-------------------------------------------------------------------------------
name: <unnamed>
log: Q:\C-modelling\runmlwin\website\logfiles\2024-10-11\18\9_Logistic_
> Models_for_Binary_and_Binomial_Responses.smcl
log type: smcl
opened on: 11 Oct 2024, 16:41:15
. *****************************************************************************
> ***
. * MLwiN User Manual
. *
. * 9 Logistic Models for Binary and Binomial Responses
> 117
. *
. * Rasbash, J., Steele, F., Browne, W. J. and Goldstein, H. (2012). A User
> 's
. * Guide to 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/
. *****************************************************************************
> ***
.
. * 9.1 Introduction and description of the example data . . . . . . . . . . .
> 117
.
. use "https://www.bristol.ac.uk/cmm/media/runmlwin/bang.dta", clear
.
. describe
Contains data from https://www.bristol.ac.uk/cmm/media/runmlwin/bang.dta
Observations: 2,867
Variables: 12 12 Mar 2014 22:22
-------------------------------------------------------------------------------
Variable Storage Display Value
name type format label Variable label
-------------------------------------------------------------------------------
woman float %9.0g Identifying code for each woman
(level 1 unit)
district float %9.0g Identifying code for each
district (level 2 unit)
use float %9.0g Contraceptive use status at a
time of survey (1 = using
contraception, 2 = not u
use4 float %9.0g use4 Contraceptive use status and
method (1 = Sterilization, 2 =
Modern reversible me
lc float %9.0g lc Number of living children at time
of survey (0 = None, 1 = 1
child, 2 = 2 childr
age float %9.0g Age of woman at time of survey
(in years), centred on the
sample mean of 30 year
urban float %9.0g Type of region of residence (1 =
Urban, 0 = Rural)
educ float %9.0g educ Womans level of education (1 =
None, 2 = Lower primary, 3 =
Upper primary, 4 = S
hindu float %9.0g Womans religion (1 = Hindu, 0 =
Muslim)
d_lit float %9.0g Proportion of women in district
who are literate
d_pray float %9.0g Proportion of Muslim women in
district who pray every day (a
measure of religios
cons float %9.0g constant vector
-------------------------------------------------------------------------------
Sorted by:
.
.
. * 9.2 Single-level logistic regression . . . . . . . . . . . . . . . . . . .
> 119
.
. * Link functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 119
.
. * Interpretation of coeficients . . . . . . . . . . . . . . . . . . . . . . .
> 120
.
. * Fitting a single-level logit model in MLwiN . . . . . . . . . . . . . . . .
> 121
.
. tabulate lc use, row
+----------------+
| Key |
|----------------|
| frequency |
| row percentage |
+----------------+
Number of |
living |
children |
at time of | Contraceptive use
survey (0 | status at a time of
= None, 1 | survey (1 = using
= 1 child, | contraception, 2 =
2 = 2 | not u
childr | 0 1 | Total
-----------+----------------------+----------
lc0 | 584 190 | 774
| 75.45 24.55 | 100.00
-----------+----------------------+----------
lc1 | 283 234 | 517
| 54.74 45.26 | 100.00
-----------+----------------------+----------
lc2 | 234 227 | 461
| 50.76 49.24 | 100.00
-----------+----------------------+----------
lc3plus | 627 488 | 1,115
| 56.23 43.77 | 100.00
-----------+----------------------+----------
Total | 1,728 1,139 | 2,867
| 60.27 39.73 | 100.00
.
. generate lc1 = (lc==1)
.
. generate lc2 = (lc==2)
.
. generate lc3plus = (lc==3)
.
. runmlwin use cons lc1 lc2 lc3plus, level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons)) nopaus
> e
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
Run time (seconds) = 3.19
Number of iterations = 4
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -1.122876 .0834809 -13.45 0.000 -1.286496 -.9592566
lc1 | .9327503 .121557 7.67 0.000 .694503 1.170998
lc2 | 1.092505 .1250913 8.73 0.000 .8473305 1.337679
lc3plus | .8722449 .10302 8.47 0.000 .6703295 1.07416
------------------------------------------------------------------------------
.
. test [FP1]lc1 = [FP1]lc2
( 1) [FP1]lc1 - [FP1]lc2 = 0
chi2( 1) = 1.55
Prob > chi2 = 0.2134
.
.
.
. * A probit model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 126
.
