------------------------------------------------------------------------------- name: log: Q:\C-modelling\runmlwin\website\logfiles\2013-03-18\12\24_Paramete > r_expansion.smcl log type: smcl opened on: 18 Mar 2013, 03:39:22 . **************************************************************************** . * MLwiN MCMC Manual . * . * 24 Parameter expansion . . . . . . . . . . . . . . . . . . . . . . . .381 . * . * 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/ . **************************************************************************** . . * 24.1 What is Parameter Expansion? . . . . . . . . . . . . . . . . . . .381 . . * 24.2 The tutorial example . . . . . . . . . . . . . . . . . . . . . . .383 . . use "http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial.dta", clear . . runmlwin normexam cons standlrt, /// > level2(school: cons) /// > level1(student: cons) /// > nopause MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model Estimation algorithm: IGLS ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Run time (seconds) = 1.16 Number of iterations = 4 Log likelihood = -4678.6211 Deviance = 9357.2422 ------------------------------------------------------------------------------ normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- cons | .0023908 .0400224 0.06 0.952 -.0760516 .0808332 standlrt | .5633712 .0124654 45.19 0.000 .5389394 .5878029 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0921275 .0181475 .0565591 .127696 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .565731 .0126585 .5409208 .5905412 ------------------------------------------------------------------------------ . . matrix b = e(b) . . matrix V = e(V) . . runmlwin normexam cons standlrt, /// > level2(school: cons) /// > level1(student: cons) /// > mcmc(on) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model 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) = 8.04 Deviance (dbar) = 9208.87 Deviance (thetabar) = 9149.17 Effective no. of pars (pd) = 59.71 Bayesian DIC = 9268.58 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0020239 .0419123 184 0.473 -.0799526 .0812852 standlrt | .5633754 .0123613 3944 0.000 .5393782 .5877464 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0969185 .0202074 2979 .064631 .1432917 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5663839 .012765 4793 .5417422 .5923283 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), detail [RP2]var(cons) ------------------------------------------------------------------------------ Percentiles Mean .0969185 0.5% .0570542 Thinned Chain Length 5000 MCSE of Mean .0003637 2.5% .064631 Effective Sample Size 2979 Std. Dev. .0202074 5% .0691225 Raftery Lewis (2.5%) 4269 Mode .0913852 25% .082483 Raftery Lewis (97.5%) 4064 P(mean) 0 Brooks Draper (mean) 10167 P(mode) 0 50% .0946459 P(median) 0 75% .1086499 95% .1333906 97.5% .1432917 99.5% .1666161 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), fiveway . . runmlwin normexam cons standlrt, /// > level2(school: cons, parexpansion) /// > level1(student: cons) /// > mcmc(on) initsb(b) initsv(V) /// > nopause Warning: variance matrix is nonsymmetric or highly singular MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model 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) = 9.59 Deviance (dbar) = 9208.73 Deviance (thetabar) = 9148.95 Effective no. of pars (pd) = 59.78 Bayesian DIC = 9268.51 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | .0021694 0 194 0.460 -.0842924 .0755407 standlrt | .5630258 0 4088 0.000 .5391444 .5879443 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0981861 0 2958 .0652009 .1466556 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5662173 0 4724 .542101 .5910803 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), detail [RP2]var(cons) ------------------------------------------------------------------------------ Percentiles Mean .0981861 0.5% .0563465 Thinned Chain Length 5000 MCSE of Mean .0003662 2.5% .0652009 Effective Sample Size 2958 Std. Dev. 0 5% .0688566 Raftery Lewis (2.5%) 4269 Mode .0924156 25% .0833823 Raftery Lewis (97.5%) 3996 P(mean) 0 Brooks Draper (mean) 10308 P(mode) 0 50% .0956072 P(median) 0 75% .1102491 95% .1356094 97.5% .1466556 99.5% .1688333 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), fiveway . . . . * 24.3 Binary responses - Voting example . . . . . . . . . . . . . . . . 