Note: This chapter uses a suite of commands, called spost, written by J. Scott Long and Jeremy Freese. The commands must be downloaded prior to their use, and this can be done by typing search spost in the Stata command line (see How can I use the search command to search for programs and get additional help? for more information about using search).
Table 5.1, page 126.
use https://stats.idre.ucla.edu/stat/stata/examples/long/ordwarm2, clear
describe
Contains data from https://stats.idre.ucla.edu/stat/stata/examples/long/ordwarm2.dta
obs: 2,293 77 & 89 General Social Survey
vars: 10 3 May 2001 09:54
size: 32,102 (96.9% of memory free) (_dta has notes)
-------------------------------------------------------------------------------
storage display value
variable name type format label variable label
-------------------------------------------------------------------------------
warm byte %10.0g SD2SA Mom can have warm relations
with child
yr89 byte %10.0g yrlbl Survey year: 1=1989 0=1977
male byte %10.0g sexlbl Gender: 1=male 0=female
white byte %10.0g racelbl Race: 1=white 0=not white
age byte %10.0g Age in years
ed byte %10.0g Years of education
prst byte %10.0g Occupational prestige
warmlt2 byte %10.0g SD 1=SD; 0=D,A,SA
warmlt3 byte %10.0g SDD 1=SD,D; 0=A,SA
warmlt4 byte %10.0g SDDA 1=SD,D,A; 0=SA
-------------------------------------------------------------------------------
Sorted by: warm
sum warm yr89 male white age ed prst
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
warm | 2293 2.607501 .9282156 1 4
yr89 | 2293 .3986044 .4897178 0 1
male | 2293 .4648932 .4988748 0 1
white | 2293 .8765809 .3289894 0 1
age | 2293 44.93546 16.77903 18 89
-------------+--------------------------------------------------------
ed | 2293 12.21805 3.160827 0 20
prst | 2293 39.58526 14.49226 12 82
Table 5.2, page 127.
*lrm
reg warm yr89 male white age ed prst
Source | SS df MS Number of obs = 2293
-------------+------------------------------ F( 6, 2286) = 52.82
Model | 240.438 6 40.073 Prob > F = 0.0000
Residual | 1734.31298 2286 .758667096 R-squared = 0.1218
-------------+------------------------------ Adj R-squared = 0.1195
Total | 1974.75098 2292 .861584198 Root MSE = .87101
------------------------------------------------------------------------------
warm | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .2624768 .0377971 6.94 0.000 .1883566 .3365969
male | -.3357608 .0366127 -9.17 0.000 -.4075583 -.2639632
white | -.1770232 .0559223 -3.17 0.002 -.2866869 -.0673596
age | -.0101114 .0011623 -8.70 0.000 -.0123907 -.007832
ed | .0312009 .0075313 4.14 0.000 .016432 .0459698
prst | .0026999 .0015574 1.73 0.083 -.0003542 .0057541
_cons | 2.780412 .1100734 25.26 0.000 2.564558 2.996266
------------------------------------------------------------------------------
NOTE: Further discussion of the calculation for the threshold can found at http://www.stata.com/support/faqs/stat/ologit_con.html .
