Simulate a multilevel ordinal logistic regression in stata

[Andrew Xavier]

Dear All,

Please could anyone help to simulate a multilevel ordinal logistic regression?

Here is an example of what I would like:

clear
webuse pig
mixed weight week || id: week
xtile weight_cate = weight, nq(5) 
meologit weight_cate  week || id: week, difficult

I would like to simulate data from the model performed "meologit weight_cate week || id: week". Basically, I would like to generate simulated data using specified estimates from the meologit.


Many thanks

Andre

[Joseph Coveney]

You can do something like the following with a user-written command, -grologit-, to convert the linear predictor into an ordered-categorical outcome variable. See below for a typical use case.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1610200")'

.ÿ
.ÿquietlyÿdrawnormÿinterceptÿslope,ÿdoubleÿsd(3ÿ2)ÿcorr(1ÿ-0.5ÿ\ÿ-0.5ÿ1)ÿn(300)

.ÿgenerateÿintÿpidÿ=ÿ_n

.ÿ
.ÿquietlyÿexpandÿ10

.ÿbysortÿpid:ÿgenerateÿbyteÿtimÿ=ÿ_n

.ÿ
.ÿgenerateÿdoubleÿxbuÿ=ÿ0ÿ+ÿ0ÿ*ÿtimÿ+ÿinterceptÿ+ÿ(timÿ-ÿ5.5)ÿ/ÿ4.5ÿ*ÿslope

.ÿ
.ÿlocalÿcut_list

.ÿforvaluesÿthresholdÿ=ÿ1/4ÿ{
ÿÿ2.ÿÿÿÿÿlocalÿcutÿ=ÿlogit(`threshold'ÿ/ÿ5)
ÿÿ3.ÿÿÿÿÿlocalÿcut_listÿ`cut_list'ÿ`cut'
ÿÿ4.ÿ}

.ÿgrologitÿxbu,ÿgenerate(sco)ÿcuts(`cut_list')

.ÿ
.ÿgenerateÿdoubleÿctiÿ=ÿ(timÿ-ÿ5.5)ÿ/ÿ4.5

.ÿmeologitÿscoÿc.ctiÿ||ÿpid:ÿcti,ÿcovariance(unstructured)ÿnolog

Mixed-effectsÿologitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ3,000
Groupÿvariable:ÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ300

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ10
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ10.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ10

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ0.24
Logÿlikelihoodÿ=ÿ-3295.9724ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.6233
--------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿscoÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
---------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿctiÿ|ÿÿÿ.0700144ÿÿÿÿ.142537ÿÿÿÿÿ0.49ÿÿÿ0.623ÿÿÿÿ-.2093531ÿÿÿÿ.3493818
---------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿ/cut1ÿ|ÿÿ-1.113663ÿÿÿ.1882026ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-1.482533ÿÿÿ-.7447928
ÿÿÿÿÿÿÿÿÿ/cut2ÿ|ÿÿ-.1185266ÿÿÿ.1872892ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-.4856067ÿÿÿÿ.2485534
ÿÿÿÿÿÿÿÿÿ/cut3ÿ|ÿÿÿ.7086144ÿÿÿ.1879387ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3402613ÿÿÿÿ1.076968
ÿÿÿÿÿÿÿÿÿ/cut4ÿ|ÿÿÿ1.615364ÿÿÿ.1901522ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.242672ÿÿÿÿ1.988055
---------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿvar(cti)|ÿÿÿ4.036835ÿÿÿ.5842765ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ3.039774ÿÿÿÿ5.360938
ÿÿÿÿÿvar(_cons)|ÿÿÿ9.473944ÿÿÿ1.080381ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ7.576388ÿÿÿÿ11.84675
---------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿcov(cti,_cons)|ÿÿ-2.425427ÿÿÿ.6641623ÿÿÿÿ-3.65ÿÿÿ0.000ÿÿÿÿ-3.727161ÿÿÿ-1.123693
--------------------------------------------------------------------------------
LRÿtestÿvs.ÿologitÿmodel:ÿchi2(3)ÿ=ÿ1871.17ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿestatÿsd
---------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿscoÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
----------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿsd(cti)|ÿÿÿ2.009188ÿÿÿ.1454012ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.743495ÿÿÿÿÿ2.31537
ÿÿÿÿÿÿÿsd(_cons)|ÿÿÿ3.077977ÿÿÿ.1755018ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ2.752524ÿÿÿÿ3.441911
ÿcorr(cti,_cons)|ÿÿ-.3921952ÿÿÿ.0867803ÿÿÿÿ-4.52ÿÿÿ0.000ÿÿÿÿ-.5479142ÿÿÿ-.2102066
---------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