386 . . use "http://www.bristol.ac.uk/cmm/media/runmlwin/bes83.dta", clear . . runmlwin votecons cons defence unemp taxes privat, /// > level2(area: cons) /// > level1(voter:) /// > discrete(distribution(binomial) link(logit) denominator(cons)) /// > nopause MLwiN 2.27 multilevel model Number of obs = 800 Binomial logit response model Estimation algorithm: IGLS, MQL1 ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ area | 110 1 7.3 16 ----------------------------------------------------------- Run time (seconds) = 1.20 Number of iterations = 6 ------------------------------------------------------------------------------ votecons | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- cons | -.3552158 .0917617 -3.87 0.000 -.5350656 -.1753661 defence | .0893889 .0181955 4.91 0.000 .0537263 .1250515 unemp | .067076 .0134056 5.00 0.000 .0408016 .0933504 taxes | .0445018 .0191789 2.32 0.020 .0069118 .0820918 privat | .1382851 .0176275 7.84 0.000 .1037358 .1728345 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 2: area | var(cons) | .1323441 .111845 -.0868681 .3515564 ------------------------------------------------------------------------------ . . matrix b = e(b) . . matrix V = e(V) . . runmlwin votecons cons defence unemp taxes privat, /// > level2(area: cons) /// > level1(voter:) /// > discrete(distribution(binomial) link(logit) denominator(cons)) /// > mcmc(on) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 800 Binomial logit response model Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ area | 110 1 7.3 16 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 13.3 Deviance (dbar) = 865.70 Deviance (thetabar) = 842.91 Effective no. of pars (pd) = 22.80 Bayesian DIC = 888.50 ------------------------------------------------------------------------------ votecons | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.3677754 .0955176 826 0.000 -.5569555 -.1759782 defence | .0930897 .0187932 868 0.000 .0584539 .1300369 unemp | .0697955 .0136687 1109 0.000 .0425739 .0971867 taxes | .0462141 .0195928 1096 0.011 .0089882 .0836381 privat | .1437097 .0187181 928 0.000 .1073744 .1816978 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: area | var(cons) | .1546002 .1062545 23 .0191032 .4068215 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), detail [RP2]var(cons) ------------------------------------------------------------------------------ Percentiles Mean .1546002 0.5% .0115901 Thinned Chain Length 5000 MCSE of Mean .0087606 2.5% .0191032 Effective Sample Size 23 Std. Dev. .1062545 5% .0314271 Raftery Lewis (2.5%) 178460 Mode .0827599 25% .0729278 Raftery Lewis (97.5%) 26001 P(mean) 0 Brooks Draper (mean) 58991 P(mode) 0 50% .1267802 P(median) 0 75% .2184099 95% .3537279 97.5% .4068215 99.5% .5061676 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), fiveway . // Note: The ACF appears to decay far less rapidly than in the manual. This . // is simply because the y-axis min in the manual is not zero. . . runmlwin votecons cons defence unemp taxes privat, /// > level2(area: cons, parexpansion) /// > level1(voter:) /// > discrete(distribution(binomial) link(logit) denominator(cons)) /// > mcmc(on) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 800 Binomial logit response model Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ area | 110 1 7.3 16 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 16 Deviance (dbar) = 862.21 Deviance (thetabar) = 835.11 Effective no. of pars (pd) = 27.10 Bayesian DIC = 889.31 ------------------------------------------------------------------------------ votecons | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.3713568 .0971259 618 0.000 -.5701553 -.1914866 defence | .0935408 .0188475 978 0.000 .0561928 .1303 unemp | .0701558 .0136152 1131 0.000 .043542 .0975144 taxes | .0458956 .019826 1113 0.010 .008498 .085324 privat | .1452987 .0189755 904 0.000 .1084891 .1831183 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: area | var(cons) | .2071945 .1487665 135 .002974 .5559662 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), detail [RP2]var(cons) ------------------------------------------------------------------------------ Percentiles Mean .2071945 0.5% .0000768 Thinned Chain Length 5000 MCSE of Mean .0080722 2.5% .002974 Effective Sample Size 135 Std. Dev. .1487665 5% .0096834 Raftery Lewis (2.5%) 27779 Mode 0 25% .0890403 Raftery Lewis (97.5%) 21078 P(mean) 0 Brooks Draper (mean) 50084 P(mode) 1 50% .1898185 P(median) 0 75% .296594 95% .480147 97.5% .5559662 99.5% .7197215 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), fiveway . . . . * 24.4 The choice of