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Re: st: Interpretation of Coefficients - Ordered Probit Regression


From   Richard Williams <[email protected]>
To   [email protected], statalist <[email protected]>
Subject   Re: st: Interpretation of Coefficients - Ordered Probit Regression
Date   Fri, 13 Sep 2013 08:54:30 -0500

At 05:47 AM 9/13/2013, Yuval Arbel wrote:
Hi Richard and thank you very much for your answer.

It turns out I didn't need to go so far. After some effort, I found
the answers in Greene (2012). All of these models can be transformed
into projected probabilities.

I would still recommend looking at Long & Freese's book, or at least their -spost9- commands (use -findit- to get them off of Long's site). Particularly with multiple outcome commands like -oprobit- the Long and Freese commands can greatly simplify things. The -spost13- commands, now in beta teting, will be even better because they take advantage of new features made possible because of margins.


For other participants, here is an example how to do this
automatically (by using -margins-) and manually in Stata:

. oprobit avg_fm_inc age rel_age orth_age  if avg_fm_inc>0

Iteration 0:   log likelihood = -295.48866
Iteration 1:   log likelihood = -290.24456
Iteration 2:   log likelihood = -290.24385
Iteration 3:   log likelihood = -290.24385

Ordered probit regression                         Number of obs   =        194
LR chi2(3) = 10.49 Prob > chi2 = 0.0148
Log likelihood = -290.24385                       Pseudo R2       =     0.0177

------------------------------------------------------------------------------
avg_fm_inc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .0125689 .0099679 1.26 0.207 -.0069678 .0321055 rel_age | -.019385 .0064948 -2.98 0.003 -.0321146 -.0066555 orth_age | -.0176433 .0070068 -2.52 0.012 -.0313764 -.0039102
-------------+----------------------------------------------------------------
/cut1 | -.9461037 .2573453 -1.450491 -.4417161 /cut2 | -.3325317 .2527136 -.8278412 .1627778 /cut3 | .4581856 .2536228 -.0389059 .9552771 /cut4 | 1.517816 .270983 .9866995 2.048933
------------------------------------------------------------------------------

. test rel_age=orth_age

 ( 1)  [avg_fm_inc]rel_age - [avg_fm_inc]orth_age = 0

           chi2(  1) =    0.06
         Prob > chi2 =    0.7995

. test age=rel_age

 ( 1)  [avg_fm_inc]age - [avg_fm_inc]rel_age = 0

           chi2(  1) =    5.26
         Prob > chi2 =    0.0219

. test age=orth_age

 ( 1)  [avg_fm_inc]age - [avg_fm_inc]orth_age = 0

           chi2(  1) =    4.53
         Prob > chi2 =    0.0333

. outreg2 using "D:\kingston\cube_erez_yossi\cube_inc2.xls", replace
dec(2) addstat(log likelihood, e(ll) )
D:\kingston\cube_erez_yossi\cube_inc2.xls
dir : seeout

.
. //here is the authomatic calculation of probabilities - secular age 20
. margins, at(age==20 rel_age==0 orth_age==0)

Adjusted predictions                              Number of obs   =        194
Model VCE    : OIM

Expression   : Pr(avg_fm_inc==1), predict()
at           : age             =          20
               rel_age         =           0
               orth_age        =           0

------------------------------------------------------------------------------
             |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .1155596 .0281306 4.11 0.000 .0604245 .1706946
------------------------------------------------------------------------------

. margins, at(age==20 rel_age==0 orth_age==0) predict(outcome(2))

Adjusted predictions                              Number of obs   =        194
Model VCE    : OIM

Expression   : Pr(avg_fm_inc==2), predict(outcome(2))
at           : age             =          20
               rel_age         =           0
               orth_age        =           0

------------------------------------------------------------------------------
             |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .1640812 .0279952 5.86 0.000 .1092115 .2189509
------------------------------------------------------------------------------

. margins, at(age==20 rel_age==0 orth_age==0) predict(outcome(3))

Adjusted predictions                              Number of obs   =        194
Model VCE    : OIM

Expression   : Pr(avg_fm_inc==3), predict(outcome(3))
at           : age             =          20
               rel_age         =           0
               orth_age        =           0

------------------------------------------------------------------------------
             |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .3022795 .0335618 9.01 0.000 .2364994 .3680595
------------------------------------------------------------------------------

. margins, at(age==20 rel_age==0 orth_age==0) predict(outcome(4))

Adjusted predictions                              Number of obs   =        194
Model VCE    : OIM

Expression   : Pr(avg_fm_inc==4), predict(outcome(4))
at           : age             =          20
               rel_age         =           0
               orth_age        =           0

------------------------------------------------------------------------------
             |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .3154018 .0405729 7.77 0.000 .2358805 .3949231
------------------------------------------------------------------------------

. margins, at(age==20 rel_age==0 orth_age==0) predict(outcome(5))

Adjusted predictions                              Number of obs   =        194
Model VCE    : OIM

Expression   : Pr(avg_fm_inc==5), predict(outcome(5))
at           : age             =          20
               rel_age         =           0
               orth_age        =           0