I've attached the command's ado-file if you want to use that (no warranty), or you can scan through it in order to see what it does if you feel like writing something analogous yourself. There's no help file, but you first generate the linear predictions and feed those to it, along with a -numlist- of thresholds (cuts), and name of the ordered-categorical outcome variable to be generated. The default is parameterization is logit, but you can specify probit as an option.

[Andrew Xavier]

Dear Joseph Coveney,


Many thanks for your help.


I don't think I was clear in my last email. I don't want to simulate data using a linear predictor. This is because I would not know which values to include there.

What I want to do is to start with a meologit model such as the one below and then simulate data assuming similar estimates

I know nothing about the linear predictor. I'm sorry if I'm not understanding something


I know how to simulate data from a linear mixed model but I do not know how to do it from a ordinal mixed model. I would like to do a similar thing for the meologit to the following that used a continuous outcome:

clear
webuse pig
mixed weight week || id: week, stddev

clear
set obs 48
gen id = _n

generate u_0i = rnormal(0,2.599301)
generate u_1i = rnormal(0,.6066851)

expand 9
bysort id: generate week = _n

generate e_ij = rnormal(0,1.264441)

generate weight = 19.35561 + 6.209896*week + u_0i + week*u_1i + e_ij

mixed weight week || id: week, stddev

Many thanks in advance for your help

Andrew

[Joseph Coveney]

What I want to do is to start with a meologit model such as the one below and then simulate data assuming similar estimates

I basically showed you how in my illustration above. But, here: let's go through an example step-by-step. I'll use the dataset from the helpfile for -meologit-. Each step is identified by a comment in the illustration below.

.ÿ
.ÿversionÿ17.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1610200")'

.ÿ
.ÿ//ÿOriginalÿdataÿandÿmodel
.ÿquietlyÿwebuseÿtvsfpors

.ÿmeologitÿthkÿc.prethkÿ||ÿschool:ÿprethk,ÿcovariance(unstructured)ÿnolog

Mixed-effectsÿologitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ1,600
Groupÿvariable:ÿschoolÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ28

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ18
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ57.1
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿ137

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿ71.47
Logÿlikelihoodÿ=ÿ-2128.0901ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000
-----------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿthkÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿprethkÿ|ÿÿÿ.3859692ÿÿÿ.0456554ÿÿÿÿÿ8.45ÿÿÿ0.000ÿÿÿÿÿ.2964862ÿÿÿÿ.4754521
------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut1ÿ|ÿÿ-.5981441ÿÿÿ.1323143ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-.8574753ÿÿÿ-.3388129
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut2ÿ|ÿÿÿ.6459577ÿÿÿ.1312459ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.3887205ÿÿÿÿ.9031948
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut3ÿ|ÿÿÿ1.830222ÿÿÿ.1383338ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1.559093ÿÿÿÿ2.101351
------------------+----------------------------------------------------------------
schoolÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿvar(prethk)|ÿÿÿ.0138004ÿÿÿ.0149784ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0016445ÿÿÿÿ.1158108
ÿÿÿÿÿÿÿÿvar(_cons)|ÿÿÿ.2137879ÿÿÿ.1248098ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0680848ÿÿÿÿ.6712994
------------------+----------------------------------------------------------------
schoolÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿcov(prethk,_cons)|ÿÿ-.0138234ÿÿÿ.0356992ÿÿÿÿ-0.39ÿÿÿ0.699ÿÿÿÿ-.0837925ÿÿÿÿ.0561457
-----------------------------------------------------------------------------------
LRÿtestÿvs.ÿologitÿmodel:ÿchi2(3)ÿ=ÿ54.36ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿ
.ÿ//ÿRetrieveÿcorrelationÿmatrixÿofÿrandomÿeffects
.ÿestatÿsd
------------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿthkÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
-------------------+----------------------------------------------------------------
schoolÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿsd(prethk)|ÿÿÿ.1174751ÿÿÿ.0637512ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0405524ÿÿÿÿ.3403098
ÿÿÿÿÿÿÿÿÿÿsd(_cons)|ÿÿÿÿ.462372ÿÿÿ.1349668ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.2609306ÿÿÿÿ.8193286
ÿcorr(prethk,_cons)|ÿÿ-.2544938ÿÿÿ.5085934ÿÿÿÿ-0.50ÿÿÿ0.617ÿÿÿÿ-.8682853ÿÿÿÿ.6671809
------------------------------------------------------------------------------------

