Mixed-effects logistic regression for panel data

Yapeng Wang

Join Date: Dec 2017

Posts: 74
#1

Mixed-effects logistic regression for panel data

29 Jun 2019, 13:39

Hello, I am using mixed-effects logistic regression for panel data in STATA 15, and I was wondering if my commands are correct.

My DV is a binary variable, and each respondent was surveyed once a year for five years. So, each respondent has five repeated measures. In the data, the respondent identifier is the variable ID. I also have time-varying covariates IV1, IV2, and time-invariant covariates IV3 and IV4, and a time variable Year. I want to use a mixed-effects logistic regression as follows:

Code:

melogit DV IV1 IV2 IV3 IV4 Year || ID: Year, cov(un)

But, this is kind of like a growth curve model except for the binary DV. I was wondering if my command is correct, and what is the difference between a growth curve model and a mixed-effects logistic model for panel data. Thank you very much!
Tags: None
Robert Wells

Join Date: Apr 2014

Posts: 16
#2

30 Jun 2019, 18:41

Hi Yapeng,

I am also working in the same area and i think i have spotted your issue.

Is you goal to have random coefficient for the year? This is not the typical approach for growth curve models so i assume this is not the case.

Furthermore, you were treat year as a continuous variable. If this was the case, do not put a factor prefix. But you might want to consider not doing this, or if you are doing it re base the number so it not the current calendar year (age or year since the study began for example).

I would change your syntax to

Code

melogit DV IV1 IV2 IV3 IV4 i.Year || ID:, cov(un)

This allows for fixed effects for the year's (as that is part of the feature of the mixed model), random intercepts for the id's.

I do not see why you are specifying the co-variance structure to be unrestrained, as you only have one level the code should change this (from my experience) to identity. So there is no need to change this.

Hope this helps
Comment
Yapeng Wang

Join Date: Dec 2017

Posts: 74
#3

30 Jun 2019, 18:56

Originally posted by Robert Wells View Post

Hi Yapeng,

I am also working in the same area and i think i have spotted your issue.

Is you goal to have random coefficient for the year? This is not the typical approach for growth curve models so i assume this is not the case.

Furthermore, you were treat year as a continuous variable. If this was the case, do not put a factor prefix. But you might want to consider not doing this, or if you are doing it re base the number so it not the current calendar year (age or year since the study began for example).

I would change your syntax to

Code

This allows for fixed effects for the year's (as that is part of the feature of the mixed model), random intercepts for the id's.

I do not see why you are specifying the co-variance structure to be unrestrained, as you only have one level the code should change this (from my experience) to identity. So there is no need to change this.

Hope this helps

Hi Robert,

Thank you for your reply! Actually, I want to add a random slope for the year since I want to get a rate of change, like people usually do in a growth curve model. I know it is doable in a growth curve model such as

Code:

mixed DV IV year || ID: year, cov(un)

However, I am not sure if this is doable when the DV is a binary rather than continuous variable. I am still confused about how to deal with time in a mixed-effects model for a binary outcome.

Best,
Yapeng
Comment
Yapeng Wang

Join Date: Dec 2017

Posts: 74
#4

30 Jun 2019, 20:31

Originally posted by Robert Wells View Post

Hi Yapeng,

I am also working in the same area and i think i have spotted your issue.

Is you goal to have random coefficient for the year? This is not the typical approach for growth curve models so i assume this is not the case.

Furthermore, you were treat year as a continuous variable. If this was the case, do not put a factor prefix. But you might want to consider not doing this, or if you are doing it re base the number so it not the current calendar year (age or year since the study began for example).

I would change your syntax to

Code

This allows for fixed effects for the year's (as that is part of the feature of the mixed model), random intercepts for the id's.

I do not see why you are specifying the co-variance structure to be unrestrained, as you only have one level the code should change this (from my experience) to identity. So there is no need to change this.

Hope this helps

Hi Robert,

Thank you for your reply! Actually, I want to add a random slope for the year since I want to get a rate of change, like people usually do in a growth curve model. I know it is doable in a growth curve model such as

Code:

mixed DV IV year || ID: year, cov(un)

However, I am not sure if this is doable when the DV is a binary rather than continuous variable. I am still confused about how to deal with time in a mixed-effects model for a binary outcome.

Best,
Yapeng
Comment
Robert Wells

Join Date: Apr 2014

Posts: 16
#5

30 Jun 2019, 21:55

Hi Yapeng,

Random Coefficient growth curve model it then. in that case, the cov(un) option is warranted.

