------------------------------------------------------------------------------- name: log: Q:\C-modelling\runmlwin\website\logfiles\2024-10-11\18\20_Multilev > el_Factor_Analysis_Modelling.smcl log type: smcl opened on: 11 Oct 2024, 17:49:09 . **************************************************************************** . * 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 . * https://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 "https://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta", clear . . describe Contains data from https://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta Observations: 2,439 Variables: 10 21 Oct 2011 12:19 ------------------------------------------------------------------------------- Variable Storage Display Value 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 https://www.bristol.ac.uk/cmm/media/runmlwin/hungary1.dta Observations: 2,439 Variables: 10 21 Oct 2011 12:19 ------------------------------------------------------------------------------- Variable Storage Display Value 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 13.28 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 13.28 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: IGLS Run time (seconds) = 3.88 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 64.9 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394974 .0312993 2375 0.000 8.333315 8.455203 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066838 .0368914 1053 0.000 6.993311 7.138848 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.89553 .0626996 1682 0.000 6.772285 7.01872 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.675865 .0771254 1157 0.000 5.52657 5.825035 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.213307 .0420038 909 0.000 7.129991 7.292249 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.315262 .0619534 919 0.000 6.190508 6.436758 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.963828 .0615651 2816 1.844705 2.087201 var(cons_2) | 1.654392 .0762641 937 1.510746 1.806213 var(cons_3) | 4.750085 .19986 1542 4.375843 5.152092 var(cons_4) | 5.641543 .261616 1218 5.153934 6.172979 var(cons_5) | 1.982358 .0955699 837 1.804159 2.17236 var(cons_6) | 3.2508 .1682517 839 2.926243 3.595087 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.894611 .1023798 126 1.714257 2.112665 f1_3 | .9368577 .1156756 716 .7153792 1.161571 f1_4 | 2.137846 .1641366 212 1.823321 2.476959 f1_5 | 2.201285 .1230866 126 1.980814 2.466804 f1_6 | 2.21177 .1499178 146 1.93256 2.515551 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .4725488 .0468473 112 .3826544 .5674493 ------------------------------------------------------------------------------ . . 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. > 27787 | +---------------------------------------------------------------------------- ------+ . . 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 1.1 > 99163 | +---------------------------------------------------------------------------- ------+ . . 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 96.1 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.393645 .031472 2254 0.000 8.330953 8.454692 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066028 .0368162 905 0.000 6.990444 7.137809 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.893954 .0623227 1503 0.000 6.772501 7.015916 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.67819 .076725 1047 0.000 5.524276 5.829566 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211509 .0409044 1006 0.000 7.129648 7.290143 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.3083 .0602475 558 0.000 6.18919 6.426024 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.920992 .0677943 185 1.787251 2.051875 var(cons_2) | 1.490017 .1097824 31 1.288387 1.701582 var(cons_3) | 4.705697 .2067109 1212 4.313139 5.106676 var(cons_4) | 5.176525 .4460918 29 4.234849 5.930268 var(cons_5) | 2.086743 .1055507 135 1.88028 2.295169 var(cons_6) | 1.95637 .8616191 5 .4351111 3.141979 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.879994 .1491647 14 1.557579 2.167203 f1_3 | .8020012 .1281717 59 .5405156 1.053207 f1_4 | 1.741194 .2156812 10 1.237139 2.11748 f1_5 | 1.965553 .1372186 56 1.660403 2.224158 f1_6 | 1.777197 .1628496 55 1.432446 2.081989 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | 3.251246 2.272037 9 .263512 9.124476 f2_4 | 9.989851 5.212493 6 2.665322 24.17047 f2_5 | 4.192847 2.148719 5 1.271012 8.68033 f2_6 | 16.24354 10.3527 3 2.252217 37.4498 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .5199881 .0580355 36 .4139537 .6423128 cov(f2,f1) | 0 0 0 0 0 var(f2) | .0303201 .0529153 7 .0022431 .2202067 ------------------------------------------------------------------------------ . . 