. runmlwin use cons lc1 lc2 lc3plus, level1(woman) ///
> discrete(distribution(binomial) link(probit) denominator(cons)) nopau
> se
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial probit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
Run time (seconds) = 3.04
Number of iterations = 4
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -.688789 .0491538 -14.01 0.000 -.7851287 -.5924492
lc1 | .5697222 .0739598 7.70 0.000 .4247637 .7146807
lc2 | .669757 .0763146 8.78 0.000 .5201832 .8193308
lc3plus | .531905 .0619477 8.59 0.000 .4104897 .6533203
------------------------------------------------------------------------------
.
. runmlwin use cons lc1 lc2 lc3plus age, level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons)) nopaus
> e
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
Run time (seconds) = 3.13
Number of iterations = 4
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -1.255983 .0977567 -12.85 0.000 -1.447583 -1.064383
lc1 | .9913076 .1237629 8.01 0.000 .7487368 1.233878
lc2 | 1.223558 .1348033 9.08 0.000 .9593484 1.487768
lc3plus | 1.116551 .1382418 8.08 0.000 .845602 1.3875
age | -.0162877 .0060931 -2.67 0.008 -.0282299 -.0043456
------------------------------------------------------------------------------
.
.
.
. * 9.3 A two-level random intercept model . . . . . . . . . . . . . . . . . .
> 128
.
. * Model specification . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 128
.
. * Estimation procedures . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 128
.
. * Fitting a two-level random intercept model in MLwiN . . . . . . . . . . . .
> 129
.
. runmlwin use cons lc1 lc2 lc3plus age, ///
> level2(district: cons) level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons)) nopaus
> e
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 3 47.8 173
-----------------------------------------------------------
Run time (seconds) = 2.95
Number of iterations = 5
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -1.367111 .1233779 -11.08 0.000 -1.608927 -1.125295
lc1 | .9899751 .1264296 7.83 0.000 .7421777 1.237773
lc2 | 1.275233 .1381648 9.23 0.000 1.004435 1.546031
lc3plus | 1.215676 .1424506 8.53 0.000 .9364783 1.494874
age | -.0187756 .0062489 -3.00 0.003 -.0310232 -.0065281
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .2740886 .0713836 .1341793 .4139978
------------------------------------------------------------------------------
.
. runmlwin use cons lc1 lc2 lc3plus age, ///
> level2(district: cons) level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons) pql2) /
> //
> initsprevious ///
> nopause
Model fitted using initial values specified as parameter estimates from previou
> s model
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 3 47.8 173
-----------------------------------------------------------
Run time (seconds) = 3.16
Number of iterations = 5
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -1.466065 .1279216 -11.46 0.000 -1.716787 -1.215343
lc1 | 1.062866 .1288259 8.25 0.000 .8103723 1.315361
lc2 | 1.370127 .1416822 9.67 0.000 1.092435 1.647819
lc3plus | 1.303942 .1459562 8.93 0.000 1.017873 1.590011
age | -.0200488 .0064053 -3.13 0.002 -.0326029 -.0074947
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .3078618 .0791322 .1527655 .4629581
------------------------------------------------------------------------------
.
. test [RP2]var(cons)=0
( 1) [RP2]var(cons) = 0
chi2( 1) = 15.14
Prob > chi2 = 0.0001
.
.
.
. * Variance partition coeficient . . . . . . . . . . . . . . . . . . . . . . .
> 131
.
. preserve
.
. set obs 5000
Number of observations (_N) was 2,867, now 5,000.
.
. set seed 12345
.
. generate u = sqrt([RP2]var(cons))*invnormal(uniform())
.
. generate p1 = invlogit(_b[cons] + u)
.
. generate p2 = invlogit(_b[cons] + _b[lc3plus] + _b[age]*-9.7 + u)
.
. generate p3 = invlogit(_b[cons] + _b[age]*15.3 + u)
.
. forvalues p = 1/3 {
2.
. generate v`p' = p`p'*(1 - p`p')
3.
. quietly summarize p`p'
4.
. scalar lev2var`p' = r(sd)^2
5.
. quietly summarize v`p'
6.
. scalar lev1var`p' = r(mean)
7.
. }
.
. display "VPC = " lev2var1/(lev2var1 + lev1var1)
VPC = .04701588
.