------------------------------------------------------------------------------
             |            Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | .1026779 .0281715 3.64 0.000 .0474628 .1578931
------------------------------------------------------------------------------

.
.
.
. //here is the manual calculation of probabilities - secular age 20
. lincom [cut1]_cons-20*age

 ( 1)  - 20*[avg_fm_inc]age + [cut1]_cons = 0

------------------------------------------------------------------------------
avg_fm_inc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -1.197481 .1444276 -8.29 0.000 -1.480554 -.914408
------------------------------------------------------------------------------

. display normal( -1.197481)
.11555956

. lincom [cut2]_cons-20*age

 ( 1)  - 20*[avg_fm_inc]age + [cut2]_cons = 0

------------------------------------------------------------------------------
avg_fm_inc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | -.5839089 .1300984 -4.49 0.000 -.8388971 -.3289207
------------------------------------------------------------------------------

. display normal(-.5839089)-normal( -1.197481)
.16408124

. lincom [cut3]_cons-20*age

 ( 1)  - 20*[avg_fm_inc]age + [cut3]_cons = 0

------------------------------------------------------------------------------
avg_fm_inc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .2068084 .1268641 1.63 0.103 -.0418407 .4554574
------------------------------------------------------------------------------

. display normal(.2068084)-normal(-.5839089)
.30227945

. lincom [cut4]_cons-20*age

 ( 1)  - 20*[avg_fm_inc]age + [cut4]_cons = 0

------------------------------------------------------------------------------
avg_fm_inc | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.266439 .157462 8.04 0.000 .9578193 1.575059
------------------------------------------------------------------------------

. display normal( 1.266439)-normal(.2068084)
.31540177

. display 1-normal( 1.266439)
.10267798



On Wed, Sep 11, 2013 at 11:20 PM, Richard Williams
<[email protected]> wrote:
> At 09:35 AM 9/11/2013, Yuval Arbel wrote:
>>
>> Dear Statalisters,
>>
>> I would like to ask whether there is any direct interpretation to the
>> coefficients obtained from the Ordered-Probit regression (apart from
>> sign and significance)
>
>
> I recommend getting Long & Freese's book:
>
> http://www.stata.com/bookstore/regression-models-categorical-dependent-variables/index.html
>
> it is a bit dated (a revision is underway) but it has a lot of good ideas
> for making the results from categorical models more interpretable.
>
>
>
>> For instance, here is an example, where the dependent variable is
>> self-ranking of household's income on a scale between 1 to 5
>>
>> As always, your answers will be highly appreciated
>>
>> . oprobit avg_fm_inc rel_age orth_age age if male==1 &  avg_fm_inc>0
>>
>> Iteration 0:   log likelihood = -150.03974
>> Iteration 1:   log likelihood = -147.51265
>> Iteration 2:   log likelihood = -147.51213
>> Iteration 3:   log likelihood = -147.51213
>>
>> Ordered probit regression                         Number of obs   =
>> 103
>>                                                   LR chi2(3)      =
>> 5.06
>>                                                   Prob > chi2     =
>> 0.1678
>> Log likelihood = -147.51213                       Pseudo R2       =
>> 0.0168
>>
>>
>> ------------------------------------------------------------------------------
>>   avg_fm_inc |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
>> Interval]
>>
>> -------------+----------------------------------------------------------------
>>      rel_age |  -.0151282   .0078644    -1.92   0.054    -.0305421
>> .0002858
>>     orth_age |  -.0171244   .0090368    -1.89   0.058    -.0348362
>> .0005875
>>          age |   .0096716   .0120724     0.80   0.423    -.0139899
>> .033333
>>
>> -------------+----------------------------------------------------------------
>>        /cut1 |  -1.249527   .3469838                     -1.929603
>> -.5694517
>>        /cut2 |  -.4162616   .3304927                     -1.064015
>> .2314923
>>        /cut3 |   .4598018   .3336116                     -.1940649
>> 1.113668
>>        /cut4 |   1.679019    .372254                      .9494143
>> 2.408623
>>
>> ------------------------------------------------------------------------------
>>
>> --
>> Dr. Yuval Arbel
>> School of Business
>> Carmel Academic Center
>> 4 Shaar Palmer Street,
>> Haifa 33031, Israel
>> e-mail1: [email protected]
>> e-mail2: [email protected]
>> You can access my latest paper on SSRN at:
>> http://ssrn.com/abstract=2263398
>> You can access previous papers on SSRN at: http://ssrn.com/author=1313670
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/faqs/resources/statalist-faq/
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  [email protected]
> WWW:    http://www.nd.edu/~rwilliam
>
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/faqs/resources/statalist-faq/
> *   http://www.ats.ucla.edu/stat/stata/



--
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: [email protected]
e-mail2: [email protected]
You can access my latest paper on SSRN at:  http://ssrn.com/abstract=2263398
You can access previous papers on SSRN at: http://ssrn.com/author=1313670
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  [email protected]
WWW:    http://www.nd.edu/~rwilliam

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/


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