Estimating marginal effects conditional on two equation outcomes using cmp

[Paul Gerrans]

Hello Statalisters,

I have 3 binary outcomes.
Var1 - Is a 1/0 if a response is received: yes/no
Var2 - Is a 1/0 whether the response indicates an event happened: yes/no
Var3 - Is a 1/0 did they choose an option after the event: yes no.

I have variables A, B, C observed for all equations and variables that are expected to predict Var 1 and Var 2 respectively but not Var3 (akin to exclusion restriction variables)

I am using cmp to estimate this series of equations which it provides output for using the following:

1) cmp (Var1 = A B C X) (Var2 = A B C Y) (Var3 = A B C Z), ///
ind($cmp_probit Var2*$cmp_probit Var3*$cmp_probit)

My first query is whether the above correctly estimates the probability of Var3 conditional on a response (Var1) and the event (Var2)?

My next step is to estimating the marginal effects for variable A for Var3 equation.

I use the help file to guide me and use:

2) margins, dydx(A) predict(pr eq(Var3) condition(0 ., eq(Var2)))

I interpret this as conditional that the event happened (Var2==1) what is the marginal effect of A on the probability of Var3==1
I'm unclear whether the above code in (1) conditions on Var1=1?

Another option is to use expression to condition on both using
3) margins, dydx(A) expression(predict(pr eq(Var3) condition(0 ., eq(Var2))) * predict(pr eq(Var2) condition(0 ., eq(Var1))) )

Both 2 & 3 provide estimates, 3 lower than 2 which makes me think (2) does not condition.

If my primary interest is the marginal effect of A on Var3 conditional on Var1 and Var2 being both yes is either combination (1) & (2) or (1) & (3) correct?

Appreciate any feedback.

Thanks
Paul

[David Roodman]

I don't really understand how the command line in 1) could work because the Var2 equation is only applied where Var2=1 and likewise for the Var3 equation. Assuming Var1=0 implies Var2=0, I think you want

cmp (Var1 = A B C X) (Var2 = A B C Y) (Var3 = A B C Z), ind($cmp_probit Var1*$cmp_probit Var2*$cmp_probit)

I don't think you should need to use any condition() clause here. The Var3 equation only applies where Var1=Var2=1, that is, the latent variables behind Var1 and Var2 are each between 0 and infinity, which is what the cond() clauses are stiuplating.

In this simulation, I'm getting essentially the same answer from three versions of the predict command. The standard errors change--not sure why. Maybe imprecision in the delta method application.

clear
set obs 100000
drawnorm A
gen byte v1 = A + rnormal() > 0
gen byte v2 = v1 & A + rnormal() > 0
gen byte v3 = v2 & A + rnormal() > 0

cap noi cmp (v1 = A) (v2 = A) (v3 = A), ind(4 4*v2 4*v3) nolr  // crashes since v2===1 and v3===1 in their equations

cmp (v1 = A) (v2 = A) (v3 = A), ind(4 4*v1 4*v2) nolr ghkdraws(13)
margins, dydx(A) predict(pr eq(v3))
margins, dydx(A) predict(pr eq(v3) cond(0 ., eq(v2)))
margins, dydx(A) expression(predict(pr eq(v3) cond(0 ., eq(v2))) * predict(pr eq(v2) cond(0 ., eq(v1))))

Output:

. margins, dydx(A) predict(pr eq(v3))

Average marginal effects                               Number of obs = 100,000
Model VCE: OIM

Expression: Pr(v3), predict(pr eq(v3))
dy/dx wrt:  A

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
           A |   .2895285   .0051061    56.70   0.000     .2795206    .2995364
------------------------------------------------------------------------------

. margins, dydx(A) predict(pr eq(v3) cond(0 ., eq(v2)))

Average marginal effects                               Number of obs = 100,000
Model VCE: OIM

Expression: Pr(0<v3), predict(pr eq(v3) cond(0 ., eq(v2)))
dy/dx wrt:  A

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
           A |   .2851489   .0060813    46.89   0.000     .2732297    .2970681
------------------------------------------------------------------------------

