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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/