In that case, i believe your current syntax is fine. I personally, would add a quadratic term for year in the fixed equation. This allows your growth curve to approach some sort of maximum (or otherwise)

The adjusted code would be

Code:

generate year2=year^2 mixed DV IV year year2 || ID: year, cov(un)

I highly recommend the book Multi-level and Longitudinal Modelling using Stata. It has a number of chapters that address your problem. Complete with code.

Cheers
Rob
Comment
Joseph Coveney

Join Date: Apr 2014

Posts: 4374
#6

30 Jun 2019, 22:02

Originally posted by Yapeng Wang View Post

I am using mixed-effects logistic regression for panel data in STATA 15. . . this is kind of like a growth curve model except for the binary DV. I was wondering if my command is correct, and what is the difference between a growth curve model and a mixed-effects logistic model for panel data.

The random slope hierarchical logistic regression model that you show for -melogit- gives the same fit as a logistic growth curve model in -gsem-. See below. (Pardon my specification for the latter if it appears clumsy.) Both models are fitted to a toy dataset created for illustration.

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ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿvar(I)|ÿÿÿ4.625699ÿÿÿ1.689133ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ2.261258ÿÿÿÿ9.462471
ÿÿÿÿÿÿÿvar(S)|ÿÿÿ.3057181ÿÿÿ.1229581ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1389865ÿÿÿÿ.6724648
-------------+----------------------------------------------------------------
ÿÿÿÿÿcov(I,S)|ÿÿ-1.017124ÿÿÿ.4196862ÿÿÿÿ-2.42ÿÿÿ0.015ÿÿÿÿ-1.839694ÿÿÿ-.1945538
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file

.
Comment
Yapeng Wang

Join Date: Dec 2017

Posts: 74
#7

01 Jul 2019, 07:14

Originally posted by Robert Wells View Post

Hi Yapeng,

Random Coefficient growth curve model it then. in that case, the cov(un) option is warranted.

In that case, i believe your current syntax is fine. I personally, would add a quadratic term for year in the fixed equation. This allows your growth curve to approach some sort of maximum (or otherwise)

The adjusted code would be

Code:

generate year2=year^2 mixed DV IV year year2 || ID: year, cov(un)

I highly recommend the book Multi-level and Longitudinal Modelling using Stata. It has a number of chapters that address your problem. Complete with code.

Cheers
Rob

Hi Rob, Thank you very much!
Comment
Yapeng Wang

Join Date: Dec 2017

Posts: 74
#8

01 Jul 2019, 07:16

Originally posted by Joseph Coveney View Post

The random slope hierarchical logistic regression model that you show for -melogit- gives the same fit as a logistic growth curve model in -gsem-. See below. (Pardon my specification for the latter if it appears clumsy.) Both models are fitted to a toy dataset created for illustration.

.ÿ
.ÿversionÿ15.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("155422")'

.ÿ
.ÿquietlyÿsetÿobsÿ200

.ÿgenerateÿintÿpidÿ=ÿ_n

.ÿquietlyÿdrawnormÿpid_interceptÿpid_slope,ÿdoubleÿcorr(1ÿ-0.25ÿ\ÿ-0.25ÿ1)

.ÿgenerateÿdoubleÿticÿ=ÿruniform()ÿ-ÿ0.5ÿ//ÿTime-invariantÿcovariate

.ÿ
.ÿquietlyÿexpandÿ5

.ÿbysortÿpid:ÿgenerateÿbyteÿtimÿ=ÿ_n

.ÿgenerateÿdoubleÿtvcÿ=ÿruniform()ÿ-ÿ0.5ÿ//ÿTime-varyingÿcovariate

.ÿ
.ÿgenerateÿdoubleÿxbÿ=ÿ///
>ÿÿÿÿÿÿÿÿÿ0ÿ+ÿpid_interceptÿ+ÿ0ÿ*ÿticÿ+ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ(timÿ-ÿ3)ÿ/ÿ2ÿ*ÿ(1/5ÿ+ÿpid_slope)ÿ+ÿ0ÿ*ÿtvc

.ÿgenerateÿbyteÿoutÿ=ÿrbinomial(1,ÿinvlogit(xb))

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿmelogitÿoutÿc.(ticÿtimÿtvc)ÿ||ÿpid:ÿtim,ÿcovariance(unstructured)ÿnolog