*ordered probit, setting the threshold = 0
oprobit warm yr89 male white age ed prst
Iteration 0: log likelihood = -2995.7704
Iteration 1: log likelihood = -2848.7542
Iteration 2: log likelihood = -2848.611
Ordered probit estimates Number of obs = 2293
LR chi2(6) = 294.32
Prob > chi2 = 0.0000
Log likelihood = -2848.611 Pseudo R2 = 0.0491
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .3188147 .0468519 6.80 0.000 .2269867 .4106427
male | -.4170287 .0455459 -9.16 0.000 -.5062971 -.3277603
white | -.2265002 .0694773 -3.26 0.001 -.3626733 -.0903272
age | -.0122213 .0014427 -8.47 0.000 -.0150489 -.0093937
ed | .0387234 .0093241 4.15 0.000 .0204485 .0569982
prst | .003283 .001925 1.71 0.088 -.0004899 .0070559
-------------+----------------------------------------------------------------
_cut1 | -1.428578 .1387742 (Ancillary parameters)
_cut2 | -.3605589 .1369219
_cut3 | .7681637 .1370564
------------------------------------------------------------------------------
*constant = -_cut1
lincom _b[_cut2] - _b[_cut1]
( 1) - _cut1 + _cut2 = 0
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1.068019 .0347528 30.73 0.000 .9999052 1.136134
------------------------------------------------------------------------------
lincom _b[_cut3] - _b[_cut1]
( 1) - _cut1 + _cut3 = 0
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.196742 .0442095 49.69 0.000 2.110093 2.283391
------------------------------------------------------------------------------
*ordered probit, setting beta_0 = 0
oprobit warm yr89 male white age ed prst
Iteration 0: log likelihood = -2995.7704
Iteration 1: log likelihood = -2848.7542
Iteration 2: log likelihood = -2848.611
Ordered probit estimates Number of obs = 2293
LR chi2(6) = 294.32
Prob > chi2 = 0.0000
Log likelihood = -2848.611 Pseudo R2 = 0.0491
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .3188147 .0468519 6.80 0.000 .2269867 .4106427
male | -.4170287 .0455459 -9.16 0.000 -.5062971 -.3277603
white | -.2265002 .0694773 -3.26 0.001 -.3626733 -.0903272
age | -.0122213 .0014427 -8.47 0.000 -.0150489 -.0093937
ed | .0387234 .0093241 4.15 0.000 .0204485 .0569982
prst | .003283 .001925 1.71 0.088 -.0004899 .0070559
-------------+----------------------------------------------------------------
_cut1 | -1.428578 .1387742 (Ancillary parameters)
_cut2 | -.3605589 .1369219
_cut3 | .7681637 .1370564
------------------------------------------------------------------------------
*ordered logistic
ologit warm yr89 male white age ed prst
Iteration 0: log likelihood = -2995.7704
Iteration 1: log likelihood = -2846.4532
Iteration 2: log likelihood = -2844.9142
Iteration 3: log likelihood = -2844.9123
Ordered logit estimates Number of obs = 2293
LR chi2(6) = 301.72
Prob > chi2 = 0.0000
Log likelihood = -2844.9123 Pseudo R2 = 0.0504
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .5239025 .0798988 6.56 0.000 .3673037 .6805013
male | -.7332997 .0784827 -9.34 0.000 -.8871229 -.5794766
white | -.3911595 .1183808 -3.30 0.001 -.6231815 -.1591374
age | -.0216655 .0024683 -8.78 0.000 -.0265032 -.0168278
ed | .0671728 .015975 4.20 0.000 .0358624 .0984831
prst | .0060727 .0032929 1.84 0.065 -.0003813 .0125267
-------------+----------------------------------------------------------------
_cut1 | -2.465362 .2389126 (Ancillary parameters)
_cut2 | -.630904 .2333155
_cut3 | 1.261854 .2340179
------------------------------------------------------------------------------
Table 5.3, page 129.
quietly ologit warm yr89 male white age ed prst
listcoef, std
ologit (N=2293): Unstandardized and Standardized Estimates
Observed SD: .9282156
Latent SD: 1.9410634
-------------------------------------------------------------------------------
warm | b z P>|z| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
yr89 | 0.52390 6.557 0.000 0.2566 0.2699 0.1322 0.4897
male | -0.73330 -9.343 0.000 -0.3658 -0.3778 -0.1885 0.4989
white | -0.39116 -3.304 0.001 -0.1287 -0.2015 -0.0663 0.3290
age | -0.02167 -8.778 0.000 -0.3635 -0.0112 -0.1873 16.7790
ed | 0.06717 4.205 0.000 0.2123 0.0346 0.1094 3.1608
prst | 0.00607 1.844 0.065 0.0880 0.0031 0.0453 14.4923
-------------------------------------------------------------------------------
quietly oprobit warm yr89 male white age ed prst
listcoef, std
oprobit (N=2293): Unstandardized and Standardized Estimates
Observed SD: .9282156
Latent SD: 1.0760449
-------------------------------------------------------------------------------
warm | b z P>|z| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
yr89 | 0.31881 6.805 0.000 0.1561 0.2963 0.1451 0.4897
male | -0.41703 -9.156 0.000 -0.2080 -0.3876 -0.1933 0.4989
white | -0.22650 -3.260 0.001 -0.0745 -0.2105 -0.0693 0.3290
age | -0.01222 -8.471 0.000 -0.2051 -0.0114 -0.1906 16.7790
ed | 0.03872 4.153 0.000 0.1224 0.0360 0.1137 3.1608
prst | 0.00328 1.705 0.088 0.0476 0.0031 0.0442 14.4923
-------------------------------------------------------------------------------
Table 5.4, page 131.
