-------------------------------------------------------------------------------
name: <unnamed>
log: Q:\C-modelling\runmlwin\website\logfiles\2024-10-11\18\13_Ordered_
> Categorical_Responses.smcl
log type: smcl
opened on: 11 Oct 2024, 17:27:26
. ****************************************************************************
. * MLwiN MCMC Manual
. *
. * 13 Ordered Categorical Responses . . . . . . . . . . . . . . . . . . .181
. *
. * 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/
. ****************************************************************************
.
. * 13.1 A level chemistry dataset . . . . . . . . . . . . . . . . . . . . 181
.
. use "https://www.bristol.ac.uk/cmm/media/runmlwin/alevchem.dta", clear
.
. describe
Contains data from https://www.bristol.ac.uk/cmm/media/runmlwin/alevchem.dta
Observations: 2,166
Variables: 8 21 Oct 2011 12:19
-------------------------------------------------------------------------------
Variable Storage Display Value
name type format label Variable label
-------------------------------------------------------------------------------
lea int %9.0g LEA ID
estab int %9.0g Establishment ID
pupil float %9.0g Pupil ID
a_point byte %9.0g a_point A-level point score
gcse_tot byte %9.0g Total GCSE point score
gcse_no byte %9.0g Number of GCSEs taken
cons byte %9.0g Constant
gender byte %9.0g gender Gender
-------------------------------------------------------------------------------
Sorted by:
.
. generate gcseav = gcse_tot/gcse_no
.
. histogram gcseav
(bin=33, start=3.1428571, width=.14718615)
.
. replace gcseav = gcseav - 6
(2,166 real changes made)
.
. generate gcseav2 = gcseav^2
.
. generate gcseav3 = gcseav^3
.
.
.
. * 13.2 Normal response models . . . . . . . . . . . . . . . . . . . . . .184
.
. quietly runmlwin a_point cons, ///
> level1(pupil: cons) ///
> nopause
.
. runmlwin a_point cons, ///
> level1(pupil: cons) ///
> mcmc(on) initsprevious nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Normal response model (hierarchical)
Estimation algorithm: MCMC
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 6.83
Deviance (dbar) = 8589.84
Deviance (thetabar) = 8587.81
Effective no. of pars (pd) = 2.03
Bayesian DIC = 8591.86
------------------------------------------------------------------------------
a_point | Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
cons | 3.518598 .0376554 5419 0.000 3.443225 3.59127
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 1: pupil |
var(cons) | 3.089023 .0954792 4888 2.911594 3.281004
------------------------------------------------------------------------------
.
. rename gender female
.
. runmlwin a_point cons gcseav gcseav2 gcseav3 female, ///
> level1(pupil: cons) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Normal response model (hierarchical)
Estimation algorithm: IGLS
Run time (seconds) = 2.71
Number of iterations = 2
Log likelihood = -3485.9223
Deviance = 6971.8447
------------------------------------------------------------------------------
a_point | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | 3.320883 .0406532 81.69 0.000 3.241204 3.400562
gcseav | 1.56154 .0515331 30.30 0.000 1.460537 1.662543
gcseav2 | .1931122 .026556 7.27 0.000 .1410633 .245161
gcseav3 | -.0732638 .0189904 -3.86 0.000 -.1104843 -.0360433
female | -.4823484 .0532934 -9.05 0.000 -.5868015 -.3778954
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 1: pupil |
var(cons) | 1.463583 .0444737 1.376417 1.55075
------------------------------------------------------------------------------
.
. runmlwin a_point cons gcseav gcseav2 gcseav3 female, ///
> level1(pupil: cons) ///
> mcmc(on) initsprevious nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Normal response model (hierarchical)
Estimation algorithm: MCMC
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 7.94
Deviance (dbar) = 6977.81
Deviance (thetabar) = 6971.85
Effective no. of pars (pd) = 5.96
Bayesian DIC = 6983.77
------------------------------------------------------------------------------
a_point | Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
cons | 3.31939 .0404338 5247 0.000 3.239266 3.397279
gcseav | 1.560796 .0514493 4660 0.000 1.45944 1.662025
gcseav2 | .1937537 .0263828 4971 0.000 .1428038 .2451032
gcseav3 | -.0729788 .0192314 4955 0.000 -.1110337 -.0349861
female | -.4805784 .0521615 5066 0.000 -.5827646 -.3789485
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 1: pupil |
var(cons) | 1.467329 .0442554 5000 1.384112 1.55798
------------------------------------------------------------------------------
.
. gen pred = [FP1]cons + [FP1]gcseav*gcseav + [FP1]gcseav2*gcseav2 ///
> + [FP1]gcseav3*gcseav3 + [FP1]female*female
.
