------------------------------------------------------------------------------- name: log: Q:\C-modelling\runmlwin\website\logfiles\2020-03-27\16\9_Modelling > _Complex_Variance_at_Level_1_Heteroscedasticity.smcl log type: smcl opened on: 27 Mar 2020, 17:49:57 . ***************************************************************************** > *** . * MLwiN MCMC Manual . * . * 9 Modelling Complex Variance at Level 1 / Heteroscedasticity. . . . . . . > 111 . * . * 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/ . ***************************************************************************** > *** . . use "http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial.dta", clear . . tabstat normexam, by(girl) stats(N mean sd) Summary for variables: normexam by categories of: girl (Girl) girl | N mean sd ---------+------------------------------ 0 | 1623 -.1403503 1.025713 1 | 2436 .0933195 .9697191 ---------+------------------------------ Total | 4059 -.0001139 .9989439 ---------------------------------------- . . gen intakecat = standlrt . . recode intakecat (-4/-1=0) (-1/-.5=1) (-.5/-.1=2) (-.1/.3=3) (.3/.7=4) /// > (.7/1.1=5) (1.1/4=6) (intakecat: 4059 changes made) . . tabstat normexam, by(intakecat) stats(N mean sd) Summary for variables: normexam by categories of: intakecat intakecat | N mean sd ----------+------------------------------ 0 | 612 -.8869798 .8547923 1 | 594 -.4987862 .77429 2 | 619 -.1907822 .8064874 3 | 710 .0439194 .8111908 4 | 547 .2784655 .8117617 5 | 428 .5709619 .8235468 6 | 549 .9633285 .8381857 ----------+------------------------------ Total | 4059 -.0001139 .9989439 ----------------------------------------- . . . . * 9.1 MCMC algorithm for a 1 level Normal model with complex variation . . . > 113 . . * 9.2 Setting up the model in MLwiN . . . . . . . . . . . . . . . . . . . . . > 115 . . quietly runmlwin normexam cons standlrt, /// > level1(student: cons standlrt) /// > nopause . . runmlwin normexam cons standlrt, /// > level1(student: cons standlrt) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: MCMC Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 3.64 Deviance (dbar) = 9764.54 Deviance (thetabar) = 9759.59 Effective no. of pars (pd) = 4.95 Bayesian DIC = 9769.50 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0020406 .0127381 4596 0.426 -.0273471 .0232062 standlrt | .5958179 .0132761 4576 0.000 .5700945 .6226636 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .6389313 .0176388 622 .6059498 .6744686 cov(cons,standlrt) | .0026157 .007477 1162 -.0118638 .0174134 var(standlrt) | .0115854 .0107126 635 -.0089616 .0328082 ------------------------------------------------------------------------------ . . mcmcsum in 4501/5000, trajectories . . generate l1varfn = [RP1]var(cons) + 2*[RP1]cov(cons\standlrt)*standlrt /// > + [RP1]var(standlrt)*standlrt^2 . . line l1varfn standlrt, sort . . . . * 9.3 Complex variance functions in multilevel models . . . . . . . . . . . . > 119 . . quietly runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons) /// > nopause . . runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 3.22 Deviance (dbar) = 9122.67 Deviance (thetabar) = 9031.18 Effective no. of pars (pd) = 91.50 Bayesian DIC = 9214.17 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0132462 .0398381 243 0.358 -.0890089 .0733577 standlrt | .5568666 .020332 769 0.000 .515988 .5963049 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0970636 .0200401 2964 .06544 .1425988 cov(cons,standlrt) | .0195519 .0073726 1709 .0064736 .0359522 var(standlrt) | .0154917 .0048418 1029 .0080367 .0268087 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5543189 .0124713 4659 .5302743 .5795808 ------------------------------------------------------------------------------ . . generate l2varfn = [RP2]var(cons) + 2*[RP2]cov(cons\standlrt)*standlrt /// > + [RP2]var(standlrt)*standlrt^2 . . replace l1varfn = [RP1]var(cons) (4,059 real changes made) . . line l2varfn l1varfn standlrt, sort . . matrix a = (1,1,0) . . quietly runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt, elements(a)) /// > nopause . . runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt, elements(a)) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 5.46 Deviance (dbar) = 9119.35 Deviance (thetabar) = 9027.65 Effective no. of pars (pd) = 91.71 Bayesian DIC = 9211.06 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0151947 .039428 231 0.344 -.0907625 .061212 standlrt | .5566101 .0200622 818 0.000 .5175159 .5963993 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0964782 .019622 3024 .0645598 .1403807 cov(cons,standlrt) | .0199114 .0071954 1682 .0073485 .0353943 var(standlrt) | .0152424 .0047141 1004 .0076768 .026243 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5554901 .0127509 978 .5312036 .5815894 cov(cons,standlrt) | -.0148285 .0063187 1143 -.0267773 -.0021092 ------------------------------------------------------------------------------ . . . . * 9.4 Relationship with gender . . . . . . . . . . . . . . . . . . . . . . . > 123 . . matrix a = (1,1,0,1,1,0) . . runmlwin normexam cons standlrt girl, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt girl, elements(a)) /// > nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: IGLS ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Run time (seconds) = 0.89 Number of iterations = 4 Log likelihood = -4635.7978 Deviance = 9271.5957 ------------------------------------------------------------------------------ normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- cons | -.1120559 .043286 -2.59 0.010 -.1968948 -.0272169 standlrt | .5538978 .0200267 27.66 0.000 .5146462 .5931494 girl | .1753161 .0322887 5.43 0.000 .1120314 .2386008 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0864349 .017195 .0527333 .1201365 cov(cons,standlrt) | .0195737 .0066755 .0064899 .0326574 var(standlrt) | .0147943 .0044509 .0060707 .0235179 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5837113 .0208961 .5427556 .6246669 cov(cons,standlrt) | -.033675 .0099613 -.0531989 -.0141512 cov(cons,girl) | -.029134 .0129647 -.0545444 -.0037236 cov(standlrt,girl) | .0320916 .0128955 .0068168 .0573664 ------------------------------------------------------------------------------ . . runmlwin normexam cons standlrt girl, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt girl, elements(a)) /// > mcmc(on) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 8.01 Deviance (dbar) = 9085.13 Deviance (thetabar) = 8991.66 Effective no. of pars (pd) = 93.47 Bayesian DIC = 9178.60 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.1162389 .0470572 256 0.004 -.2129523 -.0278925 standlrt | .5527361 .0217744 530 0.000 .5076809 .5925029 girl | .1745083 .0327546 1839 0.000 .1101794 .2380499 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0922863 .0189371 2685 .0614275 .1340163 cov(cons,standlrt) | .0212511 .0074988 1597 .0084343 .0376593 var(standlrt) | .0155846 .0048064 978 .0078559 .0265695 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5860473 .0209126 257 .5466978 .6270426 cov(cons,standlrt) | -.0334446 .0097437 328 -.0530369 -.0143889 cov(cons,girl) | -.0290592 .0128291 248 -.055089 -.0049323 cov(standlrt,girl) | .0315864 .0121888 318 .0066992 .0550526 ------------------------------------------------------------------------------ . . replace l2varfn = [RP2]var(cons) + 2*[RP2]cov(cons\standlrt)*standlrt /// > + [RP2]var(standlrt)*standlrt^2 (4,059 real changes made) . . generate l1varfnboys = [RP1]var(cons) + 2*[RP1]cov(cons\standlrt)*standlrt . . generate l1varfngirls = [RP1]var(cons) /// > + 2*[RP1]cov(cons\standlrt)*standlrt /// > + 2*[RP1]cov(cons\girl) + 2*[RP1]cov(standlrt\girl)*standlrt . . line l2varfn l1varfnboys l1varfngirls standlrt, sort . . . . * 9.5 Alternative log precision formulation . . . . . . . . . . . . . . . . . > 126 . . matrix a = (1,1,0,1,1,0) . . quietly runmlwin normexam cons standlrt girl, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt girl, elements(a)) /// > nopause . . runmlwin normexam cons standlrt girl, /// > level2(school: cons standlrt) /// > level1(student: cons standlrt girl, elements(a)) /// > mcmc(log) initsprevious nopause MLwiN 3.05 multilevel model Number of obs = 4059 Normal response model (hierarchical) Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 9.87 Deviance (dbar) = 9085.46 Deviance (thetabar) = 8991.48 Effective no. of pars (pd) = 93.99 Bayesian DIC = 9179.45 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.1156093 .0417297 369 0.001 -.1987456 -.0342224 standlrt | .5533793 .0205383 760 0.000 .5127157 .5941113 girl | .1752249 .0315939 1938 0.000 .1115293 .2361958 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0916186 .0186013 3040 .0611348 .1341794 cov(cons,standlrt) | .0209184 .0071749 1715 .00866 .0368215 var(standlrt) | .0157909 .0047147 1151 .008486 .0265979 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5442241 .0373866 291 .4713987 .6180628 cov(cons,standlrt) | .0537788 .0181402 340 .017687 .0897195 cov(cons,girl) | .0484676 .0238134 317 .0032154 .0963128 cov(standlrt,girl) | -.0507925 .0241972 345 -.0986032 -.0027738 ------------------------------------------------------------------------------ . . replace l2varfn = [RP2]var(cons) + 2*[RP2]cov(cons\standlrt)*standlrt /// > + [RP2]var(standlrt)*standlrt^2 (4,059 real changes made) . . replace l1varfnboys = [RP1]var(cons) + 2*[RP1]cov(cons\standlrt)*standlrt (4,059 real changes made) . . replace l1varfngirls = [RP1]var(cons) /// > + 2*[RP1]cov(cons\standlrt)*standlrt /// > + 2*[RP1]cov(cons\girl) + 2*[RP1]cov(standlrt\girl)*standlrt (4,059 real changes made) . . . replace l1varfnboys = 1/exp(l1varfnboys) (4,059 real changes made) . . replace l1varfngirls = 1/exp(l1varfngirls) (4,059 real changes made) . . . line l2varfn l1varfnboys l1varfngirls standlrt, sort . . . . * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . . > 128 . . . . . . ***************************************************************************** > *** . exit end of do-file