intro material goes here
Trivariate Probit
A trivariate probit example using triprobit (findit triprobit). triprobit requires exactly three equations.
use http://www.gseis.ucla.edu/courses/data/hsb2, clear
univar write math science
-------------- Quantiles --------------
Variable n Mean S.D. Min .25 Mdn .75 Max
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write 200 52.77 9.48 31.00 45.50 54.00 60.00 67.00
math 200 52.65 9.37 33.00 45.00 52.00 59.00 75.00
science 200 51.85 9.90 26.00 44.00 53.00 58.00 74.00
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generate hw=write>=60
generate hm=math>=59
generate hs=science>=58
probit hw female read
Probit estimates Number of obs = 200
LR chi2(2) = 61.31
Prob > chi2 = 0.0000
Log likelihood = -84.990569 Pseudo R2 = 0.2651
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hw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | .6340312 .2300876 2.76 0.006 .1830678 1.084995
read | .0856048 .0130065 6.58 0.000 .0601126 .1110971
_cons | -5.672047 .7798022 -7.27 0.000 -7.200431 -4.143663
------------------------------------------------------------------------------
probit hm female read
Probit estimates Number of obs = 200
LR chi2(2) = 60.81
Prob > chi2 = 0.0000
Log likelihood = -83.147044 Pseudo R2 = 0.2678
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hm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | -.0565293 .2219954 -0.25 0.799 -.4916323 .3785738
read | .0873693 .0129707 6.74 0.000 .0619471 .1127914
_cons | -5.426631 .7518587 -7.22 0.000 -6.900247 -3.953015
------------------------------------------------------------------------------
probit hs female read
Probit estimates Number of obs = 200
LR chi2(2) = 60.92
Prob > chi2 = 0.0000
Log likelihood = -97.070456 Pseudo R2 = 0.2389
------------------------------------------------------------------------------
hs | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female | -.446173 .2069653 -2.16 0.031 -.8518175 -.0405286
read | .0774906 .0115247 6.72 0.000 .0549027 .1000786
_cons | -4.351585 .6363017 -6.84 0.000 -5.598714 -3.104457
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triprobit (hw female read)(hm female read)(hs female read)
trivariate probit, GHK simulator, 25 draws
Number of obs = 200
Wald chi2(6) = 113.89
Log likelihood = -255.39444 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hw |
female | .4822861 .2174348 2.22 0.027 .0561218 .9084504
read | .0850725 .0130431 6.52 0.000 .0595085 .1106364
_cons | -5.518831 .7613767 -7.25 0.000 -7.011102 -4.02656
-------------+----------------------------------------------------------------
hm |
female | -.0372514 .2192788 -0.17 0.865 -.4670299 .3925271
read | .0885368 .0129185 6.85 0.000 .063217 .1138566
_cons | -5.523259 .7466543 -7.40 0.000 -6.986675 -4.059844
-------------+----------------------------------------------------------------
hs |
female | -.4414487 .2081496 -2.12 0.034 -.8494145 -.0334829
read | .0780318 .0116111 6.72 0.000 .0552744 .1007891
_cons | -4.397324 .6381721 -6.89 0.000 -5.648119 -3.14653
-------------+----------------------------------------------------------------
athrho12 |
_cons | .5599132 .1569287 3.57 0.000 .2523385 .8674879
-------------+----------------------------------------------------------------
athrho13 |
_cons | .1135926 .1189038 0.96 0.339 -.1194545 .3466397
-------------+----------------------------------------------------------------
athrho23 |
_cons | .2068782 .1287756 1.61 0.108 -.0455173 .4592737
------------------------------------------------------------------------------
------------------------------------------------------------------------------
rho12= .50791303 Std. Err.= .11644494 z= 4.36183 Pr>|z|= .0000129
rho13= .11310655 Std. Err.= .11738262 z= .96357152 Pr>|z|= .33526079
rho23= .20397651 Std. Err.= .12341769 z= 1.6527331 Pr>|z|= .09838519
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LR test of rho12=rho13=rho23=0: chi2(3) = 19.627249 Prob > chi2 = .00020277
test female
( 1) [hw]female = 0.0
( 2) [hm]female = 0.0
( 3) [hs]female = 0.0
chi2( 3) = 10.62
Prob > chi2 = 0.0140
test read
( 1) [hw]read = 0.0
( 2) [hm]read = 0.0
( 3) [hs]read = 0.0
chi2( 3) = 108.41
Prob > chi2 = 0.0000
Multivariate ProbitThis time we will analyze the same data using the -mvprobit- (findit mvprobit) program. mvprobit can analyze models with one or more binary response variables but there is no reason to usw it with less than three response variables since probit and biprobit can handle the other cases.
use http://www.gseis.ucla.edu/courses/data/hsb2, clear
mvprobit (hw = read female)(hm = read female)(hs = read female), draw(15)
Multivariate probit (SML, # draws = 15) Number of obs = 200
Wald chi2(6) = 109.56
Log likelihood = -254.16818 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hw |
read | .0851814 .0129554 6.57 0.000 .0597893 .1105734
female | .6073341 .2282164 2.66 0.008 .1600382 1.05463
_cons | -5.63893 .7747692 -7.28 0.000 -7.15745 -4.120411
-------------+----------------------------------------------------------------
hm |
read | .0895187 .0130687 6.85 0.000 .0639046 .1151328
female | -.0411219 .2204623 -0.19 0.852 -.4732202 .3909763
_cons | -5.573861 .7602042 -7.33 0.000 -7.063834 -4.083889
-------------+----------------------------------------------------------------
hs |
read | .0779078 .0115966 6.72 0.000 .055179 .1006367
female | -.4385348 .2064562 -2.12 0.034 -.8431815 -.0338881
_cons | -4.378325 .6407917 -6.83 0.000 -5.634254 -3.122396
-------------+----------------------------------------------------------------
/atrho21 | .5840931 .1596715 3.66 0.000 .2711428 .8970434
-------------+----------------------------------------------------------------
/atrho31 | .1544151 .1388431 1.11 0.266 -.1177123 .4265426
-------------+----------------------------------------------------------------
/atrho32 | .3668846 .1474433 2.49 0.013 .0779011 .6558681
-------------+----------------------------------------------------------------
rho21 | .525634 .1155557 4.55 0.000 .2646879 .7148552
-------------+----------------------------------------------------------------
rho31 | .1531994 .1355844 1.13 0.259 -.1171717 .4024279
-------------+----------------------------------------------------------------
rho32 | .3512637 .1292508 2.72 0.007 .0777439 .5756071
------------------------------------------------------------------------------
Likelihood ratio test of rho21 = rho31 = rho32 = 0:
chi2(3) = 22.0798 Prob > chi2 = 0.0001
test female
( 1) [hw]female = 0
( 2) [hm]female = 0
( 3) [hs]female = 0
chi2( 3) = 12.94
Prob > chi2 = 0.0048
test read
( 1) [hw]read = 0
( 2) [hm]read = 0
( 3) [hs]read = 0
chi2( 3) = 103.32
Prob > chi2 = 0.0000
Categorical Data Analysis Course
Phil Ender