. twoway ///
> (line pred gcseav if female==0, sort) ///
> (line pred gcseav if female==1, sort)
.
.
.
.
. * 13.3 Ordered multinomial modelling . . . . . . . . . . . . . . . . . . 186
.
. runmlwin a_point cons, ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Run time (seconds) = 3.77
Number of iterations = 4
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.398436 .0537743 -26.01 0.000 -1.503831 -1.29304
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.701469 .0456439 -15.37 0.000 -.7909294 -.6120086
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | -.0998058 .043027 -2.32 0.020 -.1841371 -.0154744
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | .5949758 .0448891 13.25 0.000 .5069947 .6829568
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 1.602796 .0574293 27.91 0.000 1.490236 1.715355
------------------------------------------------------------------------------
.
. runmlwin a_point cons, ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) ///
> mcmc(on) initsprevious nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: MCMC
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 26.4
Deviance (dbar) = 7726.43
Deviance (thetabar) = 7721.41
Effective no. of pars (pd) = 5.02
Bayesian DIC = 7731.46
------------------------------------------------------------------------------
| Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.404388 .0539265 241 0.000 -1.510123 -1.299689
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.7062973 .0465722 186 0.000 -.8008548 -.618658
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | -.1033712 .0436276 186 0.009 -.1893483 -.0176887
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | .5926903 .0455491 220 0.000 .503162 .6778752
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 1.602202 .057449 428 0.000 1.489708 1.71914
------------------------------------------------------------------------------
.
.
.
. * 13.4 Adding predictor variables . . . . . . . . . . . . . . . . . . . .191
.
. runmlwin a_point cons (gcseav gcseav2 gcseav3 female, contrast(1/5)), ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Run time (seconds) = 4.02
Number of iterations = 6
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.868101 .083689 -22.32 0.000 -2.032128 -1.704074
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.8270784 .0719785 -11.49 0.000 -.9681536 -.6860032
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .1383848 .0689091 2.01 0.045 .0033255 .2734442
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.304845 .0759066 17.19 0.000 1.156071 1.45362
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 2.995239 .1032021 29.02 0.000 2.792967 3.197512
-------------+----------------------------------------------------------------
gcseav_12345 | -2.077311 .0947173 -21.93 0.000 -2.262953 -1.891669
gcseav~12345 | -.4622603 .0521833 -8.86 0.000 -.5645377 -.3599829
gcseav~12345 | -.0481332 .0365272 -1.32 0.188 -.1197251 .0234588
female_12345 | .7544017 .0839844 8.98 0.000 .5897952 .9190081
------------------------------------------------------------------------------
.
. runmlwin a_point cons (gcseav gcseav2 gcseav3 female, contrast(1/5)), ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) ///
> mcmc(on) initsprevious nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: MCMC
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 34.4
Deviance (dbar) = 6099.86
Deviance (thetabar) = 6090.96
Effective no. of pars (pd) = 8.90
Bayesian DIC = 6108.76
------------------------------------------------------------------------------
| Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.883893 .0818101 170 0.000 -2.042458 -1.724321
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.8386675 .0719557 144 0.000 -.980139 -.7002914
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .1281623 .067356 157 0.028 -.0029563 .2610732
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.296688 .0730275 187 0.000 1.155459 1.438708
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 2.987038 .1013874 294 0.000 2.788264 3.182985
-------------+----------------------------------------------------------------
gcseav_12345 | -2.079406 .0986176 220 0.000 -2.276322 -1.88424
gcseav~12345 | -.4542245 .0507463 265 0.000 -.5512939 -.3553254
gcseav~12345 | -.0498362 .0391458 209 0.088 -.128801 .0267007
female_12345 | .7573509 .0824371 271 0.000 .5999215 .9225242
------------------------------------------------------------------------------
.
.
.
. * 13.5 Multilevel ordered response modelling . . . . . . . . . . . . . . 192
.
. egen school = group(lea estab)
. // Note: Establishment codes on their own do not uniquely identify schools.
. // Schools are instead uniquely identified by LEA code, establishment ID
. // combination. Thus, here we generated a unique school ID.
.
