001 -2 * Loglike = 9104.254128 Actual update 3950 of 5001, Stored update 3950 of 5001 -2 * Loglike = 9117.331443 Actual update 4000 of 5001, Stored update 4000 of 5001 -2 * Loglike = 9094.789350 Actual update 4050 of 5001, Stored update 4050 of 5001 -2 * Loglike = 9135.693654 Actual update 4100 of 5001, Stored update 4100 of 5001 -2 * Loglike = 9101.392385 Actual update 4150 of 5001, Stored update 4150 of 5001 -2 * Loglike = 9114.650394 Actual update 4200 of 5001, Stored update 4200 of 5001 -2 * Loglike = 9113.173542 Actual update 4250 of 5001, Stored update 4250 of 5001 -2 * Loglike = 9126.374967 Actual update 4300 of 5001, Stored update 4300 of 5001 -2 * Loglike = 9142.771045 Actual update 4350 of 5001, Stored update 4350 of 5001 -2 * Loglike = 9133.755790 Actual update 4400 of 5001, Stored update 4400 of 5001 -2 * Loglike = 9146.895681 Actual update 4450 of 5001, Stored update 4450 of 5001 -2 * Loglike = 9130.279064 Actual update 4500 of 5001, Stored update 4500 of 5001 -2 * Loglike = 9126.639139 Actual update 4550 of 5001, Stored update 4550 of 5001 -2 * Loglike = 9112.546091 Actual update 4600 of 5001, Stored update 4600 of 5001 -2 * Loglike = 9130.121874 Actual update 4650 of 5001, Stored update 4650 of 5001 -2 * Loglike = 9102.731900 Actual update 4700 of 5001, Stored update 4700 of 5001 -2 * Loglike = 9101.131722 Actual update 4750 of 5001, Stored update 4750 of 5001 -2 * Loglike = 9081.592796 Actual update 4800 of 5001, Stored update 4800 of 5001 -2 * Loglike = 9107.770592 Actual update 4850 of 5001, Stored update 4850 of 5001 -2 * Loglike = 9129.044185 Actual update 4900 of 5001, Stored update 4900 of 5001 -2 * Loglike = 9118.474018 Actual update 4950 of 5001, Stored update 4950 of 5001 -2 * Loglike = 9118.583370 Actual update 5000 of 5001, Stored update 5000 of 5001 -2 * Loglike = 9132.471942 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5001 Average = 9122.7 S.D. = 16.894 S.E.M. = 0.23889 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) 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 : 2s Number of obs: 4059 (from total 4059) Number of iter.: 5001 Chains: 1 Burn-in: 500 Bayesian Deviance Information Criterion (DIC) Dbar D(thetabar) pD DIC 9122.669 9031.175 91.494 9214.164 --------------------------------------------------------------------------------------------------- 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 -0.01324 0.03984 -0.33 0.7396 -0.08901 0.07336 225 standlrt 0.55686 0.02033 27.39 3.826e-165 *** 0.51599 0.59630 563 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 0.09706 0.02004 0.06544 0.14259 3137 cov_Intercept_standlrt 0.01955 0.00737 0.00647 0.03595 1646 var_standlrt 0.01549 0.00484 0.00804 0.02681 930 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55432 0.01247 0.53027 0.57958 4575 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > predLines(mymodel, xname = "standlrt", lev = 2, selected = NULL, probs = c(0.025, 0.975), legend.space = "right", + legend.ncol = 2) > dev.new() dev.new(): using pdf(file="Rplots1.pdf") > predLines(mymodel, xname = "standlrt", lev = 2, selected = c(30, 44, 53, 59), probs = c(0.025, 0.975)) > > # 6.2 Alternative priors for variance matrices . . . . . . . . . . . . . .78 > > # 6.3 WinBUGS priors (Prior 2) . . . . . . . . . . . . . . . . . . . . . .78 > > ## Change the starting values for Level 2 variance matrix to .1 on diagonal 0 otherwise. > RP.b <- c(0.1, 0, 0.1, 0.554) > names(RP.b) <- c("RP2_var_Intercept", "RP2_cov_Intercept_standlrt", "RP2_var_standlrt", "RP1_var_Intercept") > > ## Fit the model > (mymodel1 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1, + startval = list(RP.b = RP.b)), 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 JOIN 0.1 0 0.1 0.554 '_RP_b' 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 for 50 iterations out of 500 -2 * Loglike = 9115.560448 Burning in for 100 iterations out of 500 -2 * Loglike = 9129.893429 Burning in for 150 iterations out of 500 -2 * Loglike = 9103.716719 Burning in for 200 iterations out of 500 -2 * Loglike = 9097.845597 Burning in for 250 iterations out of 500 -2 * Loglike = 9132.689496 Burning in for 300 iterations out of 500 -2 * Loglike = 9122.695472 Burning in for 350 iterations out of 500 -2 * Loglike = 9151.326431 Burning in for 400 iterations out of 500 -2 * Loglike = 9117.276983 Burning in for 450 iterations out of 500 -2 * Loglike = 9127.508241 Burning in for 500 iterations out of 500 -2 * Loglike = 9088.147385 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 = 9117.713075 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9088.823283 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9094.601310 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9120.645585 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9106.139138 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9121.557505 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9113.739746 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9092.070883 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9113.482203 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9093.439236 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9088.531175 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9137.467854 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9111.414628 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9125.040145 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9113.876514 