ologit warm yr89 male white age ed prst
Iteration 0: log likelihood = -2995.7704
Iteration 1: log likelihood = -2846.4532
Iteration 2: log likelihood = -2844.9142
Iteration 3: log likelihood = -2844.9123
Ordered logit estimates Number of obs = 2293
LR chi2(6) = 301.72
Prob > chi2 = 0.0000
Log likelihood = -2844.9123 Pseudo R2 = 0.0504
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .5239025 .0798988 6.56 0.000 .3673037 .6805013
male | -.7332997 .0784827 -9.34 0.000 -.8871229 -.5794766
white | -.3911595 .1183808 -3.30 0.001 -.6231815 -.1591374
age | -.0216655 .0024683 -8.78 0.000 -.0265032 -.0168278
ed | .0671728 .015975 4.20 0.000 .0358624 .0984831
prst | .0060727 .0032929 1.84 0.065 -.0003813 .0125267
-------------+----------------------------------------------------------------
_cut1 | -2.465362 .2389126 (Ancillary parameters)
_cut2 | -.630904 .2333155
_cut3 | 1.261854 .2340179
------------------------------------------------------------------------------
predict sd d a sa
(option p assumed; predicted probabilities)
tabstat sd d a sa, stats(min mean max range)
stats | sd d a sa
---------+----------------------------------------
min | .0153572 .073616 .1279493 .0268523
mean | .1293539 .3152335 .3738817 .1815308
max | .4657959 .4289543 .4407727 .6067042
range | .4504387 .3553383 .3128235 .5798519
--------------------------------------------------
Figure 5.3, page 132.
quietly ologit warm yr89 male white age ed prst
prgen age, from(20) to(80) x(male = 0 yr89 = 1) ncases(7) generate(w89)
ologit: Predicted values as age varies from 20 to 80.
yr89 male white age ed prst
x= 1 0 .8765809 44.935456 12.218055 39.585259
label var w89p1 "SD"
label var w89p2 "D"
label var w89p3 "A"
label var w89p4 "SA"
label var w89s1 "SD"
label var w89s2 "SD & D"
label var w89s3 "SD, D & A"
Panel A: Predicted Probabilities
graph twoway (scatter w89p1 w89p2 w89p3 w89p4 w89x, msymbol(Oh Dh Sh Th) c(l l l l) xtitle("Age") ///
ytitle("Predicted Probability") xlabel(20(20)80) ylabel(0 .25 .50 ) )
Panel B: Cumulative Probabilities
graph twoway (scatter w89s1 w89s2 w89s3 w89x, msymbol(Oh Dh Sh) c(l l l) xtitle("Age") ///
ytitle("Cumulative Probability") xlabel(20(20)80) ylabel(0(.25)1) )
Table 5.5, page 134.
quietly ologit warm yr89 male white age ed prst
prtab yr89 male, novarlbl
ologit: Predicted probabilities for warm
Predicted probability of outcome 1 (SD)
--------------------------
| male
yr89 | Women Men
----------+---------------
1977 | 0.0989 0.1859
1989 | 0.0610 0.1191
--------------------------
Predicted probability of outcome 2 (D)
--------------------------
| male
yr89 | Women Men
----------+---------------
1977 | 0.3083 0.4026
1989 | 0.2282 0.3394
--------------------------
Predicted probability of outcome 3 (A)
--------------------------
| male
yr89 | Women Men
----------+---------------
1977 | 0.4129 0.3162
1989 | 0.4406 0.3904
--------------------------
Predicted probability of outcome 4 (SA)
--------------------------
| male
yr89 | Women Men
----------+---------------
1977 | 0.1799 0.0953
1989 | 0.2703 0.1510
--------------------------
yr89 male white age ed prst
x= .39860445 .46489315 .8765809 44.935456 12.218055 39.585259
NOTE: The output from prtab needs to be rearranged to match Table 5.5 exactly.