. margins, dydx(A) expression(predict(pr eq(v3) cond(0 ., eq(v2))) * predict(pr eq(v2) cond(0 ., eq(v1))))

Average marginal effects                               Number of obs = 100,000
Model VCE: OIM

Expression: predict(pr eq(v3) cond(0 ., eq(v2))) * predict(pr eq(v2) cond(0 ., eq(v1)))
dy/dx wrt:  A

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
           A |   .2814198   .0010721   262.50   0.000     .2793186     .283521
------------------------------------------------------------------------------

[Paul Gerrans]

Hi David
Thanks for the explanation - that makes sense.
Greatly appreciate your help, and the program.
Thanks
Paul

[Sandra Tamakloe]

Hi experts, I have been trying to run my multivariate probit model using CMP. I could not achieve convergence with higher draws; however, when I decreased the draws to 23, convergence was achieved. Now, I am trying to estimate marginal effects for all covariates for each model. However, I am unsure about the results I am obtaining. The significance after estimating marginal effects changes, and covariates not included in some of the equations appear as omitted. Could you please advise if I am doing something wrong?





cmp (Consultation = i.Gender i.Marstat i.sdcgvvm i.Educ i.inc i.Accessibility i.Mood_disorder i.Anxiety_disorder i.scrdm
> en)(psychi = log_spsdcon i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof)(psycho =
> log_spsdcon i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof)(famdoc = log_spsdcon
> i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof), indicators($cmp_probit $cmp_pro
> bit $cmp_probit $cmp_probit) svy ghkdraws(23)



Fitting full model.
Likelihoods for 2834 observations involve cumulative normal distributions above dimension 2.
Using ghk2() to simulate them. Settings:
Sequence type = halton
Number of draws per observation = 23
Include antithetic draws = no
Scramble = no
Prime bases = 2 3 5
Each observation gets different draws, so changing the order of observations in the data set would change the results.


Iteration 0: log pseudolikelihood = -8120170.4
Iteration 1: log pseudolikelihood = -7718198.6 (not concave)
Iteration 2: log pseudolikelihood = -7677183.3
Iteration 3: log pseudolikelihood = -7625418.3
Iteration 4: log pseudolikelihood = -7588970.2
Iteration 5: log pseudolikelihood = -7582348
Iteration 6: log pseudolikelihood = -7580399.7
Iteration 7: log pseudolikelihood = -7580191.4
Iteration 8: log pseudolikelihood = -7580190.8

Mixed-process regression

Number of strata = 1 Number of obs = 3,015
Number of PSUs = 3,015 Population size = 8,686,077
Design df = 3,014
F( 19, 2996) = 10.34
Prob > F = 0.0000