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9116.688513 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9118.283003 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9111.174952 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9125.655426 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9086.989104 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9095.719374 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9115.897166 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9105.006367 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9103.829463 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9131.792594 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9113.323091 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9127.762332 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9101.843646 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9105.746841 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9122.767960 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9115.469710 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9096.140662 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9115.288373 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9095.276503 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9097.653322 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9118.606545 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9116.472837 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9115.553862 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9088.432430 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9112.193360 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9096.083316 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9127.734372 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9108.667612 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9109.288911 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9109.401290 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9124.659007 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9134.120959 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9108.470038 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9102.143927 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9103.485089 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9083.170537 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9111.958186 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9114.276270 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9104.859246 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9099.611816 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9130.593912 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9137.609861 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9092.233566 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9132.519214 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9084.858000 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9115.655316 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9095.503013 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9133.624742 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9122.542176 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9132.037462 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9134.381285 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9131.422392 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9105.301337 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9124.657557 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9109.797426 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9092.770937 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9086.493005 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9117.236595 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9108.141648 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9110.070865 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9131.198340 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9096.627185 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9097.781483 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9099.571865 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9091.046815 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9127.889337 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9097.638546 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9111.630128 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9098.352140 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9108.630313 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9135.941541 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9125.667057 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9134.344196 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9109.588347 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9121.126382 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9114.010157 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9118.726619 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9101.383584 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9085.313342 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9080.618251 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9101.697283 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9115.297209 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9114.294319 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9109.500471 