Table 5.6, page 135.
quietly ologit warm yr89 male white age ed prst
prchange age ed prst, x(male = 0 yr89 = 1) rest(mean)
ologit: Changes in Predicted Probabilities for warm
age
Avg|Chg| SD D A SA
Min->Max .16441458 .10941909 .21941006 -.05462247 -.27420671
-+1/2 .00222661 .00124099 .00321223 -.0001803 -.00427291
-+sd/2 .0373125 .0208976 .05372739 -.00300205 -.07162295
MargEfct .00222662 .00124098 .00321226 -.00018032 -.00427292
ed
Avg|Chg| SD D A SA
Min->Max .14300264 -.09153163 -.19447364 .04167268 .2443326
-+1/2 .0069032 -.00384806 -.00995836 .00055891 .01324749
-+sd/2 .02181124 -.01217654 -.03144595 .00176239 .04186009
MargEfct .00690351 -.00384759 -.00995944 .00055906 .01324796
prst
Avg|Chg| SD D A SA
Min->Max .04278038 -.02352008 -.06204067 .00013945 .08542132
-+1/2 .00062411 -.00034784 -.00090037 .00005054 .00119767
-+sd/2 .00904405 -.00504204 -.01304607 .00073212 .01735598
MargEfct .00062411 -.00034784 -.00090038 .00005054 .00119767
SD D A SA
Pr(y|x) .06099996 .22815652 .44057754 .27026597
yr89 male white age ed prst
x= 1 0 .876581 44.9355 12.2181 39.5853
sd(x)= .489718 .498875 .328989 16.779 3.16083 14.4923
Table 5.7, page 137.
NOTE: You may have to increase the matrix size in order to run this model. Type help matsize for more information.
quietly ologit warm yr89 male white age ed prst
prchange
ologit: Changes in Predicted Probabilities for warm
yr89
Avg|Chg| SD D A SA
0->1 .06372773 -.04993673 -.07751873 .05391335 .0735421
male
Avg|Chg| SD D A SA
0->1 .08961766 .07461427 .10462105 -.08137083 -.09786447
white
Avg|Chg| SD D A SA
0->1 .04694162 .03452424 .05935898 -.03557652 -.05830672
age
Avg|Chg| SD D A SA
Min->Max .18319855 .18012119 .1862759 -.17905769 -.18733941
-+1/2 .00266841 .00214228 .00319454 -.00240716 -.00292964
-+sd/2 .0446563 .03602537 .05328724 -.0401054 -.0492072
MargEfct .00266844 .00214226 .00319461 -.00240723 -.00292964
ed
Avg|Chg| SD D A SA
Min->Max .16156666 -.15235534 -.17077798 .15631917 .16681415
-+1/2 .00827261 -.00664248 -.00990272 .0074617 .00908352
-+sd/2 .02612717 -.02101015 -.03124419 .02353376 .02872056
MargEfct .00827335 -.00664198 -.00990472 .0074635 .00908319
prst
Avg|Chg| SD D A SA
Min->Max .05186236 -.04070839 -.06301633 .04440692 .05931778
-+1/2 .00074795 -.00060046 -.00089544 .00067475 .00082116
-+sd/2 .01083777 -.00870322 -.01297233 .00977433 .0119012
MargEfct .00074795 -.00060046 -.00089543 .00067473 .00082116
SD D A SA
Pr(y|x) .11125716 .32816544 .39936733 .16121005
yr89 male white age ed prst
x= .398604 .464893 .876581 44.9355 12.2181 39.5853
sd(x)= .489718 .498875 .328989 16.779 3.16083 14.4923
Table 5.8, page 142.
NOTE: We do not know why the z-scores are slightly different from those shown in the text.