.ÿtempnameÿSDsÿCorr

.ÿmatrixÿdefineÿ`SDs'ÿ=ÿr(b)[1,ÿ6],ÿr(b)[1,ÿ5]

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿr(b)[1,ÿ7]

.ÿmatrixÿdefineÿ`Corr'ÿ=ÿ(1,ÿ`Corr'ÿ\ÿ`Corr',ÿ1)

.ÿ
.ÿ//ÿRetrieveÿthresholdsÿinÿaÿnumlist
.ÿlocalÿcut_listÿ`=_b[/cut1]'ÿ`=_b[/cut2]'ÿ`=_b[/cut3]'

.ÿ
.ÿ//ÿRetrieveÿfixedÿeffectsÿregressionÿcoefficient
.ÿtempnameÿprethk

.ÿscalarÿdefineÿ`prethk'ÿ=ÿ_b[prethk]

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿ//ÿGenerateÿrandomÿeffects
.ÿquietlyÿdrawnormÿinterceptÿslope,ÿdoubleÿsd(`SDs')ÿcorr(`Corr')ÿn(300)ÿclear

.ÿgenerateÿintÿschoolÿ=ÿ_n

.ÿ
.ÿ//ÿGenerateÿfixedÿeffects
.ÿquietlyÿexpandÿ60

.ÿgenerateÿbyteÿprethkÿ=ÿruniformint(0,ÿ6)

.ÿ
.ÿ//ÿAssembleÿlinearÿpredictions
.ÿgenerateÿdoubleÿxbuÿ=ÿ0ÿ+ÿ`prethk'ÿ*ÿprethkÿ+ÿinterceptÿ+ÿprethkÿ*ÿslope

.ÿ
.ÿ//ÿDrawÿorderedÿcategoricalÿoutcomeÿvariableÿfromÿlinearÿpredictorÿvariable
.ÿgrologitÿxbu,ÿgenerate(thk)ÿcut(`cut_list')

.ÿ
.ÿ//ÿFitÿsameÿmodelÿtoÿrandomlyÿgeneratedÿdataset
.ÿmeologitÿthkÿc.prethkÿ||ÿschool:ÿprethk,ÿcovariance(unstructured)ÿnolog

Mixed-effectsÿologitÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿ18,000
Groupÿvariable:ÿschoolÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ300

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ60
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ60.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ60