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 f2rank | |---------------------------------------------------------------------------- ----------------------------| | 774 10 8 . 0 6 1.4 -.1 > 500787 -.2467529 1 | | 1572 10 8 5 . 8 0 .0 > 836205 -.2413658 2 | +---------------------------------------------------------------------------- ----------------------------+ . . 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 1.879994 0.5% 1.474534 Thinned Chain Length 5000 MCSE of Mean .0126407 2.5% 1.557579 Effective Sample Size 14 Std. Dev. .1491647 5% 1.616367 Raftery Lewis (2.5%) 61930 Mode 1.890996 25% 1.785708 Raftery Lewis (97.5%) 57858 P(mean) 0.000 Brooks Draper (mean) 1228 P(mode) 0.000 50% 1.885691 P(median) 0.000 75% 1.976951 95% 2.117679 97.5% 2.167203 99.5% 2.251553 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f1_2, fiveway . . mcmcsum RP1FL:f2_3, detail RP1FL:f2_3 ------------------------------------------------------------------------------ Percentiles Mean 3.251246 0.5% -.4922637 Thinned Chain Length 5000 MCSE of Mean .1842603 2.5% .263512 Effective Sample Size 9 Std. Dev. 2.272037 5% .6354841 Raftery Lewis (2.5%) 24236 Mode 2.191633 25% 1.617013 Raftery Lewis (97.5%) 45904 P(mean) 0.015 Brooks Draper (mean) 260850 P(mode) 0.015 50% 2.728296 P(median) 0.015 75% 4.324655 95% 7.905884 97.5% 9.124476 99.5% 11.48396 ------------------------------------------------------------------------------ . . 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 5000 Chain = 10000 Thinning = 1 Run time (seconds) = 239 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394122 .0316908 2231 0.000 8.331874 8.455536 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.065905 .0372733 254 0.000 6.991987 7.138978 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.896274 .0637544 3109 0.000 6.769836 7.020162 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.6752 .0774841 1581 0.000 5.522846 5.828872 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.211763 .0424611 230 0.000 7.128601 7.293459 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.316408 .0632288 40 0.000 6.197615 6.444683 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.941117 .062113 4187 1.822398 2.065093 var(cons_2) | 1.434075 .0948751 160 1.243528 1.622262 var(cons_3) | 4.748605 .2014062 2889 4.363268 5.159129 var(cons_4) | 5.519352 .3021998 149 4.877379 6.078442 var(cons_5) | 2.141518 .0982085 175 1.946807 2.334934 var(cons_6) | .5277918 .7300973 6 .0066852 2.273388 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.96405 .112143 67 1.76117 2.207294 f1_3 | .8660528 .1179915 260 .6398815 1.101708 f1_4 | 1.915004 .1625546 64 1.607183 2.23553 f1_5 | 2.023716 .1212209 55 1.814099 2.290274 f1_6 | 1.841146 .1271322 55 1.602193 2.144995 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | 7.927042 6.35542 21 -1.277774 26.83056 f2_4 | 25.89296 13.13848 14 11.01563 69.65484 f2_5 | 11.76218 4.819909 14 4.943222 26.38908 f2_6 | 70.58849 20.01415 7 29.91202 98.98973 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .4977253 .0495348 56 .3997628 .5933931 cov(f2,f1) | 0 0 0 0 0 var(f2) | .0009147 .0007818 9 .0001861 .0028506 ------------------------------------------------------------------------------ . . mcmcsum RP1FL:f2_3, detail RP1FL:f2_3 ------------------------------------------------------------------------------ Percentiles Mean 7.927042 0.5% -4.320844 Thinned Chain Length 10000 MCSE of Mean .3116488 2.5% -1.277774 Effective Sample Size 21 Std. Dev. 6.35542 5% .178869 Raftery Lewis (2.5%) 57618 Mode 6.66856 25% 4.21898 Raftery Lewis (97.5%) 101088 P(mean) 0.046 Brooks Draper (mean) 1492407 P(mode) 0.046 50% 7.005067 P(median) 0.046 75% 10.19788 95% 19.80703 97.5% 26.83056 99.5% 35.80981 ------------------------------------------------------------------------------ . . 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 3.13 multilevel model Number of obs = 2439 Multivariate response model (hierarchical) Estimation algorithm: MCMC Burnin = 5000 Chain = 10000 Thinning = 1 Run time (seconds) = 431 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.394376 .0318059 4155 0.000 8.333068 8.456346 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.066613 .0373175 1878 0.000 6.9931 7.138736 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.894205 .0638224 3098 0.000 6.770137 7.019397 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.68076 .0761732 1855 0.000 5.533331 5.834538 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.212164 .0417099 1860 0.000 7.129713 7.294956 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.310999 .0626374 1585 0.000 