. runmlwin a_point cons (gcseav gcseav2 female, contrast(1/5)), ///
> level2(school: (cons, contrast(1/5))) ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6) pql2) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 220 1 9.8 94
-----------------------------------------------------------
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Run time (seconds) = 5.63
Number of iterations = 10
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.96551 .1092139 -18.00 0.000 -2.179565 -1.751454
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.7743616 .0992623 -7.80 0.000 -.9689122 -.579811
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .3175344 .0975968 3.25 0.001 .1262482 .5088205
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.602257 .1044415 15.34 0.000 1.397556 1.806959
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 3.431818 .1287165 26.66 0.000 3.179539 3.684098
-------------+----------------------------------------------------------------
gcseav_12345 | -2.295235 .0711587 -32.26 0.000 -2.434703 -2.155766
gcseav~12345 | -.4650907 .0467127 -9.96 0.000 -.556646 -.3735355
female_12345 | .7484153 .0938655 7.97 0.000 .5644424 .9323882
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
var(cons_12345) | .6596637 .1107802 .4425385 .8767888
------------------------------------------------------------------------------
.
. runmlwin a_point cons (gcseav gcseav2 female, contrast(1/5)), ///
> level2(school: (cons, contrast(1/5))) ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) ///
> mcmc(on) initsprevious nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: MCMC
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 220 1 9.8 94
-----------------------------------------------------------
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 42.5
Deviance (dbar) = 5814.59
Deviance (thetabar) = 5692.04
Effective no. of pars (pd) = 122.55
Bayesian DIC = 5937.14
------------------------------------------------------------------------------
| Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.923212 .1229307 63 0.000 -2.152823 -1.671016
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.767638 .1160738 48 0.000 -.9890748 -.5330881
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .300251 .1138173 48 0.003 .0875123 .5349658
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.56449 .1215162 55 0.000 1.346591 1.81906
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 3.363311 .140462 73 0.000 3.099479 3.653081
-------------+----------------------------------------------------------------
gcseav_12345 | -2.263649 .0684852 337 0.000 -2.405055 -2.122373
gcseav~12345 | -.4578595 .0504218 218 0.000 -.5584839 -.3565204
female_12345 | .7412699 .0985752 210 0.000 .5442226 .9299094
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: school |
var(cons_12345) | .6442749 .1402424 208 .3916605 .9493606
------------------------------------------------------------------------------
.
. runmlwin a_point cons (gcseav gcseav2 female, contrast(1/5)), ///
> level2(school: (cons gcseav, contrast(1/5))) ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 220 1 9.8 94
-----------------------------------------------------------
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Run time (seconds) = 4.13
Number of iterations = 8
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.779416 .097665 -18.22 0.000 -1.970836 -1.587996
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.7340901 .0891126 -8.24 0.000 -.9087475 -.5594327
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .2367004 .0876772 2.70 0.007 .0648562 .4085446
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.406258 .0940467 14.95 0.000 1.22193 1.590586
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 3.080954 .1169318 26.35 0.000 2.851772 3.310136
-------------+----------------------------------------------------------------
gcseav_12345 | -2.106252 .0699045 -30.13 0.000 -2.243263 -1.969242
gcseav~12345 | -.4236112 .0464491 -9.12 0.000 -.5146498 -.3325727
female_12345 | .6798565 .0909794 7.47 0.000 .5015402 .8581727
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: school |
var(gcseav_12345) | .0570307 .0506351 -.0422122 .1562736
cov(gcseav_12345,cons_12345) | -.0288127 .0448175 -.1166534 .0590279
var(cons_12345) | .390208 .0811649 .2311277 .5492883
------------------------------------------------------------------------------
.
. matrix b = e(b)
.
. matrix V = e(V)
.
. runmlwin a_point cons (gcseav gcseav2 female, contrast(1/5)), ///
> level2(school: (cons gcseav, contrast(1/5))) ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) ///
> mcmc(on) initsb(b) initsv(V) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: MCMC
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 220 1 9.8 94
-----------------------------------------------------------
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Burnin = 500
Chain = 5000
Thinning = 1
Run time (seconds) = 54.7
Deviance (dbar) = 5773.70
Deviance (thetabar) = 5621.36
Effective no. of pars (pd) = 152.34
Bayesian DIC = 5926.04
------------------------------------------------------------------------------
| Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.932868 .1140593 68 0.000 -2.15146 -1.710196
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.7558737 .1032155 57 0.000 -.952064 -.5492296
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .3251431 .1025718 55 0.000 .1404013 .5399959
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.595631 .1103621 58 0.000 1.394653 1.829386
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 3.412361 .1345968 72 0.000 3.143861 3.68627
-------------+----------------------------------------------------------------
gcseav_12345 | -2.314011 .081088 265 0.000 -2.470335 -2.15774
gcseav~12345 | -.4434276 .0492435 326 0.000 -.5405809 -.3456572
female_12345 | .7354497 .0951585 154 0.000 .5607752 .9216768
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: school |
var(gcseav_12345) | .1566335 .0678255 57 .0541734 .3156172
cov(gcseav_12345,cons_12345) | -.0249766 .0762324 51 -.1711138 .1210128
var(cons_12345) | .6226776 .1361175 207 .4007601 .9174535
------------------------------------------------------------------------------
.
