------------------------------------------------------------------------------- name: log: Q:\C-modelling\runmlwin\website\logfiles\2020-03-27\16\20_Multilev > el_Factor_Analysis_Modelling.smcl log type: smcl opened on: 27 Mar 2020, 18:03:28 . **************************************************************************** . * MLwiN MCMC Manual . * . * 20 Multilevel Factor Analysis Modelling . . . . . . . . . . . . . . . 303 . * . * Browne, W. J. (2009). MCMC Estimation in MLwiN, v2.26. Centre for . * Multilevel Modelling, University of Bristol. . **************************************************************************** . * Stata do-file to replicate all analyses using runmlwin . * . * George Leckie and Chris Charlton, . * Centre for Multilevel Modelling, 2012 . * http://www.bristol.ac.uk/cmm/software/runmlwin/ . **************************************************************************** . . * 20.1 Factor analysis modelling . . . . . . . . . . . . . . . . . . . . 303 . . * 20.2 MCMC algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .304 . . * 20.3 Hungarian science exam dataset . . . . . . . . . . . . . . . . . .304 . . use "http://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta", clear . . describe Contains data from http://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta obs: 2,439 vars: 10 21 Oct 2011 12:19 ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- school int %8.2g female byte %6.2g es_core float %7.2g biol_core float %9.2g biol_r3 float %7.2g biol_r4 float %7.2g phys_core float %9.2g phys_r2 float %7.2g cons byte %4.2g student int %7.2g ------------------------------------------------------------------------------- Sorted by: . . summarize es_core biol_core phys_core Variable | Obs Mean Std. Dev. Min Max -------------+--------------------------------------------------------- es_core | 2,439 8.394142 1.565037 0 10 biol_core | 2,439 7.066421 1.827154 0 10 phys_core | 2,439 7.211972 2.062737 0 10 . . correlate es_core biol_core phys_core (obs=2,439) | es_core biol_c~e phys_c~e -------------+--------------------------- es_core | 1.0000 biol_core | 0.3471 1.0000 phys_core | 0.3128 0.5247 1.0000 . . describe Contains data from http://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta obs: 2,439 vars: 10 21 Oct 2011 12:19 ------------------------------------------------------------------------------- storage display value variable name type format label variable label ------------------------------------------------------------------------------- school int %8.2g female byte %6.2g es_core float %7.2g biol_core float %9.2g biol_r3 float %7.2g biol_r4 float %7.2g phys_core float %9.2g phys_r2 float %7.2g cons byte %4.2g student int %7.2g ------------------------------------------------------------------------------- Sorted by: . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > ) /// > nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 7.71 Number of iterations = 4 Log likelihood = -22211.808 Deviance = 44423.616 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394142 .0316833 264.94 0.000 8.332044 8.45624 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066421 .0369896 191.04 0.000 6.993922 7.138919 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.896998 .0637923 108.12 0.000 6.771967 7.022028 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.674448 .0756423 75.02 0.000 5.526192 5.822705 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211972 .0417589 172.71 0.000 7.130126 7.293818 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.316009 .0616666 102.42 0.000 6.195145 6.436873 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 2.448338 .0701101 2.310924 2.585751 cov(cons_1,cons_2) | .9922662 .0612665 .872186 1.112346 var(cons_2) | 3.337122 .0955611 3.149825 3.524418 cov(cons_1,cons_3) | .5702113 .100482 .3732702 .7671525 cov(cons_2,cons_3) | .8195881 .1177102 .5888803 1.050296 var(cons_3) | 5.153738 .2082372 4.7456 5.561875 cov(cons_1,cons_4) | .9049017 .1197695 .6701577 1.139646 cov(cons_2,cons_4) | 1.859648 .1432177 1.578946 2.14035 cov(cons_3,cons_4) | 