Mixed-effectsÿlogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ1,000
Groupÿvariable:ÿÿÿÿÿÿÿÿÿÿÿÿÿpidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿ200

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ5
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ5.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ5

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(3)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ3.55
Logÿlikelihoodÿ=ÿ-664.71764ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.3138
--------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿoutÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
---------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1959145ÿÿÿ.3754731ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5399992ÿÿÿÿ.9318281
ÿÿÿÿÿÿÿÿÿÿÿtimÿ|ÿÿÿ.1197285ÿÿÿÿ.067201ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119832ÿÿÿÿ.2514401
ÿÿÿÿÿÿÿÿÿÿÿtvcÿ|ÿÿ-.1141664ÿÿÿ.2831145ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6690607ÿÿÿÿ.4407279
ÿÿÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3988859ÿÿÿÿ.238745ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668175ÿÿÿÿ.0690458
---------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿvar(tim)|ÿÿÿ.3061836ÿÿÿ.1232728ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1390846ÿÿÿÿ.6740387
ÿÿÿÿÿvar(_cons)|ÿÿÿ4.633829ÿÿÿÿ1.69718ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ2.260373ÿÿÿÿ9.499482
---------------+----------------------------------------------------------------
pidÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿcov(tim,_cons)|ÿÿ-1.019001ÿÿÿ.4213028ÿÿÿÿ-2.42ÿÿÿ0.016ÿÿÿÿ-1.844739ÿÿÿ-.1932623
--------------------------------------------------------------------------------
LRÿtestÿvs.ÿlogisticÿmodel:ÿchi2(3)ÿ=ÿ52.48ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿ0.0000

Note:ÿLRÿtestÿisÿconservativeÿandÿprovidedÿonlyÿforÿreference.

.ÿ
.ÿkeepÿpidÿt*ÿout

.ÿgenerateÿbyteÿtimeÿ=ÿtim

.ÿquietlyÿreshapeÿwideÿticÿtvcÿtimÿout,ÿi(pid)ÿj(time)

.ÿrenameÿtic1ÿtic

.ÿdropÿtic?

.ÿ
.ÿforvaluesÿiÿ=ÿ2/5ÿ{
ÿÿ2.ÿÿÿÿÿÿÿÿÿconstraintÿdefineÿ`i'ÿ_b[out`i':_cons]ÿ=ÿ_b[out1:_cons]
ÿÿ3.ÿÿÿÿÿÿÿÿÿconstraintÿdefineÿ10`i'ÿ_b[out`i':tim`i']ÿ=ÿ_b[out1:tim1]
ÿÿ4.ÿ}

.ÿgsemÿ///
>ÿÿÿÿÿÿÿÿÿ(out1ÿ<-ÿc.tic@iÿc.tim1ÿc.tvc1@vÿI@1ÿS@1,ÿlogit)ÿ///
>ÿÿÿÿÿÿÿÿÿ(out2ÿ<-ÿc.tic@iÿc.tim2ÿc.tvc2@vÿI@1ÿS@2,ÿlogit)ÿ///
>ÿÿÿÿÿÿÿÿÿ(out3ÿ<-ÿc.tic@iÿc.tim3ÿc.tvc3@vÿI@1ÿS@3,ÿlogit)ÿ///
>ÿÿÿÿÿÿÿÿÿ(out4ÿ<-ÿc.tic@iÿc.tim4ÿc.tvc4@vÿI@1ÿS@4,ÿlogit)ÿ///
>ÿÿÿÿÿÿÿÿÿ(out5ÿ<-ÿc.tic@iÿc.tim5ÿc.tvc5@vÿI@1ÿS@5,ÿlogit),ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcollinearÿconstraints(2/5ÿ102/105)ÿ///
>ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿnodvheaderÿnocnsreportÿnolog

GeneralizedÿstructuralÿequationÿmodelÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ200
Logÿlikelihoodÿ=ÿ-664.72063