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿ1250.44
Logÿlikelihoodÿ=ÿ-17743.669ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0000
-----------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿthkÿ|ÿCoefficientÿÿStd.ÿerr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿconf.ÿinterval]
------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿprethkÿ|ÿÿÿ.3886831ÿÿÿ.0109917ÿÿÿÿ35.36ÿÿÿ0.000ÿÿÿÿÿ.3671398ÿÿÿÿ.4102263
------------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut1ÿ|ÿÿ-1.787299ÿÿÿ.0442344ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-1.873997ÿÿÿ-1.700601
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut2ÿ|ÿÿ-.6130374ÿÿÿ.0388468ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-.6891757ÿÿÿ-.5368991
ÿÿÿÿÿÿÿÿÿÿÿÿ/cut3ÿ|ÿÿÿ.6316631ÿÿÿ.0385692ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.5560689ÿÿÿÿ.7072573
------------------+----------------------------------------------------------------
schoolÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿvar(prethk)|ÿÿÿ.0132339ÿÿÿ.0028087ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.0087304ÿÿÿÿ.0200605
ÿÿÿÿÿÿÿÿvar(_cons)|ÿÿÿ.2150665ÿÿÿ.0348413ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1565582ÿÿÿÿ.2954402
------------------+----------------------------------------------------------------
schoolÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿcov(prethk,_cons)|ÿÿ-.0123389ÿÿÿÿ.007877ÿÿÿÿ-1.57ÿÿÿ0.117ÿÿÿÿ-.0277776ÿÿÿÿ.0030997
-----------------------------------------------------------------------------------
LRÿtestÿvs.ÿologitÿmodel:ÿchi2(3)ÿ=ÿ554.68ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿ
.ÿexit

endÿofÿdo-file


.

[Andrew Xavier]

Many thanks for your help on this. Your example is very clear.

Could I ask you one more question:

Let's say I have a dataset and I want to simulate a variable that is correlated/associated by a specific amount with a categorical and continuous variable in that dataset. Let's say that the variable I want to simulate is either categorical or continuous

How do I do that?

Again thanks in advance for your help.

Andrew

[Joseph Coveney]

You're not clear to me, I'm sorry.

I'm assuming that you mean ordered categorical when you say categorical, and that you mean Pearson correlation coefficient when you say "correlated/associated . . . by a specific amount".

But I can't tell what you mean by a variable that is "either categorical or continuous", and by another that is "a categorical and continuous variable in the dataset".

In general, you can fit mixed-response regression models with the user-written command -gllamm- (SSC) and with -gsem- (official Stata), and represent association between two or more outcome variables by a latent factor (random effect). You can simulate using -drawnorm- with correlation matrix to yield the desired latent factor variance in a manner directly analogous to the two illustrations above. You can also simulate as if for a conventional random effect and then discretize one or more observations per cluster. You might need to hone in on the desired variance in a trial-and-error manner.

[Andrew Xavier]

Sorry if I was not clear in my last email. My other question was a lot simpler

Lets say I have the following

webuse tvsfpors, clear

in the dataset there is the continuous variable prethk and categorical ordinal variable thk

The dataset is clustered

What i would like to do is the following:
- generate a continuous variable (x) that is associated prethk with a correlation of 0.75
- generate a categorical ordinal variable with 4 categories (y) that is associated with prethk in terms of a specific linear increase
- generate a continuous variable (w) that is associated with thk in terms of s specific increase in the odds
- is there a way to generate a categorical ordinal variable (A) that is both associated with prethk and thk so I could have a model such as this: meologit thk c.prethk i.A || school: prethk, covariance(unstructured)
- Is there a way to generate a continuous variable (B) that is both associated with weight (continuous) and week (continuous) so I could have a model such as this: mixed weight c.week c.B || id: week

Basically, I would like to simulate variables that are both associated with other predictors and response in multilevel models (linear and ordinal models) using existing data and existing variables

I suppose this may involve simulating some form of interaction but I don't know exactly how to do it...

I hope this makes sense

Many Thanks

A

[Joseph Coveney]

Basically, I would like to simulate variables that are both associated with other predictors and response in multilevel models (linear and ordinal models) using existing data and existing variables

I suppose this may involve simulating some form of interaction but I don't know exactly how to do it...

You would do it using the same general method illustrated above, that is, emulating the data-generating process that you are modeling and using estimates from the earlier fitted model for the parameter values. It wouldn't involve an interaction term unless you posit an interaction of the predictors.

[Andrew Xavier]

Many thanks for your advice. You helped me to solve my problem, BW, A