prior distribution . . . . . . . . . . . . . . . . .390 . . runmlwin votecons cons defence unemp taxes privat, /// > level2(area: cons) /// > level1(voter:) /// > discrete(distribution(binomial) link(logit) denominator(cons)) /// > mcmc(rppriors(uniform)) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 800 Binomial logit response model Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ area | 110 1 7.3 16 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 12.6 Deviance (dbar) = 857.00 Deviance (thetabar) = 825.39 Effective no. of pars (pd) = 31.61 Bayesian DIC = 888.61 ------------------------------------------------------------------------------ votecons | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.3772603 .1004986 644 0.000 -.5728125 -.1821937 defence | .0955107 .019245 1030 0.000 .0583144 .1323777 unemp | .0694702 .0139098 1008 0.000 .0419809 .0978095 taxes | .0470865 .0198962 1087 0.012 .0070314 .0872677 privat | .1460815 .0178312 1071 0.000 .1106574 .1812928 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: area | var(cons) | .2666102 .1421131 65 .0449727 .5823514 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), detail [RP2]var(cons) ------------------------------------------------------------------------------ Percentiles Mean .2666102 0.5% .0177441 Thinned Chain Length 5000 MCSE of Mean .0096449 2.5% .0449727 Effective Sample Size 65 Std. Dev. .1421131 5% .0629286 Raftery Lewis (2.5%) 286250 Mode .2095607 25% .1597741 Raftery Lewis (97.5%) 31143 P(mean) 0 Brooks Draper (mean) 71501 P(mode) 0 50% .2493142 P(median) 0 75% .3578477 95% .5215185 97.5% .5823514 99.5% .7085666 ------------------------------------------------------------------------------ . . mcmcsum [RP2]var(cons), fiveway . . . . * 24.5 Parameter expansion and WinBUGS . . . . . . . . . . . . . . . . . 391 . . runmlwin votecons cons defence unemp taxes privat, /// > level2(area: cons, parexpansion) /// > level1(voter:) /// > discrete(distribution(binomial) link(logit) denominator(cons)) /// > mcmc(savewinbugs( /// > model("votecons_model.txt", replace) /// > inits("votecons_inits.txt", replace) /// > data("votecons_data.txt", replace) /// > )) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 800 Binomial logit response model Estimation algorithm: MCMC ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ area | 110 1 7.3 16 ----------------------------------------------------------- Burnin = 500 Chain = 5000 Thinning = 1 Run time (seconds) = 15.9 Deviance (dbar) = 862.21 Deviance (thetabar) = 835.11 Effective no. of pars (pd) = 27.10 Bayesian DIC = 889.31 ------------------------------------------------------------------------------ votecons | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.3713568 .0971259 618 0.000 -.5701553 -.1914866 defence | .0935408 .0188475 978 0.000 .0561928 .1303 unemp | .0701558 .0136152 1131 0.000 .043542 .0975144 taxes | .0458956 .019826 1113 0.010 .008498 .085324 privat | .1452987 .0189755 904 0.000 .1084891 .1831183 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: area | var(cons) | .2071945 .1487665 135 .002974 .5559662 ------------------------------------------------------------------------------ . . type "votecons_model.txt" # WINBUGS 1.4 code generated from MLwiN program #----MODEL Definition---------------- model { # Level 1 definition for(i in 1:N) { votecons[i] ~ dbin(p[i],denom[i]) logit(p[i]) <- beta[1] * cons[i] + beta[2] * defence[i] + beta[3] * unemp[i] + beta[4] * taxes[i] + beta[5] * privat[i] + alpha2 * u2[area[i]] * cons[i] } # Higher level definitions for (j in 1:n2) { u2[j] ~ dnorm(0,tau.u2) v2[j] <- u2[j]*alpha2 } # Priors for fixed effects for (k in 1:5) { beta[k] ~ dflat() } alpha2 ~ dflat() # Priors for random terms tau.u2 ~ dgamma(0.001000,0.001000) sigma2.u2 <- 1/tau.u2 sigma2.v2 <- sigma2.u2*alpha2*alpha2 } . . wbscript, /// > model("`c(pwd)'\votecons_model.txt") /// > data("`c(pwd)'\votecons_data.txt") /// > inits("`c(pwd)'\votecons_inits.txt") /// > log("`c(pwd)'\votecons_log.txt") /// > coda("`c(pwd)'\out") /// > set(beta sigma2.v2 sigma2.u2 alpha2) /// > burn(4000) update(5000) quit /// > saving("`c(pwd)'\votecons_script.txt", replace) display('log') check('Q:/C-modelling/runmlwin/votecons_model.txt') data('Q:/C-modelling/runmlwin/votecons_data.txt') compile(1) inits(1,'Q:/C-modelling/runmlwin/votecons_inits.txt') gen.inits() update(4000) set('beta') set('sigma2.v2') set('sigma2.u2') set('alpha2') update(5000) coda(*,'Q:/C-modelling/runmlwin/out') save('Q:/C-modelling/runmlwin/votecons_log.txt') quit() . . . wbrun, /// > script("`c(pwd)'\votecons_script.txt") /// > winbugs("C:\WinBUGS14\winbugs14.exe") . . wbcoda, root("`c(pwd)'\out") clear . . mcmcsum alpha2, variables ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- alpha2 | -.9779327 6.156457 108 0.454 -14.47075 11.581 ------------------------------------------------------------------------------ . . mcmcsum alpha2, variables fiveway . . mcmcsum sigma2_v2, variables ------------------------------------------------------------------------------ | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- sigma2_v2 | .1821067 .1411485 939 0.000 .0016584 .51641 ------------------------------------------------------------------------------ . . mcmcsum sigma2_v2, variables fiveway . . . . * 24.6 Parameter expansion and random slopes . . . . . . . . . . . . . . 396 . . use "http://www.bristol.ac.uk/cmm/media/runmlwin/tutorial.dta", clear . . runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons) /// > nopause MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model Estimation algorithm: IGLS ----------------------------------------------------------- | No. of Observations per Group Level Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ school | 65 2 62.4 198 ----------------------------------------------------------- Run time (seconds) = 1.50 Number of iterations = 4 Log likelihood = -4658.4351 Deviance = 9316.8701 ------------------------------------------------------------------------------ normexam | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- cons | -.0115052 .039783 -0.29 0.772 -.0894784 .066468 standlrt | .5567305 .019937 27.92 0.000 .5176548 .5958063 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0904446 .017924 .0553143 .1255749 cov(cons,standlrt) | .0180414 .0067229 .0048649 .031218 var(standlrt) | .0145361 .0044139 .0058851 .0231872 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5536575 .0124818 .5291936 .5781214 ------------------------------------------------------------------------------ . . matrix b = e(b) . . matrix V = e(V) . . runmlwin normexam cons standlrt, /// > level2(school: cons standlrt) /// > level1(student: cons) /// > mcmc(on) initsb(b) initsv(V) /// > nopause MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model 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) = 10.7 Deviance (dbar) = 9122.92 Deviance (thetabar) = 9031.23 Effective no. of pars (pd) = 91.69 Bayesian DIC = 9214.61 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0149964 .0405191 175 0.361 -.0933106 .0644844 standlrt | .5558079 .0200401 819 0.000 .5151299 .593533 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0963496 .0201372 2692 .064631 .1427894 cov(cons,standlrt) | .019418 .0075962 1632 .0060746 .0364841 var(standlrt) | .0154749 .0047789 995 .0080684 .026673 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .5544874 .0126639 4886 .5306531 .5804207 ------------------------------------------------------------------------------ . . . runmlwin normexam cons standlrt, /// > level2(school: cons standlrt, parexpansion) /// > level1(student: cons) /// > mcmc(on) initsb(b) initsv(V) /// > nopause Warning: variance matrix is nonsymmetric or highly singular MLwiN 2.27 multilevel model Number of obs = 4059 Normal response model 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) = 12.6 Deviance (dbar) = 9122.26 Deviance (thetabar) = 9030.06 Effective no. of pars (pd) = 92.21 Bayesian DIC = 9214.47 ------------------------------------------------------------------------------ normexam | Mean Std. Dev. ESS P [95% Cred. Interval] -------------+---------------------------------------------------------------- cons | -.0143199 0 206 0.354 -.0910937 .062027 standlrt | .5563017 0 921 0.000 .5161093 .5945459 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int] -----------------------------+------------------------------------------------ Level 2: school | var(cons) | .0985297 0 2747 .0651008 .1468893 cov(cons,standlrt) | .0197575 0 1917 .0067531 .0362645 var(standlrt) | .0159832 0 878 .0078989 .027005 -----------------------------+------------------------------------------------ Level 1: student | var(cons) | .553943 0 4291 .5293624 .5790754 ------------------------------------------------------------------------------ . . . . * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .399 . . . . . . **************************************************************************** . end of do-file