gen mle1 = (warm>1)
gen mle2 = (warm>2)
gen mle3 = (warm>3)
ologit warm yr89 male white age ed prst
Iteration 0: log likelihood = -2995.7704
Iteration 1: log likelihood = -2846.4532
Iteration 2: log likelihood = -2844.9142
Iteration 3: log likelihood = -2844.9123
Ordered logit estimates Number of obs = 2293
LR chi2(6) = 301.72
Prob > chi2 = 0.0000
Log likelihood = -2844.9123 Pseudo R2 = 0.0504
------------------------------------------------------------------------------
warm | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .5239025 .0798988 6.56 0.000 .3673037 .6805013
male | -.7332997 .0784827 -9.34 0.000 -.8871229 -.5794766
white | -.3911595 .1183808 -3.30 0.001 -.6231815 -.1591374
age | -.0216655 .0024683 -8.78 0.000 -.0265032 -.0168278
ed | .0671728 .015975 4.20 0.000 .0358624 .0984831
prst | .0060727 .0032929 1.84 0.065 -.0003813 .0125267
-------------+----------------------------------------------------------------
_cut1 | -2.465362 .2389126 (Ancillary parameters)
_cut2 | -.630904 .2333155
_cut3 | 1.261854 .2340179
------------------------------------------------------------------------------
logit mle1 yr89 male white age ed prst
Iteration 0: log likelihood = -883.91038
Iteration 1: log likelihood = -824.35787
Iteration 2: log likelihood = -819.6587
Iteration 3: log likelihood = -819.61993
Iteration 4: log likelihood = -819.61992
Logit estimates Number of obs = 2293
LR chi2(6) = 128.58
Prob > chi2 = 0.0000
Log likelihood = -819.61992 Pseudo R2 = 0.0727
------------------------------------------------------------------------------
mle1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .9647422 .1542064 6.26 0.000 .6625033 1.266981
male | -.3053643 .1291546 -2.36 0.018 -.5585025 -.052226
white | -.5526576 .2305396 -2.40 0.017 -1.004507 -.1008082
age | -.0164704 .0040571 -4.06 0.000 -.0244221 -.0085187
ed | .1047962 .0253348 4.14 0.000 .0551409 .1544516
prst | -.0014112 .0056702 -0.25 0.803 -.0125246 .0097023
_cons | 1.858405 .3958164 4.70 0.000 1.082619 2.63419
------------------------------------------------------------------------------
logit mle2 yr89 male white age ed prst
Iteration 0: log likelihood = -1575.4005
Iteration 1: log likelihood = -1450.7598
Iteration 2: log likelihood = -1449.7869
Iteration 3: log likelihood = -1449.7863
Logit estimates Number of obs = 2293
LR chi2(6) = 251.23
Prob > chi2 = 0.0000
Log likelihood = -1449.7863 Pseudo R2 = 0.0797
------------------------------------------------------------------------------
mle2 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .5654063 .0928433 6.09 0.000 .3834368 .7473757
male | -.6905423 .0898786 -7.68 0.000 -.8667012 -.5143834
white | -.3142708 .1405978 -2.24 0.025 -.5898374 -.0387042
age | -.0253345 .0028644 -8.84 0.000 -.0309486 -.0197203
ed | .0528527 .0184571 2.86 0.004 .0166774 .0890279
prst | .0095322 .0038184 2.50 0.013 .0020482 .0170162
_cons | .7303287 .269163 2.71 0.007 .202779 1.257878
------------------------------------------------------------------------------
logit mle3 yr89 male white age ed prst
Iteration 0: log likelihood = -1087.3382
Iteration 1: log likelihood = -1015.4742
Iteration 2: log likelihood = -1011.973
Iteration 3: log likelihood = -1011.9542
Iteration 4: log likelihood = -1011.9542
Logit estimates Number of obs = 2293
LR chi2(6) = 150.77
Prob > chi2 = 0.0000
Log likelihood = -1011.9542 Pseudo R2 = 0.0693
------------------------------------------------------------------------------
mle3 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yr89 | .3190732 .1140756 2.80 0.005 .0954891 .5426572
male | -1.083789 .1220668 -8.88 0.000 -1.323035 -.8445422
white | -.3929984 .1577582 -2.49 0.013 -.7021989 -.083798
age | -.0185905 .0037659 -4.94 0.000 -.0259715 -.0112096
ed | .0575547 .0253812 2.27 0.023 .0078085 .1073008
prst | .0055304 .0048413 1.14 0.253 -.0039584 .0150193
_cons | -1.024517 .3463123 -2.96 0.003 -1.703276 -.3457571
------------------------------------------------------------------------------
Table 5.9, page 144.
NOTE: The brant, detail command produces the same results as Table 5.8.
quietly ologit warm yr89 male white age ed prst
brant, detail
Estimated coefficients from j-1 binary regressions
y>1 y>2 y>3
yr89 .9647422 .56540626 .31907316
male -.30536425 -.69054232 -1.0837888
white -.55265759 -.31427081 -.39299842
age -.0164704 -.02533448 -.01859051
ed .10479624 .05285265 .05755466
prst -.00141118 .00953216 .00553043
_cons 1.8584045 .73032873 -1.0245168
Brant Test of Parallel Regression Assumption
Variable | chi2 p>chi2 df
-------------+--------------------------
All | 49.18 0.000 12
-------------+--------------------------
yr89 | 13.01 0.001 2
male | 22.24 0.000 2
white | 1.27 0.531 2
age | 7.38 0.025 2
ed | 4.31 0.116 2
prst | 4.33 0.115 2
----------------------------------------
A significant test statistic provides evidence that the parallel
regression assumption has been violated.