1.51518 .2862645 .9541123 2.076249 var(cons_4) | 7.761961 .3121525 7.150153 8.373768 cov(cons_1,cons_5) | 1.009383 .0684628 .8751981 1.143567 cov(cons_2,cons_5) | 1.9769 .0861489 1.808052 2.145749 cov(cons_3,cons_5) | .8557613 .1326959 .595682 1.11584 cov(cons_4,cons_5) | 2.119436 .1617941 1.802325 2.436547 var(cons_5) | 4.253141 .121792 4.014433 4.491849 cov(cons_1,cons_6) | .9949198 .0985802 .8017062 1.188133 cov(cons_2,cons_6) | 1.806032 .1184465 1.573881 2.038182 cov(cons_3,cons_6) | 1.119516 .2307594 .6672362 1.571797 cov(cons_4,cons_6) | 2.914786 .2649211 2.395551 3.434022 cov(cons_5,cons_6) | 2.402011 .1361698 2.135123 2.668899 var(cons_6) | 5.535584 .2179035 5.108501 5.962667 ------------------------------------------------------------------------------ . . runmlwin, correlation MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 7.71 Number of iterations = 4 Log likelihood = -22211.808 Deviance = 44423.616 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394142 .0316833 264.94 0.000 8.332044 8.45624 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066421 .0369896 191.04 0.000 6.993922 7.138919 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.896998 .0637923 108.12 0.000 6.771967 7.022028 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.674448 .0756423 75.02 0.000 5.526192 5.822705 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211972 .0417589 172.71 0.000 7.130126 7.293818 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.316009 .0616666 102.42 0.000 6.195145 6.436873 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 2.448338 .0701101 2.310924 2.585751 corr(cons_1,cons_2) | .3471415 .0178085 .3122375 .3820454 var(cons_2) | 3.337122 .0955611 3.149825 3.524418 corr(cons_1,cons_3) | .1605236 .0274667 .1066899 .2143574 corr(cons_2,cons_3) | .197628 .027138 .1444384 .2508176 var(cons_3) | 5.153738 .2082372 4.7456 5.561875 corr(cons_1,cons_4) | .2075774 .026134 .1563556 .2587991 corr(cons_2,cons_4) | .365392 .0239649 .3184217 .4123623 corr(cons_3,cons_4) | .2395618 .0438522 .1536131 .3255105 var(cons_4) | 7.761961 .3121525 7.150153 8.373768 corr(cons_1,cons_5) | .312799 .0182674 .2769956 .3486024 corr(cons_2,cons_5) | .5247397 .0146731 .495981 .5534984 corr(cons_3,cons_5) | .1827833 .0272778 .1293198 .2362469 corr(cons_4,cons_5) | .3688754 .0239014 .3220295 .4157214 var(cons_5) | 4.253141 .121792 4.014433 4.491849 corr(cons_1,cons_6) | .2702531 .0245374 .2221607 .3183456 corr(cons_2,cons_6) | .4202015 .0221211 .3768449 .4635581 corr(cons_3,cons_6) | .2095982 .042112 .1270602 .2921362 corr(cons_4,cons_6) | .4446715 .035467 .3751575 .5141855 corr(cons_5,cons_6) | .4950379 .0204826 .4548927 .5351831 var(cons_6) | 5.535584 .2179035 5.108501 5.962667 ------------------------------------------------------------------------------ . . . . * 20.4 A single factor Bayesian model . . . . . . . . . . . . . . . . . .307 . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)), diagonal /// > ) /// > nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 1.03 Number of iterations = 2 Log likelihood = -23181.093 Deviance = 46362.186 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394142 .0316833 264.94 0.000 8.332044 8.45624 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066421 .0369896 191.04 0.000 6.993922 7.138919 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.88216 .0649325 105.99 0.000 6.754895 7.009426 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.713101 .0799606 71.45 0.000 5.556381 5.869821 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211972 .0417589 172.71 0.000 7.130126 7.293818 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.298067 .0674454 93.38 0.000 6.165876 6.430257 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 2.448338 .0701101 2.310924 2.585751 var(cons_2) | 3.337122 .0955611 3.149825 3.524418 var(cons_3) | 5.152235 .2084371 4.743706 5.560764 var(cons_4) | 7.710807 .3140083 7.095362 8.326252 var(cons_5) | 4.253141 .121792 4.014433 4.491849 var(cons_6) | 5.576921 .2252497 5.13544 6.018403 ------------------------------------------------------------------------------ . . matrix flinit = (1\0\0\0\0\0) . . matrix flconstr = (1\0\0\0\0\0) . . matrix fvinit = (1) . . matrix fvconstr = (0) . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal flinits(flinit) flconstraints(flconstr) fvinits(fv > init) fvconstraints(fvconstr) fscores(f) /// > ) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 27.6 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.393853 .0315962 2294 0.000 8.331796 8.45559 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066432 .0365538 935 0.000 6.995427 7.137725 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.89185 .0644307 1620 0.000 6.76592 7.01614 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.677166 .0775935 1162 0.000 5.524043 5.830398 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211287 .0416177 944 0.000 7.129069 7.289267 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.312344 .0630663 840 0.000 6.188666 6.437182 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.962427 .0615493 2907 1.844109 2.085535 var(cons_2) | 1.656433 .0747929 859 1.506351 1.801206 var(cons_3) | 4.758292 .2013284 1606 4.370496 5.16581 var(cons_4) | 5.656289 .2621211 1191 5.158921 6.186232 var(cons_5) | 1.977386 .0980439 549 1.791184 2.174221 var(cons_6) | 3.261432 .1676524 954 2.950257 3.604244 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.881196 .1069256 104 1.685697 2.102312 f1_3 | .9307464 .1185994 431 .7036948 1.168265 f1_4 | 2.11546 .1650183 150 1.813618 2.462221 f1_5 | 2.187338 .1311137 93 1.958346 2.463995 f1_6 | 2.193351 .1483755 110 1.925851 2.504234 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .4798749 .0505216 89 .3834784 .5833372 ------------------------------------------------------------------------------ . . sort f1 . . generate f1rank = _n . . scatter f1 f1rank . . list student es_core biol_core biol_r3 biol_r4 phys_core phys_r2 f1 if f1rank > ==1, noobs +---------------------------------------------------------------------------- ------+ | student es_core biol_c~e biol_r3 biol_r4 phys_c~e phys_r2 > f1 | |---------------------------------------------------------------------------- ------| | 664 1.7 0 . . 0 5.7 -2. > 29791 | +---------------------------------------------------------------------------- ------+ . . list student es_core biol_core biol_r3 biol_r4 phys_core phys_r2 f1 if f1rank > ==_N, noobs +---------------------------------------------------------------------------- ------+ | student es_core biol_c~e biol_r3 biol_r4 phys_c~e phys_r2 > f1 | |---------------------------------------------------------------------------- ------| | 2132 10 10 . 10 10 10 1.2 > 10127 | +---------------------------------------------------------------------------- ------+ . . drop f1* . . . . * 20.5 Adding a second factor to the model . . . . . . . . . . . . . . . 313 . . sort school student . . quietly runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal /// > ) /// > nopause . . matrix flinit = (1,0\0,1\0,0\0,0\0,0\0,0) . . matrix flconstr = (1,1\0,1\0,0\0,0\0,0\0,0) . . matrix fvinit = (1,.\.,1) . . matrix fvconstr = (0,.\.,0) . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal flinits(flinit) flconstraints(flconstr) fvinits(fv > init) fvconstraints(fvconstr) fscores(f) /// > ) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 40.9 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.393817 .0322564 1849 0.000 8.331692 8.457939 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.065719 .0381003 787 0.000 6.990055 7.13988 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.894367 .06436 1451 0.000 6.770535 7.024236 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.674764 .0782857 1134 0.000 5.521406 5.827527 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211161 .0429777 840 0.000 7.122687 7.294669 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.311346 .0622808 581 0.000 6.187002 6.431299 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.905762 .092907 17 1.663249 2.04622 var(cons_2) | 1.469402 .1271428 11 1.239484 1.727717 var(cons_3) | 4.713906 .2075256 1059 4.311779 5.124603 