6.189707 6.433801 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.844571 .0773535 74 1.686939 1.991224 var(cons_2) | 1.597297 .0869591 597 1.423525 1.766657 var(cons_3) | 4.696805 .2105705 1934 4.289807 5.122777 var(cons_4) | 4.953686 .7906067 21 2.154452 5.927099 var(cons_5) | 2.014015 .1106417 219 1.77557 2.21584 var(cons_6) | 2.706624 .4089201 32 1.675437 3.332423 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.510629 .3545862 9 .9577784 2.240004 f1_3 | .6771009 .3841122 10 .0124221 1.584507 f1_4 | 1.19268 1.123005 7 -.3046114 4.01163 f1_5 | 1.516749 .5623433 8 .6264151 2.637693 f1_6 | 1.114695 1.057505 8 -.845548 3.244897 f2_1 | 0 0 0 0 0 f2_2 | 1 0 0 1 1 f2_3 | .8976135 .5601621 35 -.1114499 2.111163 f2_4 | 3.241959 1.261261 19 1.500987 7.338956 f2_5 | 1.624517 .2955503 85 1.040844 2.242139 f2_6 | 3.050563 .7422502 25 1.748897 4.564542 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .6045287 .0725619 47 .4681859 .7571294 cov(f2,f1) | .0746452 .1813861 8 -.293821 .3517795 var(f2) | .235459 .0901063 25 .1128049 .4577928 ------------------------------------------------------------------------------ . . . . * 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 3.13 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) = 32.05 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 3.13 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) = 113 Deviance (dbar) = . Deviance (thetabar) = . Effective no. of pars (pd) = . Bayesian DIC = . ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- es_core | cons_1 | 8.373057 .0666917 221 0.000 8.2423 8.500873 -------------+---------------------------------------------------------------- biol_core | cons_2 | 7.042274 .0895039 94 0.000 6.869823 7.211927 -------------+---------------------------------------------------------------- biol_r3 | cons_3 | 6.87127 .0828796 399 0.000 6.709684 7.03382 -------------+---------------------------------------------------------------- biol_r4 | cons_4 | 5.679506 .1506211 141 0.000 5.378368 5.969381 -------------+---------------------------------------------------------------- phys_core | cons_5 | 7.181648 .1072432 101 0.000 6.97911 7.394845 -------------+---------------------------------------------------------------- phys_r2 | cons_6 | 6.291223 .1059916 164 0.000 6.089334 6.514005 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons_1) | .2375564 .0496336 1268 .1552462 .3466511 var(cons_2) | .049541 .0381194 39 .0011411 .1346083 var(cons_3) | .1642842 .0865364 110 .0205074 .3588781 var(cons_4) | .9986433 .2223924 947 .6238239 1.492402 var(cons_5) | .1522926 .0567084 98 .0485131 .2700106 var(cons_6) | .3181979 .1000299 363 .1473978 .5415434 -----------------------------+------------------------------------------------ Level 2 factors: | f1_1 | 1 0 0 1 1 f1_2 | 1.796167 .1341175 22 1.648709 3.77738 f1_3 | .8347947 .1450095 32 .6770003 2.158871 f1_4 | 1.964796 .1958742 25 1.525108 4.334552 f1_5 | 2.179676 .1710454 21 1.788171 4.372797 f1_6 | 2.336363 .2022903 24 1.412717 3.59543 -----------------------------+------------------------------------------------ Level 2 factor covariances: | var(f1) | .1451359 .0567664 27 .0455487 .26816 -----------------------------+------------------------------------------------ Level 1: student | var(cons_1) | 1.742113 .0569741 2377 1.633873 1.855999 var(cons_2) | 1.615646 .0728929 831 1.475233 1.761359 var(cons_3) | 4.607967 .1994471 1341 4.239665 5.012714 var(cons_4) | 4.732136 .2254709 909 4.303079 5.189854 var(cons_5) | 1.797902 .0958524 575 1.607673 1.984978 var(cons_6) | 2.944424 .1757772 529 2.60638 3.305698 -----------------------------+------------------------------------------------ Level 1 factors: | f1_1 | 1 0 0 1 1 f1_2 | 2.345443 .5195744 91 1.55632 2.081834 f1_3 | 1.245393 .3668539 504 .5573162 1.13061 f1_4 | 2.553284 .6921792 152 1.598146 2.360402 f1_5 | 2.619474 .6224485 73 1.882689 2.560615 f1_6 | 2.177754 .5351642 77 1.971628 2.7595 -----------------------------+------------------------------------------------ Level 1 factor covariances: | var(f1) | .3138097 .040835 64 .2345557 .3990827 ------------------------------------------------------------------------------ . . 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 -.8123965 1 | +-----------------------------+ . . list if f1rank==_N +----------------------------+ | school f1 f1rank | |----------------------------| 99. | 8033 .8538833 99 | +----------------------------+ . . . . * 20.10 Extensions and some warnings . . . . . . . . . . . . . . . . . . 324 . . * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .325 . . . . . . **************************************************************************** . exit end of do-file