. display "VPC for a young women with 3+ children (low probability use)
> = " lev2var2/(lev2var2 + lev1var2)
VPC for a young women with 3+ children (low probability use) = .06713939
.
. display "VPC for an old woman with no children (high probability use)
> = " lev2var3/(lev2var3 + lev1var3)
VPC for an old woman with no children (high probability use) = .04011108
.
. restore
.
.
.
. * Adding further explanatory variables . . . . . . . . . . . . . . . . . . .
> 134
.
. tabulate educ
Womans |
level of |
education |
(1 = None, |
2 = Lower |
primary, 3 |
= Upper |
primary, 4 |
= S | Freq. Percent Cum.
------------+-----------------------------------
ed_none | 1,806 62.99 62.99
ed_lprim | 357 12.45 75.44
ed_uprim | 265 9.24 84.69
ed_secplus | 439 15.31 100.00
------------+-----------------------------------
Total | 2,867 100.00
.
. generate ed_lprim = (educ==2)
.
. generate ed_uprim = (educ==3)
.
. generate ed_secplus = (educ==4)
.
. runmlwin use cons lc1 lc2 lc3plus age urban ///
> ed_lprim ed_uprim ed_secplus hindu, ///
> level2(district: cons) level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons) pql2) /
> //
> initsprevious ///
> nopause
Model fitted using initial values specified as parameter estimates from previou
> s model
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 3 47.8 173
-----------------------------------------------------------
Run time (seconds) = 3.41
Number of iterations = 5
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -2.052701 .1382067 -14.85 0.000 -2.323581 -1.781821
lc1 | 1.151532 .1341357 8.58 0.000 .8886307 1.414433
lc2 | 1.512435 .1473516 10.26 0.000 1.223631 1.801239
lc3plus | 1.502071 .1527244 9.84 0.000 1.202737 1.801405
age | -.0173581 .006648 -2.61 0.009 -.030388 -.0043282
urban | .5331155 .1048243 5.09 0.000 .3276636 .7385674
ed_lprim | .2465644 .1283691 1.92 0.055 -.0050344 .4981633
ed_uprim | .724403 .1438131 5.04 0.000 .4425344 1.006271
ed_secplus | 1.170312 .1271726 9.20 0.000 .9210582 1.419565
hindu | .4328669 .1276563 3.39 0.001 .1826652 .6830686
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .2336909 .0656384 .1050419 .3623398
------------------------------------------------------------------------------
.
.
.
. * 9.4 A two-level random coeficient model . . . . . . . . . . . . . . . . . .
> 135
.
. runmlwin use cons lc1 lc2 lc3plus age urban ///
> ed_lprim ed_uprim ed_secplus hindu, ///
> level2(district: cons urban) level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons) pql2) /
> //
> initsprevious ///
> nopause
Model fitted using initial values specified as parameter estimates from previou
> s model
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 3 47.8 173
-----------------------------------------------------------
Run time (seconds) = 3.81
Number of iterations = 6
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -2.093553 .1482139 -14.13 0.000 -2.384047 -1.803059
lc1 | 1.16591 .1348819 8.64 0.000 .9015459 1.430273
lc2 | 1.526202 .1483987 10.28 0.000 1.235346 1.817058
lc3plus | 1.522709 .154066 9.88 0.000 1.220745 1.824673
age | -.0181749 .0066994 -2.71 0.007 -.0313055 -.0050444
urban | .5741606 .1363773 4.21 0.000 .3068661 .8414551
ed_lprim | .2451684 .1295018 1.89 0.058 -.0086505 .4989873
ed_uprim | .7332251 .1453219 5.05 0.000 .4483995 1.018051
ed_secplus | 1.179629 .128384 9.19 0.000 .9280011 1.431257
hindu | .5094263 .1329043 3.83 0.000 .2489387 .7699139
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .3596003 .0985204 .1665039 .5526967
cov(cons,urban) | -.2575624 .1112809 -.4756689 -.0394559
var(urban) | .3479358 .17282 .0092148 .6866568
------------------------------------------------------------------------------
.
. test ([RP2]cov(cons\urban)=0) ([RP2]var(urban)=0), mtest
( 1) [RP2]cov(cons\urban) = 0
( 2) [RP2]var(urban) = 0
--------------------------------------
| chi2 df p > chi2
-------+------------------------------
(1) | 5.36 1 0.0206*
(2) | 4.05 1 0.0441*
-------+------------------------------
All | 5.47 2 0.0648
--------------------------------------
* Unadjusted p-values
.