---------------------------------------------------------------------------------------------
| Linearized
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
Consultation |
Gender |
Female | .4796175 .0707201 6.78 0.000 .3409529 .618282
|
Marstat |
Unmarried | .1884576 .0909082 2.07 0.038 .0102093 .3667059
|
sdcgvvm |
Chinese | .1504474 .1057601 1.42 0.155 -.0569219 .3578166
Black | .0649873 .1030405 0.63 0.528 -.1370495 .2670242
Filipino | .3835923 .1164655 3.29 0.001 .1552325 .6119522
Other ethnic groups | .3037092 .1064109 2.85 0.004 .095064 .5123544
Not a visible minority | .3680866 .0820231 4.49 0.000 .2072598 .5289134
|
Educ |
Some/above high school | -.0785782 .1077084 -0.73 0.466 -.2897677 .1326112
University Education | .1938769 .122018 1.59 0.112 -.04537 .4331238
Post-graduate | .0466602 .1452427 0.32 0.748 -.2381246 .3314451
|
inc |
above $70,000 | .1661787 .0927885 1.79 0.073 -.0157565 .3481139
$150,000 or more | .1917006 .09718 1.97 0.049 .0011548 .3822465
|
Accessibility |
Yes | .4570894 .0821309 5.57 0.000 .296051 .6181277
|
Mood_disorder |
Yes | .4120839 .1036865 3.97 0.000 .2087804 .6153874
|
Anxiety_disorder |
Yes | .221834 .0863383 2.57 0.010 .052546 .3911221
|
scrdmen |
Fair | -.048639 .1576494 -0.31 0.758 -.3577504 .2604723
Good | -.3608224 .1559039 -2.31 0.021 -.6665113 -.0551336
Very good | -.6120807 .1650523 -3.71 0.000 -.9357072 -.2884541
Excellent | -.8470549 .1834877 -4.62 0.000 -1.206829 -.4872811
|
_cons | -1.325479 .2174499 -6.10 0.000 -1.751844 -.8991137
----------------------------+----------------------------------------------------------------
psychi |
log_spsdcon | -.6845597 .3004699 -2.28 0.023 -1.273707 -.0954129
|
Gender |
Female | .1792515 .1091843 1.64 0.101 -.0348318 .3933347
|
Marstat |
Unmarried | .1034872 .1435657 0.72 0.471 -.1780095 .3849838
|
immig |
Immigrant | -.2077337 .1186283 -1.75 0.080 -.4403343 .0248669
|
Educ |
Some/above high school | .1150455 .1447266 0.79 0.427 -.1687274 .3988184
University Education | .0927934 .1747031 0.53 0.595 -.249756 .4353428
Post-graduate | -.444091 .3197745 -1.39 0.165 -1.071089 .1829073
|
inc |
above $70,000 | -.1022465 .1671777 -0.61 0.541 -.4300405 .2255475
$150,000 or more | .3227294 .1650973 1.95 0.051 -.0009854 .6464441
|
Accessibility |
Yes | .4248367 .1292217 3.29 0.001 .1714651 .6782083
|
workstat |
Has a job | -.1218438 .1099616 -1.11 0.268 -.3374512 .0937636
|
spibef |
somewhat important | .1445721 .1580079 0.91 0.360 -.165242 .4543862
Not very important | -.0208893 .1590721 -0.13 0.896 -.3327901 .2910116
Not important | .0634402 .1486502 0.43 0.670 -.2280258 .3549062
|
Nonprof |
Consulted non-professional | .2627016 .1406123 1.87 0.062 -.0130042 .5384074
_cons | .1858784 1.062272 0.17 0.861 -1.896973 2.268729
----------------------------+----------------------------------------------------------------
psycho |
log_spsdcon | .2863743 .3211919 0.89 0.373 -.343403 .9161517
|
Gender |
Female | .4810005 .1050238 4.58 0.000 .2750749 .6869261
|
Marstat |
Unmarried | .1799798 .1254381 1.43 0.151 -.0659731 .4259328
|
immig |