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9124.238533 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9114.7 S.D. = 15.799 S.E.M. = 0.22342 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 1.91s 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 9114.701 9015.787 98.913 9213.614 --------------------------------------------------------------------------------------------------- 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 -0.01420 0.03993 -0.36 0.7221 -0.08987 0.07262 224 standlrt 0.55506 0.02309 24.04 1.17e-127 *** 0.50882 0.59935 663 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 0.09733 0.02010 0.06572 0.14294 3143 cov_Intercept_standlrt 0.01810 0.00811 0.00339 0.03572 2037 var_standlrt 0.02291 0.00581 0.01380 0.03638 1768 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55323 0.01243 0.52903 0.57829 4606 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 6.4 Uniform prior . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 > > ## Diffuse priors (Uniform priors) > (mymodel2 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1, + mcmcMeth = list(priorcode = 0)), 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 0 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9145.249053 Burning in for 100 iterations out of 500 -2 * Loglike = 9140.782308 Burning in for 150 iterations out of 500 -2 * Loglike = 9108.068002 Burning in for 200 iterations out of 500 -2 * Loglike = 9105.408633 Burning in for 250 iterations out of 500 -2 * Loglike = 9113.662998 Burning in for 300 iterations out of 500 -2 * Loglike = 9123.845391 Burning in for 350 iterations out of 500 -2 * Loglike = 9154.507399 Burning in for 400 iterations out of 500 -2 * Loglike = 9118.685525 Burning in for 450 iterations out of 500 -2 * Loglike = 9143.149194 Burning in for 500 iterations out of 500 -2 * Loglike = 9103.726550 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 = 9123.535596 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9123.204350 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9121.102710 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9126.160198 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9094.177904 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9121.934356 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9146.075922 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9112.449745 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9127.300291 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9132.486044 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9111.488263 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9130.670607 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9101.857915 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9109.189736 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9127.208839 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9122.427142 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9122.774585 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9125.373506 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9133.883886 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9107.961434 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9100.216118 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9121.289288 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9113.282508 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9103.338367 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9115.532668 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9121.311868 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9117.630799 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9104.021257 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9109.683099 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9125.403364 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9124.277133 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9106.491607 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9115.520988 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9084.589359 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9090.120547 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9112.829139 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9119.812628 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9118.544125 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9090.832632 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9114.435501 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9097.277363 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9130.187823 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9129.015631 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9110.552856 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9110.514071 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9126.449946 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9134.880931 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9106.693998 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9120.692428 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9135.727462 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9126.827956 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9124.050824 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9148.638346 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9119.854534 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9103.320477 