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Re: st: Interpretation of Coefficients - Ordered Probit Regression


From   Yuval Arbel <[email protected]>
To   statalist <[email protected]>
Subject   Re: st: Interpretation of Coefficients - Ordered Probit Regression
Date   Fri, 13 Sep 2013 13:47:13 +0300

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.

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/


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