Immigrant | -.1974399 .1266289 -1.56 0.119 -.4457276 .0508478
|
Educ |
Some/above high school | -.1918601 .1477345 -1.30 0.194 -.4815308 .0978106
University Education | -.046092 .1616068 -0.29 0.776 -.3629628 .2707788
Post-graduate | -.192151 .2177866 -0.88 0.378 -.6191764 .2348744
|
inc |
above $70,000 | .0643393 .1493129 0.43 0.667 -.2284263 .3571049
$150,000 or more | .1933904 .1492387 1.30 0.195 -.0992296 .4860104
|
Accessibility |
Yes | .1947195 .1158005 1.68 0.093 -.0323365 .4217756
|
workstat |
Has a job | .0750704 .1131892 0.66 0.507 -.1468655 .2970062
|
spibef |
somewhat important | .1528832 .1535672 1.00 0.320 -.1482238 .4539903
Not very important | .2362282 .1456138 1.62 0.105 -.0492843 .5217406
Not important | .2222653 .1431838 1.55 0.121 -.0584826 .5030132
|
Nonprof |
Consulted non-professional | .5621213 .1400352 4.01 0.000 .287547 .8366956
_cons | -3.592622 1.180341 -3.04 0.002 -5.906978 -1.278266
----------------------------+----------------------------------------------------------------
famdoc |
log_spsdcon | -.7349477 .2992322 -2.46 0.014 -1.321668 -.1482277
|
Gender |
Female | .3762202 .0909589 4.14 0.000 .1978724 .554568
|
Marstat |
Unmarried | .069982 .1104076 0.63 0.526 -.1464997 .2864638
|
immig |
Immigrant | -.3934558 .1107177 -3.55 0.000 -.6105458 -.1763659
|
Educ |
Some/above high school | -.0717378 .1367946 -0.52 0.600 -.339958 .1964825
University Education | .144163 .1504966 0.96 0.338 -.1509234 .4392494
Post-graduate | -.0014996 .1826502 -0.01 0.993 -.3596313 .356632
|
inc |
above $70,000 | .0541161 .1348153 0.40 0.688 -.2102232 .3184555
$150,000 or more | .0457803 .134667 0.34 0.734 -.2182681 .3098287
|
Accessibility |
Yes | .3336361 .0947796 3.52 0.000 .1477968 .5194755
|
workstat |
Has a job | -.001444 .0896478 -0.02 0.987 -.1772211 .1743331
|
spibef |
somewhat important | -.0002748 .1162368 -0.00 0.998 -.2281863 .2276367
Not very important | .1186325 .1125123 1.05 0.292 -.1019762 .3392412
Not important | .2376277 .1097024 2.17 0.030 .0225287 .4527268
|
Nonprof |
Consulted non-professional | .5197157 .1433352 3.63 0.000 .2386711 .8007603
_cons | .7085546 1.065495 0.67 0.506 -1.380617 2.797726
----------------------------+----------------------------------------------------------------
/atanhrho_12 | 1.100063 .1222318 9.00 0.000 .8603967 1.339729
/atanhrho_13 | 1.055889 .0920186 11.47 0.000 .8754632 1.236315
/atanhrho_14 | 1.268118 .1163391 10.90 0.000 1.040006 1.49623
/atanhrho_23 | .6383076 .0750095 8.51 0.000 .4912325 .7853827
/atanhrho_24 | .7257945 .0888717 8.17 0.000 .5515392 .9000497
/atanhrho_34 | .4997038 .0587016 8.51 0.000 .3846046 .614803
----------------------------+----------------------------------------------------------------
rho_12 | .8005216 .0439014 .696462 .8716072
rho_13 | .7840853 .0354465 .7041392 .8444012
rho_14 | .8532868 .0316328 .7778905 .9044647
rho_23 | .5637461 .0511708 .4551941 .6557854
rho_24 | .6204857 .0546559 .5016729 .7163221
rho_34 | .4618842 .0461783 .3666996 .5474992
---------------------------------------------------------------------------------------------