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9115.889265 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9131.873010 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9127.016281 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9117.050484 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9088.209593 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9131.092710 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9147.495609 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9124.446340 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9118.342549 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9131.210163 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9135.108040 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9145.956376 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9108.916416 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9131.963337 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9114.510493 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9096.033016 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9089.403619 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9120.892413 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9110.772010 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9117.860514 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9142.787740 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9103.587496 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9101.038615 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9112.892770 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9092.132153 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9132.439735 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9099.002640 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9112.895801 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9154.524344 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9121.156803 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9139.387558 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9129.934773 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9142.522249 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9119.820434 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9130.578898 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9112.652619 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9117.839562 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9101.918121 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9096.374752 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9080.629587 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9104.763520 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9121.999258 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9116.058896 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9114.418295 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9128.450844 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9119.1 S.D. = 16.566 S.E.M. = 0.23428 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 1.88s 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 9119.059 9024.397 94.662 9213.720 --------------------------------------------------------------------------------------------------- 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 -0.01558 0.04319 -0.36 0.7183 -0.09622 0.07643 189 standlrt 0.55590 0.02149 25.87 1.479e-147 *** 0.51250 0.59706 416 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 0.10383 0.02196 0.06862 0.15308 3101 cov_Intercept_standlrt 0.02046 0.00852 0.00582 0.03927 1695 var_standlrt 0.01808 0.00566 0.00913 0.03100 1023 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55422 0.01236 0.53030 0.57927 4530 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 6.5 Informative prior . . . . . . . . . . . . . . . . . . . . . . . . . 80 > > ## Informative normal prior for Sigma_u > (mymodel3 <- runMLwiN(normexam ~ 1 + standlrt + (1 + standlrt | school) + (1 | student), estoptions = list(EstM = 1, + mcmcMeth = list(priorParam = list(rp2 = list(estimate = matrix(c(0.09, 0.018, 0.018, 0.015), 2, 2), size = 65)))), + 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] c1092 1 1 1 1 1 1 Burning in for 50 iterations out of 500 -2 * Loglike = 9133.265784 Burning in for 100 iterations out of 500 -2 * Loglike = 9137.138531 Burning in for 150 iterations out of 500 -2 * Loglike = 9145.684684 Burning in for 200 iterations out of 500 -2 * Loglike = 9118.272190 Burning in for 250 iterations out of 500 -2 * Loglike = 9119.333117 Burning in for 300 iterations out of 500 -2 * Loglike = 9128.724129 Burning in for 350 iterations out of 500 -2 * Loglike = 9122.626161 Burning in for 400 iterations out of 500 -2 * Loglike = 9138.855845 Burning in for 450 iterations out of 500 -2 * Loglike = 9126.231579 Burning in for 500 iterations out of 500 -2 * Loglike = 9125.978804 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 = 9120.319408 Actual update 100 of 5000, Stored update 100 of 5000 -2 * Loglike = 9137.595406 Actual update 150 of 5000, Stored update 150 of 5000 -2 * Loglike = 9102.006096 Actual update 200 of 5000, Stored update 200 of 5000 -2 * Loglike = 9152.909373 Actual update 250 of 5000, Stored update 250 of 5000 -2 * Loglike = 9092.651917 Actual update 300 of 5000, Stored update 300 of 5000 -2 * Loglike = 9103.623070 Actual update 350 of 5000, Stored update 350 of 5000 -2 * Loglike = 9146.034162 Actual update 400 of 5000, Stored update 400 of 5000 -2 * Loglike = 9112.674324 Actual update 450 of 5000, Stored update 450 of 5000 -2 * Loglike = 9119.157429 Actual update 500 of 5000, Stored update 500 of 5000 -2 * Loglike = 9113.069876 Actual update 550 of 5000, Stored update 550 of 5000 -2 * Loglike = 9120.583142 Actual update 600 of 5000, Stored update 600 of 5000 -2 * Loglike = 9114.495766 Actual update 650 of 5000, Stored update 650 of 5000 -2 * Loglike = 9106.080458 Actual update 700 of 5000, Stored update 700 of 5000 -2 * Loglike = 9127.616536 Actual update 750 of 5000, Stored update 750 of 5000 -2 * Loglike = 9113.721029 Actual update 800 of 5000, Stored update 800 of 5000 -2 * Loglike = 9128.469655 Actual update 850 of 5000, Stored update 850 of 5000 -2 * Loglike = 9121.818453 Actual update 900 of 5000, Stored update 900 of 5000 -2 * Loglike = 9120.702689 Actual update 950 of 5000, Stored update 950 of 5000 -2 * Loglike = 9096.128888 Actual update 1000 of 5000, Stored update 1000 of 5000 -2 * Loglike = 9120.029738 Actual update 1050 of 5000, Stored update 1050 of 5000 -2 * Loglike = 9104.256485 Actual update 1100 of 5000, Stored update 1100 of 5000 -2 * Loglike = 9083.854768 Actual update 1150 of 5000, Stored update 1150 of 5000 -2 * Loglike = 9108.299870 Actual update 1200 of 5000, Stored update 1200 of 5000 -2 * Loglike = 9142.773147 Actual update 1250 of 5000, Stored update 1250 of 5000 -2 * Loglike = 9138.029363 Actual update 1300 of 5000, Stored update 1300 of 5000 -2 * Loglike = 9113.377389 Actual update 1350 of 5000, Stored update 1350 of 5000 -2 * Loglike = 9129.664268 Actual update 1400 of 5000, Stored update 1400 of 5000 -2 * Loglike = 9148.155311 Actual update 1450 of 5000, Stored update 1450 of 5000 -2 * Loglike = 9111.532736 Actual update 1500 of 5000, Stored update 1500 of 5000 -2 * Loglike = 9134.792508 Actual update 1550 of 5000, Stored update 1550 of 5000 -2 * Loglike = 9118.867243 Actual update 1600 of 5000, Stored update 1600 of 5000 -2 * Loglike = 9104.808773 Actual update 1650 of 5000, Stored update 1650 of 5000 -2 * Loglike = 9111.514024 Actual update 1700 of 5000, Stored update 1700 of 5000 -2 * Loglike = 9092.764102 Actual update 1750 of 5000, Stored update 1750 of 5000 -2 * Loglike = 9099.575619 Actual update 1800 of 5000, Stored update 1800 of 5000 -2 * Loglike = 9121.028454 Actual update 1850 of 5000, Stored update 1850 of 5000 -2 * Loglike = 9120.574667 Actual update 1900 of 5000, Stored update 1900 of 5000 -2 * Loglike = 9117.655427 Actual update 1950 of 5000, Stored update 1950 of 5000 -2 * Loglike = 9121.157674 Actual update 2000 of 5000, Stored update 2000 of 5000 -2 * Loglike = 9099.920280 Actual update 2050 of 5000, Stored update 2050 of 5000 -2 * Loglike = 9107.205734 Actual update 2100 of 5000, Stored update 2100 of 5000 -2 * Loglike = 9127.233038 Actual update 2150 of 5000, Stored update 2150 of 5000 -2 * Loglike = 9109.897319 Actual update 2200 of 5000, Stored update 2200 of 5000 -2 * Loglike = 9137.471137 Actual update 2250 of 5000, Stored update 2250 of 5000 -2 * Loglike = 9117.718146 Actual update 2300 of 5000, Stored update 2300 of 5000 -2 * Loglike = 9143.827830 Actual update 2350 of 5000, Stored update 2350 of 5000 -2 * Loglike = 9112.529179 Actual update 2400 of 5000, Stored update 2400 of 5000 -2 * Loglike = 9118.225781 Actual update 2450 of 5000, Stored update 2450 of 5000 -2 * Loglike = 9119.594564 Actual update 2500 of 5000, Stored update 2500 of 5000 -2 * Loglike = 9104.844429 Actual update 2550 of 5000, Stored update 2550 of 5000 -2 * Loglike = 9136.791755 Actual update 2600 of 5000, Stored update 2600 of 5000 -2 * Loglike = 9113.912583 Actual update 2650 of 5000, Stored update 2650 of 5000 -2 * Loglike = 9116.012063 Actual update 2700 of 5000, Stored update 2700 of 5000 -2 * Loglike = 9118.598705 Actual update 2750 of 5000, Stored update 2750 of 5000 -2 * Loglike = 9103.592024 Actual update 2800 of 5000, Stored update 2800 of 5000 -2 * Loglike = 9103.949246 Actual update 2850 of 5000, Stored update 2850 of 5000 -2 * Loglike = 9103.693340 Actual update 2900 of 5000, Stored update 2900 of 5000 -2 * Loglike = 9105.380796 Actual update 2950 of 5000, Stored update 2950 of 5000 -2 * Loglike = 9134.155654 Actual update 3000 of 5000, Stored update 3000 of 5000 -2 * Loglike = 9096.692604 Actual update 3050 of 5000, Stored update 3050 of 5000 -2 * Loglike = 9111.475026 Actual update 3100 of 5000, Stored update 3100 of 5000 -2 * Loglike = 9113.995240 Actual update 3150 of 5000, Stored update 3150 of 5000 -2 * Loglike = 9125.181852 Actual update 3200 of 5000, Stored update 3200 of 5000 -2 * Loglike = 9128.512895 Actual update 3250 of 5000, Stored update 3250 of 5000 -2 * Loglike = 9150.793622 Actual update 3300 of 5000, Stored update 3300 of 5000 -2 * Loglike = 9129.350379 Actual update 3350 of 5000, Stored update 3350 of 5000 -2 * Loglike = 9117.396484 Actual update 3400 of 5000, Stored update 3400 of 5000 -2 * Loglike = 9120.809746 Actual update 3450 of 5000, Stored update 3450 of 5000 -2 * Loglike = 9089.716626 Actual update 3500 of 5000, Stored update 3500 of 5000 -2 * Loglike = 9131.574268 Actual update 3550 of 5000, Stored update 3550 of 5000 -2 * Loglike = 9124.311396 Actual update 3600 of 5000, Stored update 3600 of 5000 -2 * Loglike = 9115.431603 Actual update 3650 of 5000, Stored update 3650 of 5000 -2 * Loglike = 9128.364042 Actual update 3700 of 5000, Stored