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
out1ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1960443ÿÿÿ.3754558ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5398356ÿÿÿÿ.9319243
ÿÿÿÿÿÿÿÿtim1ÿ|ÿÿÿ.1197392ÿÿÿ.0671983ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119671ÿÿÿÿ.2514456
ÿÿÿÿÿÿÿÿtvc1ÿ|ÿÿ-.1140352ÿÿÿ.2830953ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6688917ÿÿÿÿ.4408213
ÿÿÿÿÿÿÿÿÿÿÿIÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿ2.42e-17ÿÿ4.1e+16ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿSÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿ1.40e-16ÿÿ7.2e+15ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
out2ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1960443ÿÿÿ.3754558ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5398356ÿÿÿÿ.9319243
ÿÿÿÿÿÿÿÿtim2ÿ|ÿÿÿ.1197392ÿÿÿ.0671983ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119671ÿÿÿÿ.2514456
ÿÿÿÿÿÿÿÿtvc2ÿ|ÿÿ-.1140352ÿÿÿ.2830953ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6688917ÿÿÿÿ.4408213
ÿÿÿÿÿÿÿÿÿÿÿIÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿ5.73e-44ÿÿ1.7e+43ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿSÿ|ÿÿÿÿÿÿÿÿÿÿ2ÿÿÿ2.22e-43ÿÿ9.0e+42ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ2ÿÿÿÿÿÿÿÿÿÿÿ2
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
out3ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1960443ÿÿÿ.3754558ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5398356ÿÿÿÿ.9319243
ÿÿÿÿÿÿÿÿtim3ÿ|ÿÿÿ.1197392ÿÿÿ.0671983ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119671ÿÿÿÿ.2514456
ÿÿÿÿÿÿÿÿtvc3ÿ|ÿÿ-.1140352ÿÿÿ.2830953ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6688917ÿÿÿÿ.4408213
ÿÿÿÿÿÿÿÿÿÿÿIÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿ3.25e-43ÿÿ3.1e+42ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿSÿ|ÿÿÿÿÿÿÿÿÿÿ3ÿÿÿ1.61e-43ÿÿ1.9e+43ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ3ÿÿÿÿÿÿÿÿÿÿÿ3
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
out4ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1960443ÿÿÿ.3754558ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5398356ÿÿÿÿ.9319243
ÿÿÿÿÿÿÿÿtim4ÿ|ÿÿÿ.1197392ÿÿÿ.0671983ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119671ÿÿÿÿ.2514456
ÿÿÿÿÿÿÿÿtvc4ÿ|ÿÿ-.1140352ÿÿÿ.2830953ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6688917ÿÿÿÿ.4408213
ÿÿÿÿÿÿÿÿÿÿÿIÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿÿ1.64e-43ÿÿ6.1e+42ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿSÿ|ÿÿÿÿÿÿÿÿÿÿ4ÿÿÿ2.49e-43ÿÿ1.6e+43ÿÿÿ0.000ÿÿÿÿÿÿÿÿÿÿÿÿ4ÿÿÿÿÿÿÿÿÿÿÿ4
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
out5ÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿticÿ|ÿÿÿ.1960443ÿÿÿ.3754558ÿÿÿÿÿ0.52ÿÿÿ0.602ÿÿÿÿ-.5398356ÿÿÿÿ.9319243
ÿÿÿÿÿÿÿÿtim5ÿ|ÿÿÿ.1197392ÿÿÿ.0671983ÿÿÿÿÿ1.78ÿÿÿ0.075ÿÿÿÿ-.0119671ÿÿÿÿ.2514456
ÿÿÿÿÿÿÿÿtvc5ÿ|ÿÿ-.1140352ÿÿÿ.2830953ÿÿÿÿ-0.40ÿÿÿ0.687ÿÿÿÿ-.6688917ÿÿÿÿ.4408213
ÿÿÿÿÿÿÿÿÿÿÿIÿ|ÿÿÿÿÿÿÿÿÿÿ1ÿÿ(constrained)
ÿÿÿÿÿÿÿÿÿÿÿSÿ|ÿÿÿÿÿÿÿÿÿÿ5ÿÿ(constrained)
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.3989264ÿÿÿ.2387248ÿÿÿÿ-1.67ÿÿÿ0.095ÿÿÿÿ-.8668185ÿÿÿÿ.0689657
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿvar(I)|ÿÿÿ4.625699ÿÿÿ1.689133ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ2.261258ÿÿÿÿ9.462471
ÿÿÿÿÿÿÿvar(S)|ÿÿÿ.3057181ÿÿÿ.1229581ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1389865ÿÿÿÿ.6724648
-------------+----------------------------------------------------------------
ÿÿÿÿÿcov(I,S)|ÿÿ-1.017124ÿÿÿ.4196862ÿÿÿÿ-2.42ÿÿÿ0.015ÿÿÿÿ-1.839694ÿÿÿ-.1945538
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file

.

Hi Joseph, thank you for your detailed post! It is very helpful!
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