. mcmcsum [RP2]var(cons_12345), detail
[RP2]var(cons_12345)
------------------------------------------------------------------------------
Percentiles
Mean .6226776 0.5% .3554488 Thinned Chain Length 5000
MCSE of Mean .0057074 2.5% .4007601 Effective Sample Size 207
Std. Dev. .1361175 5% .4233403 Raftery Lewis (2.5%) 16040
Mode .5916733 25% .5221309 Raftery Lewis (97.5%) 17865
P(mean) 0.000 Brooks Draper (mean) 25027
P(mode) 0.000 50% .6114691
P(median) 0.000
75% .7088134
95% .8649659
97.5% .9174535
99.5% 1.026945
------------------------------------------------------------------------------
.
. mcmcsum [RP2]var(cons_12345), fiveway
.
. runmlwin a_point cons (gcseav gcseav2 female, contrast(1/5)), ///
> level2(school: (cons gcseav, contrast(1/5))) ///
> level1(pupil:) ///
> discrete(distribution(multinomial) link(ologit) denominator(cons) bas
> ecategory(6)) ///
> mcmc(chain(50000)) initsb(b) initsv(V) nopause
MLwiN 3.13 multilevel model Number of obs = 2166
Ordered multinomial logit response model (hierarchical)
Estimation algorithm: MCMC
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
school | 220 1 9.8 94
-----------------------------------------------------------
----------------------------------
Contrast | Log-odds
-------------+--------------------
1 | 1 vs. 2 3 4 5 6
2 | 1 2 vs. 3 4 5 6
3 | 1 2 3 vs. 4 5 6
4 | 1 2 3 4 vs. 5 6
5 | 1 2 3 4 5 vs. 6
----------------------------------
Burnin = 500
Chain = 50000
Thinning = 1
Run time (seconds) = 363
Deviance (dbar) = 5781.18
Deviance (thetabar) = 5633.46
Effective no. of pars (pd) = 147.72
Bayesian DIC = 5928.90
------------------------------------------------------------------------------
| Mean Std. Dev. ESS P [95% Cred. Interval]
-------------+----------------------------------------------------------------
Contrast 1 |
cons_1 | -1.937736 .1090278 1061 0.000 -2.153318 -1.726042
-------------+----------------------------------------------------------------
Contrast 2 |
cons_2 | -.7616613 .0990766 809 0.000 -.9560805 -.5663348
-------------+----------------------------------------------------------------
Contrast 3 |
cons_3 | .3143735 .0976817 720 0.000 .1272104 .5075435
-------------+----------------------------------------------------------------
Contrast 4 |
cons_4 | 1.581964 .1058022 773 0.000 1.379558 1.793592
-------------+----------------------------------------------------------------
Contrast 5 |
cons_5 | 3.393485 .1318771 943 0.000 3.142371 3.662788
-------------+----------------------------------------------------------------
gcseav_12345 | -2.309124 .0807148 2488 0.000 -2.470854 -2.154511
gcseav~12345 | -.4440399 .0505988 3228 0.000 -.5404284 -.3443306
female_12345 | .7383702 .094705 2389 0.000 .5528581 .9244734
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Mean Std. Dev. ESS [95% Cred. Int]
-----------------------------+------------------------------------------------
Level 2: school |
var(gcseav_12345) | .1308195 .0734776 203 .0233414 .3042243
cov(gcseav_12345,cons_12345) | -.0310316 .0687734 792 -.1680551 .106125
var(cons_12345) | .6130687 .1337439 1941 .3841597 .906824
------------------------------------------------------------------------------
.
. mcmcsum [RP2]var(cons_12345), detail
[RP2]var(cons_12345)
------------------------------------------------------------------------------
Percentiles
Mean .6130687 0.5% .3282724 Thinned Chain Length 50000
MCSE of Mean .0017781 2.5% .3841597 Effective Sample Size 1941
Std. Dev. .1337439 5% .414058 Raftery Lewis (2.5%) 11118
Mode .5884722 25% .5185931 Raftery Lewis (97.5%) 8276
P(mean) 0.000 Brooks Draper (mean) 24291
P(mode) 0.000 50% .6015386
P(median) 0.000
75% .6961889
95% .8476434
97.5% .906824
99.5% 1.024229
------------------------------------------------------------------------------
.
. mcmcsum [RP2]var(cons_12345), fiveway
.
.
.
. * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .196
.
.
.
.
.
. ****************************************************************************
. exit
end of do-file