update 3700 of 5000 -2 * Loglike = 9127.121010 Actual update 3750 of 5000, Stored update 3750 of 5000 -2 * Loglike = 9101.543317 Actual update 3800 of 5000, Stored update 3800 of 5000 -2 * Loglike = 9113.085784 Actual update 3850 of 5000, Stored update 3850 of 5000 -2 * Loglike = 9134.139653 Actual update 3900 of 5000, Stored update 3900 of 5000 -2 * Loglike = 9110.348463 Actual update 3950 of 5000, Stored update 3950 of 5000 -2 * Loglike = 9113.958259 Actual update 4000 of 5000, Stored update 4000 of 5000 -2 * Loglike = 9100.870823 Actual update 4050 of 5000, Stored update 4050 of 5000 -2 * Loglike = 9141.143152 Actual update 4100 of 5000, Stored update 4100 of 5000 -2 * Loglike = 9143.038606 Actual update 4150 of 5000, Stored update 4150 of 5000 -2 * Loglike = 9129.807611 Actual update 4200 of 5000, Stored update 4200 of 5000 -2 * Loglike = 9106.379658 Actual update 4250 of 5000, Stored update 4250 of 5000 -2 * Loglike = 9127.691813 Actual update 4300 of 5000, Stored update 4300 of 5000 -2 * Loglike = 9123.613650 Actual update 4350 of 5000, Stored update 4350 of 5000 -2 * Loglike = 9133.387956 Actual update 4400 of 5000, Stored update 4400 of 5000 -2 * Loglike = 9119.346535 Actual update 4450 of 5000, Stored update 4450 of 5000 -2 * Loglike = 9133.553601 Actual update 4500 of 5000, Stored update 4500 of 5000 -2 * Loglike = 9106.231836 Actual update 4550 of 5000, Stored update 4550 of 5000 -2 * Loglike = 9114.651149 Actual update 4600 of 5000, Stored update 4600 of 5000 -2 * Loglike = 9159.342243 Actual update 4650 of 5000, Stored update 4650 of 5000 -2 * Loglike = 9125.006232 Actual update 4700 of 5000, Stored update 4700 of 5000 -2 * Loglike = 9127.320254 Actual update 4750 of 5000, Stored update 4750 of 5000 -2 * Loglike = 9135.494493 Actual update 4800 of 5000, Stored update 4800 of 5000 -2 * Loglike = 9081.855904 Actual update 4850 of 5000, Stored update 4850 of 5000 -2 * Loglike = 9134.743725 Actual update 4900 of 5000, Stored update 4900 of 5000 -2 * Loglike = 9122.337090 Actual update 4950 of 5000, Stored update 4950 of 5000 -2 * Loglike = 9133.342599 Actual update 5000 of 5000, Stored update 5000 of 5000 -2 * Loglike = 9125.146897 PUPN c1003 c1004 AVER c1091 b99 b100 Count = 5000 Average = 9121.2 S.D. = 15.729 S.E.M. = 0.22245 ECHO 0 Execution completed -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- MLwiN (version: 3.05) multilevel model (Normal) N min mean max N_complete min_complete mean_complete max_complete school 65 2 62.44615 198 65 2 62.44615 198 Estimation algorithm: MCMC Elapsed time : 1.89s 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 9121.235 9030.405 90.830 9212.065 --------------------------------------------------------------------------------------------------- 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 -0.01412 0.03884 -0.36 0.7162 -0.09542 0.06060 234 standlrt 0.55599 0.01956 28.42 1.186e-177 *** 0.51651 0.59357 842 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 0.09094 0.01236 0.06955 0.11803 3316 cov_Intercept_standlrt 0.01811 0.00412 0.01077 0.02710 2926 var_standlrt 0.01484 0.00227 0.01096 0.01984 2533 --------------------------------------------------------------------------------------------------- The random part estimates at the student level: Coef. Std. Err. [95% Cred. Interval] ESS var_Intercept 0.55410 0.01225 0.53029 0.57849 4912 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > # 6.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 > > if (!require(texreg)) { + warning("texreg package required to use screenreg() function") + } else { + screenreg(list(mymodel0a, mymodel0, mymodel1, mymodel2, mymodel3), custom.model.names=c("IGLS", "default", "prior 2", "uniform", "prior 4"), groups = list("Fixed Part" = 1:2, "Level-2" = 3:5, "Level-1" = 6:6), + stars = numeric(0), include.nobs=FALSE, include.loglik=FALSE, include.deviance=FALSE, include.dbar=FALSE, include.dthetabar=FALSE, include.pd=FALSE, include.dic=FALSE) + } Loading required package: texreg Version: 1.36.23 Date: 2017-03-03 Author: Philip Leifeld (University of Glasgow) Please cite the JSS article in your publications -- see citation("texreg"). ================================================================================================== IGLS default prior 2 uniform prior 4 -------------------------------------------------------------------------------------------------- Fixed Part FP_Intercept -0.01 -0.01 -0.01 -0.02 -0.01 (0.04) [-0.09; 0.07] [-0.09; 0.07] [-0.10; 0.08] [-0.10; 0.06] FP_standlrt 0.56 0.56 * 0.56 * 0.56 * 0.56 * (0.02) [ 0.52; 0.60] [ 0.51; 0.60] [ 0.51; 0.60] [ 0.52; 0.59] Level-2 RP2_var_Intercept 0.09 0.10 * 0.10 * 0.10 * 0.09 * (0.02) [ 0.07; 0.14] [ 0.07; 0.14] [ 0.07; 0.15] [ 0.07; 0.12] RP2_cov_Intercept_standlrt 0.02 0.02 * 0.02 * 0.02 * 0.02 * (0.01) [ 0.01; 0.04] [ 0.00; 0.04] [ 0.01; 0.04] [ 0.01; 0.03] RP2_var_standlrt 0.01 0.02 * 0.02 * 0.02 * 0.01 * (0.00) [ 0.01; 0.03] [ 0.01; 0.04] [ 0.01; 0.03] [ 0.01; 0.02] Level-1 RP1_var_Intercept 0.55 0.55 * 0.55 * 0.55 * 0.55 * (0.01) [ 0.53; 0.58] [ 0.53; 0.58] [ 0.53; 0.58] [ 0.53; 0.58] ================================================================================================== * 0 outside the confidence interval > > # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . 81 > > > > > > ############################################################################ > > proc.time() user system elapsed 16.32 2.39 45.98