[Sandra Tamakloe]

This is what i get for the marginal effects



margins, dydx(*) predict(pr eq(psychi))

Average marginal effects Number of obs = 2,778
Model VCE : Linearized

Expression : Pr(psychi), predict(pr eq(psychi))
dy/dx w.r.t. : 1.Gender 1.Marstat 2.sdcgvvm 3.sdcgvvm 4.sdcgvvm 5.sdcgvvm 6.sdcgvvm 2.Educ 3.Educ 4.Educ 2.inc 3.inc
1.Accessibility 1.Mood_disorder 1.Anxiety_disorder 1.scrdmen 2.scrdmen 3.scrdmen 4.scrdmen log_spsdcon
1.immig 1.workstat 2.spibef 3.spibef 4.spibef 1.Nonprof

---------------------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. t P>|t| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
Gender |
Female | .0138463 .0083109 1.67 0.096 -.0024494 .030142
|
Marstat |
Unmarried | .0076959 .0102704 0.75 0.454 -.0124418 .0278337
|
sdcgvvm |
Chinese | 0 (omitted)
Black | 0 (omitted)
Filipino | 0 (omitted)
Other ethnic groups | 0 (omitted)
Not a visible minority | 0 (omitted)
|
Educ |
Some/above high school | .0089295 .0107393 0.83 0.406 -.0121275 .0299866
University Education | .0070688 .0132911 0.53 0.595 -.0189918 .0331294
Post-graduate | -.0214789 .0129348 -1.66 0.097 -.0468407 .003883
|
inc |
above $70,000 | -.0063389 .0109737 -0.58 0.564 -.0278555 .0151778
$150,000 or more | .0288313 .0126313 2.28 0.023 .0040645 .0535981
|
Accessibility |
Yes | .040517 .0150047 2.70 0.007 .0110966 .0699374
|
Mood_disorder |
Yes | 0 (omitted)
|
Anxiety_disorder |
Yes | 0 (omitted)
|
scrdmen |
Fair | 0 (omitted)
Good | 0 (omitted)
Very good | 0 (omitted)
Excellent | 0 (omitted)
|
log_spsdcon | -.0531687 .0235477 -2.26 0.024 -.0993399 -.0069976
|
immig |
Immigrant | -.0145842 .0079733 -1.83 0.067 -.030218 .0010495
|
workstat |
Has a job | -.0098774 .0091853 -1.08 0.282 -.0278874 .0081327
|
spibef |
somewhat important | .0116368 .0126493 0.92 0.358 -.0131653 .0364389
Not very important | -.0014645 .0111881 -0.13 0.896 -.0234015 .0204725
Not important | .0047732 .011019 0.43 0.665 -.0168323 .0263787
|
Nonprof |
Consulted non-professional | .0210054 .0102429 2.05 0.040 .0009217 .0410892
---------------------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

.

[David Roodman]

Unfortunately, I find your output to be nearly impossible to read because it is not wrapped in code tags ("#"). Perhaps this is why I don't really know what "covariates not included in some of the equations appear as omitted" refers to.

It is a bad sign if increasing the number of draws, in order to increase the accuracy of the estimator, leads to convergence problems. There is in general no guarantee that these models will converge in finite samples, and you seem to be trying to estimate a lot of parameters, which makes it harder.

[Sandra Tamakloe]

Hi David, thanks for the reply. below is the code i used

cmp (Consultation = i.Gender i.Marstat i.sdcgvvm i.Educ i.inc i.Accessibility i.Mood_disorder i.Anxiety_disorder i.scrdmen)(psychi = log_spsdcon i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof)(psycho = log_spsdcon i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof)(famdoc = log_spsdcon i.Gender i.Marstat i.immig i.Educ i.inc i.Accessibility i.workstat i.spibef i.Nonprof), indicators($cmp_probit $cmp_probit $cmp_probit $cmp_probit) svy ghkdraws(23)

output:

Fitting full model.
Likelihoods for 2834 observations involve cumulative normal distributions above dimension 2.
Using ghk2() to simulate them. Settings:
Sequence type = halton
Number of draws per observation = 23
Include antithetic draws = no
Scramble = no
Prime bases = 2 3 5
Each observation gets different draws, so changing the order of observations in the data set would change the results.


Iteration 0: log pseudolikelihood = -8120170.4
Iteration 1: log pseudolikelihood = -7718198.6 (not concave)
Iteration 2: log pseudolikelihood = -7677183.3
Iteration 3: log pseudolikelihood = -7625418.3
Iteration 4: log pseudolikelihood = -7588970.2
Iteration 5: log pseudolikelihood = -7582348
Iteration 6: log pseudolikelihood = -7580399.7
Iteration 7: log pseudolikelihood = -7580191.4
Iteration 8: log pseudolikelihood = -7580190.8

Mixed-process regression

Number of strata = 1 Number of obs = 3,015
Number of PSUs = 3,015 Population size = 8,686,077
Design df = 3,014
F( 19, 2996) = 10.34
Prob > F = 0.0000