var(cons_4) | 5.295579 .377071 120 4.463551 5.947342 var(cons_5) | 2.081563 .1196699 25 1.815392 2.299455 var(cons_6) | 2.072401 .6792045 6 .7911825 3.241254 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.852411 .2069945 8 1.257707 2.149383 f1_3 | .8064128 .1241827 241 .5728287 1.058212 f1_4 | 1.708954 .2388058 9 1.07288 2.095984 f1_5 | 1.896334 .2046851 9 1.29263 2.192597 f1_6 | 1.719796 .2188011 8 1.154458 2.083471 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | 5.184466 4.725559 5 -.1159846 17.77937 f2_4 | 14.68764 9.60686 4 1.579057 34.51042 f2_5 | 6.457909 3.964584 4 1.430375 14.73736 f2_6 | 22.76607 15.29767 3 1.608623 48.27541 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .5414408 .0864528 15 .4269885 .7934544 cov(f2,f1) | 0 0 0 0 0 var(f2) | .0483003 .1100965 7 .00093 .4472583 ------------------------------------------------------------------------------ . . scatter f1 f2 . . twoway /// > (scatter f1 f2 if ~inlist(student,664,1572)) /// > (scatter f1 f2 if student==664) /// > (scatter f1 f2 if student==1572) /// > , legend(order(2 "Student 664" 3 "Student 1572")) . . sort f2 . . generate f2rank = _n . . list student es_core biol_core biol_r3 biol_r4 phys_core phys_r2 f1 f2 f2rank > if f2rank==1 | student==1572, noobs +---------------------------------------------------------------------------- -------------------+ | student | es_core | biol_c~e | biol_r3 | biol_r4 | phys_c~e | phys_r2 | > f1 | f2 | | 774 | 10 | 8 | . | 0 | 6 | 1.4 | -.1 > 258314 | -.2392557 | |---------------------------------------------------------------------------- -------------------| | f2rank > | | 1 > | +---------------------------------------------------------------------------- -------------------+ +---------------------------------------------------------------------------- -------------------+ | student | es_core | biol_c~e | biol_r3 | biol_r4 | phys_c~e | phys_r2 | > f1 | f2 | | 1572 | 10 | 8 | 5 | . | 8 | 0 | .0 > 921744 | -.2190236 | |---------------------------------------------------------------------------- -------------------| | f2rank > | | 4 > | +---------------------------------------------------------------------------- -------------------+ . . drop f1* f2* . . . . * 20.6 Examining the chains of the loading estimates . . . . . . . . . . 317 . . sort school student . . mcmcsum RP1FL:f1_2, detail RP1FL:f1_2 ------------------------------------------------------------------------------ Percentiles Mean 1.852411 0.5% 1.050902 Thinned Chain Length 5000 MCSE of Mean .0244769 2.5% 1.257707 Effective Sample Size 8 Std. Dev. .2069945 5% 1.390497 Raftery Lewis (2.5%) 105210 Mode 1.917348 25% 1.773611 Raftery Lewis (97.5%) 40662 P(mean) 0.000 Brooks Draper (mean) 4603 P(mode) 0.000 50% 1.893856 P(median) 0.000 75% 1.979438 95% 2.107599 97.5% 2.149383 99.5% 2.227629 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f1_2, fiveway . . mcmcsum RP1FL:f2_3, detail RP1FL:f2_3 ------------------------------------------------------------------------------ Percentiles Mean 5.184466 0.5% -.650778 Thinned Chain Length 5000 MCSE of Mean .5245695 2.5% -.1159846 Effective Sample Size 5 Std. Dev. 4.725559 5% .1286054 Raftery Lewis (2.5%) 36284 Mode 2.212932 25% 1.41292 Raftery Lewis (97.5%) 44316 P(mean) 0.034 Brooks Draper (mean) 2114133 P(mode) 0.034 50% 4.022373 P(median) 0.034 75% 7.611383 95% 14.57706 97.5% 17.77937 99.5% 21.60015 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f2_3, fiveway . . quietly runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal /// > ) /// > nopause . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal flinits(flinit) flconstraints(flconstr) fvinits(fv > init) fvconstraints(fvconstr) /// > ) /// > mcmc(burnin(5000) chain(10000)) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 5000 Chain = 10000 Thinning = 1 Run time (seconds) = 102 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.395242 .0314554 3914 0.000 8.334148 8.458528 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.068479 .0367684 1031 0.000 6.996292 7.139867 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.895657 .0645616 2987 0.000 6.76984 7.023516 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.67794 .0761776 2038 0.000 5.526517 5.825054 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.214158 .0411086 1024 0.000 7.133979 7.293599 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.32217 .0690124 61 0.000 6.185627 6.452015 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.931981 .0625931 3138 1.810852 2.056358 var(cons_2) | 1.461238 .1013596 155 1.253635 1.651548 var(cons_3) | 4.739755 .2031879 2725 4.353461 5.153417 var(cons_4) | 5.440001 .3294735 31 4.710498 6.029072 var(cons_5) | 2.113577 .0986032 364 1.916202 2.307352 var(cons_6) | .924088 .8734795 6 .0293902 2.653538 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.91382 .1244644 27 1.696384 2.19554 f1_3 | .8462553 .1157778 788 .626597 1.081979 f1_4 | 1.841787 .1654229 119 1.547027 2.198321 f1_5 | 1.987405 .1302907 56 1.770084 2.261967 f1_6 | 1.777309 .1658088 16 1.484478 2.124255 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | 5.677113 5.95412 10 -.1193065 23.15888 f2_4 | 17.45156 13.5455 7 5.80782 56.84074 f2_5 | 7.539299 5.368681 7 2.549805 23.05617 f2_6 | 33.755 14.21865 7 20.51821 80.5386 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .5166407 .056063 43 .4010109 .6248225 cov(f2,f1) | 0 0 0 0 0 var(f2) | .0039722 .0025377 6 .0002643 .0085054 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f2_3, detail RP1FL:f2_3 ------------------------------------------------------------------------------ Percentiles Mean 5.677113 0.5% -1.160281 Thinned Chain Length 10000 MCSE of Mean .4538981 2.5% -.1193065 Effective Sample Size 10 Std. Dev. 5.95412 5% .416883 Raftery Lewis (2.5%) 21172 Mode 2.98709 25% 2.037727 Raftery Lewis (97.5%) 116620 P(mean) 0.029 Brooks Draper (mean) 3165723 P(mode) 0.029 50% 3.54068 P(median) 0.029 75% 7.099544 95% 18.442 97.5% 23.15888 99.5% 31.4693 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f2_3, fiveway . . . . * 20.7 Correlated factors . . . . . . . . . . . . . . . . . . . . . . . .319 . . quietly runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal /// > ) /// > nopause . . matrix flinit = (1,0\0,1\0,0\0,0\0,0\0,0) . . matrix flconstr = (1,1\0,1\0,0\0,0\0,0\0,0) . . matrix fvinit = (1,0\0,1) . . matrix fvconstr = (0,0\0,0) . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)), /// > diagonal flinits(flinit) flconstraints(flconstr) fvinits(fvin > it) fvconstraints(fvconstr) /// > ) /// > mcmc(burnin(5000) chain(10000)) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 5000 Chain = 10000 Thinning = 1 Run time (seconds) = 172 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.393385 .0316989 4342 0.000 8.331829 8.454996 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.065112 .0369678 1760 0.000 6.992724 7.138038 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.895873 .0641941 3164 0.000 6.771508 7.020405 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.679719 .0772723 2125 0.000 5.526488 5.831413 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211044 .0423022 1700 0.000 7.128438 7.295354 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.307863 .0615345 1470 0.000 6.19091 6.430144 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.840942 .0800905 57 1.672516 1.988911 var(cons_2) | 1.5977 .0895651 219 1.420991 1.774935 var(cons_3) | 4.710459 .2150917 1750 4.295209 5.129563 var(cons_4) | 5.183448 .5421449 66 3.686598 5.980093 var(cons_5) | 1.995629 .1427173 47 1.606828 2.217867 var(cons_6) | 2.628416 .4943465 20 1.456228 3.364639 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.72428 .3081612 7 1.152139 2.227579 f1_3 | .7767058 .2672625 11 .1170903 1.219336 f1_4 | 1.571756 .8978362 7 -.33341 2.923032 f1_5 | 1.877926 .5515932 7 .8642817 2.95162 f1_6 | 1.592311 .9536746 6 -.3648751 2.934721 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | .6610446 .5458172 54 -.566881 1.681608 f2_4 | 2.797783 .918327 17 .9348919 4.74499 f2_5 | 1.704315 .3132079 72 1.131007 2.38068 f2_6 | 3.151178 1.084025 15 1.314051 5.456747 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .6053805 .0775911 41 .4661014 .7689209 cov(f2,f1) | -.0701864 .2200749 7 -.5406015 .2692696 var(f2) | .2648807 .173013 12 .0975089 .7843496 ------------------------------------------------------------------------------ . . . . * 20.8 Multilevel factor analysis . . . . . . . . . . . . . . . . . . . .320 . . sort school student . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level2(school: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > ) /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > ) correlation /// > nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 99 12 24.6 34 ----------------------------------------------------------- Run time (seconds) = 12.73 Number of iterations = 4 Log likelihood = -21741.722 Deviance = 43483.443 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.364562 .0704801 118.68 0.000 8.226423 8.5027 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.029626 .0932864 75.36 0.000 6.846788 7.212464 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.866313 .087137 78.80 0.000 6.695527 7.037098 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.662552 .1512465 37.44 0.000 5.366114 5.95899 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.165979 .1074912 66.67 0.000 6.9553 7.376658 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.284618 .1119299 56.15 0.000 6.06524 6.503997 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 2: school | var(cons_1) | .4049916 .0698771 .2680351 .5419481 corr(cons_1,cons_2) | .6815802 .0688797 .5465784 .816582 var(cons_2) | .7514723 .1224169 .5115397 .991405 corr(cons_1,cons_3) | .5106061 .1340139 .2479436 .7732686 corr(cons_2,cons_3) | .6788894 .1133341 .4567586 .9010202 var(cons_3) | .3664443 .1073972 .1559497 .5769389 corr(cons_1,cons_4) | .4629469 .1020107 .2630097 .6628841 corr(cons_2,cons_4) | .6728564 .0732969 .5291972 .8165157 corr(cons_3,cons_4) | .4574422 .1415392 .1800306 .7348539 var(cons_4) | 1.796522 .3219404 1.16553 2.427513 corr(cons_1,cons_5) | .5708068 .0829857 .4081577 .7334558 corr(cons_2,cons_5) | .8928788 .0299284 .8342202 .9515374 corr(cons_3,cons_5) | .7619241 .1046771 .5567608 .9670874 corr(cons_4,cons_5) | .6177791 .0799344 .4611105 .7744477 var(cons_5) | 1.005949 .1625646 .6873279 1.32457 corr(cons_1,cons_6) | .5503183 .0973376 .3595401 .7410964 corr(cons_2,cons_6) | .7739483 .0628138 .6508355 .8970611 corr(cons_3,cons_6) | .5771906 .138182 .3063588 .8480223 corr(cons_4,cons_6) | .6378019 .0889696 .4634246 .8121792 corr(cons_5,cons_6) | .7715538 .0612622 .651482 .8916255 var(cons_6) | .9041645 .1765052 .5582206 1.250108 -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 2.058377 .0601739 1.940438 2.176315 corr(cons_1,cons_2) | .2743343 .0191152 .2368692 .3117995 var(cons_2) | 2.611478 .0763433 2.461848 2.761108 corr(cons_1,cons_3) | .1231025 .0287046 .0668425 .1793624 corr(cons_2,cons_3) | .1338324 .0286347 .0777094 .1899554 var(cons_3) | 4.785152 .2014345 4.390348 5.179957 corr(cons_1,cons_4) | .1360584 .0282022 .0807831 .1913336 corr(cons_2,cons_4) | .2701169 .0268453 .2175011 .3227326 corr(cons_3,cons_4) | .1931866 .0479581 .0991905 .2871828 var(cons_4) | 5.90951 .2491346 5.421216 6.397805 corr(cons_1,cons_5) | .2565805 .0193105 .2187327 .2944283 corr(cons_2,cons_5) | .4188344 .0170441 .3854286 .4522402 corr(cons_3,cons_5) | .1031616 .0288185 .0466783 .1596449 corr(cons_4,cons_5) | .2853163 .0266321 .2331182 .3375143 var(cons_5) | 3.267099 .0955101 3.079903 3.454296 corr(cons_1,cons_6) | .2180781 .026395 .1663449 .2698114 corr(cons_2,cons_6) | .3375598 .0247939 .2889646 .3861549 corr(cons_3,cons_6) | .1495413 .0458075 .0597602 .2393225 corr(cons_4,cons_6) | .386245 .0405391 .3067897 .4657002 corr(cons_5,cons_6) | .4321438 .0230034 .3870579 .4772296 var(cons_6) | 4.626571 .1908185 4.252573 5.000568 ------------------------------------------------------------------------------ . . . . * 20.9 Two level factor model . . . . . . . . . . . . . . . . . . . . . .321 . . quietly runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level2(school: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal /// > ) /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal /// > ) /// > nopause . . matrix flinit1 = (1\0\0\0\0\0) . . matrix flconstr1 = (1\0\0\0\0\0) . . matrix fvinit1 = (1) . . matrix fvconstr1 = (0) . . matrix flinit2 = (1\0\0\0\0\0) . . matrix flconstr2 = (1\0\0\0\0\0) . . matrix fvinit2 = (1) . . matrix fvconstr2 = (0) . . runmlwin /// > (es_core cons, eq(1)) /// > (biol_core cons, eq(2)) /// > (biol_r3 cons, eq(3)) /// > (biol_r4 cons, eq(4)) /// > (phys_core cons, eq(5)) /// > (phys_r2 cons, eq(6)) /// > , /// > level2(school: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal flinits(flinit2) flconstraints(flconstr2) fvinits( > fvinit2) fvconstraints(fvconstr2) fscores(f) /// > ) /// > level1(student: /// > (cons, eq(1)) /// > (cons, eq(2)) /// > (cons, eq(3)) /// > (cons, eq(4)) /// > (cons, eq(5)) /// > (cons, eq(6)) /// > , diagonal flinits(flinit1) flconstraints(flconstr1) fvinits( > fvinit1) fvconstraints(fvconstr1) /// > ) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 99 12 24.6 34 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 47 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.361861 .0677994 262 0.000 8.224669 8.495609 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.02323 .0894754 133 0.000 6.832047 7.193552 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.865917 .085786 357 0.000 6.691154 7.032067 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.657194 .1590848 176 0.000 5.340254 5.963201 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.160004 .1045302 132 0.000 6.939216 7.355132 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.27077 .1139525 158 0.000 6.040634 6.486161 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons_1) | .2443588 .0496642 1289 .160576 .3571571 var(cons_2) | .0634011 .0461993 28 .0014932 .1676839 var(cons_3) | .1638741 .079528 162 .0303927 .3408651 var(cons_4) | 1.000605 .2176991 992 .6388755 1.486812 var(cons_5) | .1360664 .0643474 33 .0040972 .2638049 var(cons_6) | .3122792 .0976914 290 .1404416 .5252018 -----------------------------+------------------------------------------------ Level 2 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.809772 .1351784 18 1.808857 3.471331 f1_3 | .8446907 .1504195 29 .7571042 2.049586 f1_4 | 1.976356 .2041609 24 1.7716 4.200485 f1_5 | 2.191402 .177367 13 1.973974 4.118021 f1_6 | 2.356317 .2061788 19 1.600485 3.292224 -----------------------------+------------------------------------------------ Level 2 factor covariances: | var(f1) | .1280841 .0465355 19 .0542716 .2411368 -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.742365 .0561492 2245 1.635205 1.853611 var(cons_2) | 1.612151 .0716385 730 1.474995 1.757332 var(cons_3) | 4.589357 .1989414 1488 4.208368 5.007984 var(cons_4) | 4.743246 .2276066 975 4.315283 5.194709 var(cons_5) | 1.801202 .0986467 478 1.603332 1.991553 var(cons_6) | 2.935219 .1658297 464 2.621756 3.26998 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 2.435336 .403806 77 1.56551 2.102756 f1_3 | 1.3141 .3269515 544 .5631752 1.144232 f1_4 | 2.704051 .6142709 129 1.611425 2.409255 f1_5 | 2.767075 .5327303 67 1.877222 2.562401 f1_6 | 2.297602 .4406307 74 1.975926 2.781584 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .310836 .0425793 60 .2299971 .3974274 ------------------------------------------------------------------------------ . . keep school f1 . . duplicates drop Duplicates in terms of all variables (2,340 observations deleted) . . sort f1 . . generate f1rank = _n . . scatter f1 f1rank . . list if f1rank==1 +-----------------------------+ | school f1 f1rank | |-----------------------------| 1. | 2089 -.7599515 1 | +-----------------------------+ . . list if f1rank==_N +----------------------------+ | school f1 f1rank | |----------------------------| 99. | 8033 .8226771 99 | +----------------------------+ . . . . * 20.10 Extensions and some warnings . . . . . . . . . . . . . . . . . . 324 . . * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .325 . . . . . . **************************************************************************** . exit end of do-file