. runmlwin use cons lc1 lc2 lc3plus age urban ///
> ed_lprim ed_uprim ed_secplus hindu d_lit d_pray, ///
> level2(district: cons urban) level1(woman) ///
> discrete(distribution(binomial) link(logit) denominator(cons) pql2) /
> //
> initsprevious ///
> nopause
Model fitted using initial values specified as parameter estimates from previou
> s model
MLwiN 3.13 multilevel model Number of obs = 2867
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 3 47.8 173
-----------------------------------------------------------
Run time (seconds) = 3.92
Number of iterations = 6
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -1.722902 .2632283 -6.55 0.000 -2.23882 -1.206984
lc1 | 1.170099 .1350131 8.67 0.000 .9054781 1.43472
lc2 | 1.533891 .1485973 10.32 0.000 1.242646 1.825136
lc3plus | 1.528153 .1542348 9.91 0.000 1.225858 1.830448
age | -.0181398 .0066973 -2.71 0.007 -.0312663 -.0050133
urban | .528236 .1380133 3.83 0.000 .2577349 .7987371
ed_lprim | .2376898 .1299372 1.83 0.067 -.0169824 .492362
ed_uprim | .742241 .1455787 5.10 0.000 .456912 1.02757
ed_secplus | 1.195861 .1289305 9.28 0.000 .9431618 1.44856
hindu | .5093639 .1324719 3.85 0.000 .2497238 .769004
d_lit | 2.074494 1.705624 1.22 0.224 -1.268468 5.417455
d_pray | -1.407985 .5337808 -2.64 0.008 -2.454176 -.3617942
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .3047796 .0879458 .132409 .4771502
cov(cons,urban) | -.232913 .1050934 -.4388924 -.0269337
var(urban) | .3502613 .1731283 .010936 .6895866
------------------------------------------------------------------------------
.
.
.
. * 9.5 Modelling binomial data . . . . . . . . . . . . . . . . . . . . . . . .
> 139
.
. * Modelling district-level variation with district-level proportions . . . .
> 139
.
. * Creating a district-level data set . . . . . . . . . . . . . . . . . . . .
> 140
.
. collapse (mean) use cons (sum) denom = cons, by(district d_lit d_pray)
.
.
.
. * Fitting the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
> 142
.
. runmlwin use cons d_lit d_pray, ///
> level2(district: cons) level1(district) ///
> discrete(distribution(binomial) link(logit) denominator(denom)) nopau
> se
MLwiN 3.13 multilevel model Number of obs = 60
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, MQL1
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 1 1.0 1
-----------------------------------------------------------
Run time (seconds) = 2.78
Number of iterations = 4
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -.3979703 .2339486 -1.70 0.089 -.8565012 .0605606
d_lit | 3.759683 1.617902 2.32 0.020 .5886535 6.930713
d_pray | -1.195713 .5010576 -2.39 0.017 -2.177768 -.2136579
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .2106125 .0589008 .095169 .326056
------------------------------------------------------------------------------
.
. runmlwin use cons d_lit d_pray, ///
> level2(district: cons) level1(district) ///
> discrete(distribution(binomial) link(logit) denominator(denom) pql2)
> ///
> initsprevious ///
> nopause
Model fitted using initial values specified as parameter estimates from previou
> s model
MLwiN 3.13 multilevel model Number of obs = 60
Binomial logit response model (hierarchical)
Estimation algorithm: IGLS, PQL2
-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
district | 60 1 1.0 1
-----------------------------------------------------------
Run time (seconds) = 3.01
Number of iterations = 6
------------------------------------------------------------------------------
use | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | -.4266337 .2406829 -1.77 0.076 -.8983636 .0450961
d_lit | 3.997347 1.687761 2.37 0.018 .6893952 7.305298
d_pray | -1.250717 .5219554 -2.40 0.017 -2.273731 -.2277034
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 2: district |
var(cons) | .2251485 .062199 .1032407 .3470563
------------------------------------------------------------------------------
. // Note: The screenshot in the manual incorrectly dispalys the PQL1 estimates
. // when it should show the PQL2 estimates.
.
.
.
. * Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . .
> 143
.
.
.
. ****************************************************************************
. exit
end of do-file