---------------------------------------------------------------------------------------------
| Linearized
| Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
Consultation |
Gender |
Female | .4796175 .0707201 6.78 0.000 .3409529 .618282
|
Marstat |
Unmarried | .1884576 .0909082 2.07 0.038 .0102093 .3667059
|
sdcgvvm |
Chinese | .1504474 .1057601 1.42 0.155 -.0569219 .3578166
Black | .0649873 .1030405 0.63 0.528 -.1370495 .2670242
Filipino | .3835923 .1164655 3.29 0.001 .1552325 .6119522
Other ethnic groups | .3037092 .1064109 2.85 0.004 .095064 .5123544
Not a visible minority | .3680866 .0820231 4.49 0.000 .2072598 .5289134
|
Educ |
Some/above high school | -.0785782 .1077084 -0.73 0.466 -.2897677 .1326112
University Education | .1938769 .122018 1.59 0.112 -.04537 .4331238
Post-graduate | .0466602 .1452427 0.32 0.748 -.2381246 .3314451
|
inc |
above $70,000 | .1661787 .0927885 1.79 0.073 -.0157565 .3481139
$150,000 or more | .1917006 .09718 1.97 0.049 .0011548 .3822465
|
Accessibility |
Yes | .4570894 .0821309 5.57 0.000 .296051 .6181277
|
Mood_disorder |
Yes | .4120839 .1036865 3.97 0.000 .2087804 .6153874
|
Anxiety_disorder |
Yes | .221834 .0863383 2.57 0.010 .052546 .3911221
|
scrdmen |
Fair | -.048639 .1576494 -0.31 0.758 -.3577504 .2604723
Good | -.3608224 .1559039 -2.31 0.021 -.6665113 -.0551336
Very good | -.6120807 .1650523 -3.71 0.000 -.9357072 -.2884541
Excellent | -.8470549 .1834877 -4.62 0.000 -1.206829 -.4872811
|
_cons | -1.325479 .2174499 -6.10 0.000 -1.751844 -.8991137
----------------------------+----------------------------------------------------------------
psychi |
log_spsdcon | -.6845597 .3004699 -2.28 0.023 -1.273707 -.0954129
|
Gender |
Female | .1792515 .1091843 1.64 0.101 -.0348318 .3933347
|
Marstat |
Unmarried | .1034872 .1435657 0.72 0.471 -.1780095 .3849838
|
immig |
Immigrant | -.2077337 .1186283 -1.75 0.080 -.4403343 .0248669
|
Educ |
Some/above high school | .1150455 .1447266 0.79 0.427 -.1687274 .3988184
University Education | .0927934 .1747031 0.53 0.595 -.249756 .4353428
Post-graduate | -.444091 .3197745 -1.39 0.165 -1.071089 .1829073
|
inc |
above $70,000 | -.1022465 .1671777 -0.61 0.541 -.4300405 .2255475
$150,000 or more | .3227294 .1650973 1.95 0.051 -.0009854 .6464441
|
Accessibility |
Yes | .4248367 .1292217 3.29 0.001 .1714651 .6782083
|
workstat |
Has a job | -.1218438 .1099616 -1.11 0.268 -.3374512 .0937636
|
spibef |
somewhat important | .1445721 .1580079 0.91 0.360 -.165242 .4543862
Not very important | -.0208893 .1590721 -0.13 0.896 -.3327901 .2910116
Not important | .0634402 .1486502 0.43 0.670 -.2280258 .3549062
|
Nonprof |
Consulted non-professional | .2627016 .1406123 1.87 0.062 -.0130042 .5384074
_cons | .1858784 1.062272 0.17 0.861 -1.896973 2.268729
----------------------------+----------------------------------------------------------------
psycho |
log_spsdcon | .2863743 .3211919 0.89 0.373 -.343403 .9161517
|
Gender |
Female | .4810005 .1050238 4.58 0.000 .2750749 .6869261
|
Marstat |
Unmarried | .1799798 .1254381 1.43 0.151 -.0659731 .4259328
|
immig |
Immigrant | -.1974399 .1266289 -1.56 0.119 -.4457276 .0508478
|
Educ |
Some/above high school | -.1918601 .1477345 -1.30 0.194 -.4815308 .0978106
University Education | -.046092 .1616068 -0.29 0.776 -.3629628 .2707788
Post-graduate | -.192151 .2177866 -0.88 0.378 -.6191764 .2348744
|
inc |
above $70,000 | .0643393 .1493129 0.43 0.667 -.2284263 .3571049
$150,000 or more | .1933904 .1492387 1.30 0.195 -.0992296 .4860104
|
Accessibility |
Yes | .1947195 .1158005 1.68 0.093 -.0323365 .4217756
|
workstat |
Has a job | .0750704 .1131892 0.66 0.507 -.1468655 .2970062
|
spibef |
somewhat important | .1528832 .1535672 1.00 0.320 -.1482238 .4539903
Not very important | .2362282 .1456138 1.62 0.105 -.0492843 .5217406
Not important | .2222653 .1431838 1.55 0.121 -.0584826 .5030132
|
Nonprof |
Consulted non-professional | .5621213 .1400352 4.01 0.000 .287547 .8366956
_cons | -3.592622 1.180341 -3.04 0.002 -5.906978 -1.278266
----------------------------+----------------------------------------------------------------
famdoc |
log_spsdcon | -.7349477 .2992322 -2.46 0.014 -1.321668 -.1482277
|
Gender |
Female | .3762202 .0909589 4.14 0.000 .1978724 .554568
|
Marstat |
Unmarried | .069982 .1104076 0.63 0.526 -.1464997 .2864638
|
immig |
Immigrant | -.3934558 .1107177 -3.55 0.000 -.6105458 -.1763659
|
Educ |
Some/above high school | -.0717378 .1367946 -0.52 0.600 -.339958 .1964825
University Education | .144163 .1504966 0.96 0.338 -.1509234 .4392494
Post-graduate | -.0014996 .1826502 -0.01 0.993 -.3596313 .356632
|
inc |
above $70,000 | .0541161 .1348153 0.40 0.688 -.2102232 .3184555
$150,000 or more | .0457803 .134667 0.34 0.734 -.2182681 .3098287
|
Accessibility |
Yes | .3336361 .0947796 3.52 0.000 .1477968 .5194755
|
workstat |
Has a job | -.001444 .0896478 -0.02 0.987 -.1772211 .1743331
|
spibef |
somewhat important | -.0002748 .1162368 -0.00 0.998 -.2281863 .2276367
Not very important | .1186325 .1125123 1.05 0.292 -.1019762 .3392412
Not important | .2376277 .1097024 2.17 0.030 .0225287 .4527268
|
Nonprof |
Consulted non-professional | .5197157 .1433352 3.63 0.000 .2386711 .8007603
_cons | .7085546 1.065495 0.67 0.506 -1.380617 2.797726
----------------------------+----------------------------------------------------------------
/atanhrho_12 | 1.100063 .1222318 9.00 0.000 .8603967 1.339729
/atanhrho_13 | 1.055889 .0920186 11.47 0.000 .8754632 1.236315
/atanhrho_14 | 1.268118 .1163391 10.90 0.000 1.040006 1.49623
/atanhrho_23 | .6383076 .0750095 8.51 0.000 .4912325 .7853827
/atanhrho_24 | .7257945 .0888717 8.17 0.000 .5515392 .9000497
/atanhrho_34 | .4997038 .0587016 8.51 0.000 .3846046 .614803
----------------------------+----------------------------------------------------------------
rho_12 | .8005216 .0439014 .696462 .8716072
rho_13 | .7840853 .0354465 .7041392 .8444012
rho_14 | .8532868 .0316328 .7778905 .9044647
rho_23 | .5637461 .0511708 .4551941 .6557854
rho_24 | .6204857 .0546559 .5016729 .7163221
rho_34 | .4618842 .0461783 .3666996 .5474992
---------------------------------------------------------------------------------------------

Initially, I faced convergence problems with higher GHK draws. However, reducing the draws to 23 allowed the model to converge.

• Is it problematic to use a lower number of GHK draws (23) for such a model?
• Could this affect the reliability of my results, and how can I check this