Section 9.1.1 McNemar Test.
The code below for creating the data set can be copied to the Stata Do-file Editor and be executed through the Do-file Editor.
clear
input r1 r2 count
0 0 794
0 1 150
1 0 86
1 1 570
end
symmetry r1 r2 [fw=count]
-------------------------------
| r2
r1 | 0 1 Total
----------+--------------------
0 | 794 150 944
1 | 86 570 656
|
Total | 880 720 1600
-------------------------------
chi2 df Prob>chi2
------------------------------------------------------------------------
Symmetry (asymptotic) | 17.36 1 0.0000
Marginal homogeneity (Stuart-Maxwell) | 17.36 1 0.0000
------------------------------------------------------------------------
di sqrt(r(chi2))
4.1660452
Section 9.1.2 Estimating Differences of Proportions
mcc r2 r1 [fw=count]
| Controls |
Cases | Exposed Unexposed | Total
-----------------+------------------------+----------
Exposed | 570 150 | 720
Unexposed | 86 794 | 880
-----------------+------------------------+----------
Total | 656 944 | 1600
McNemar's chi2(1) = 17.36 Prob > chi2 = 0.0000
Exact McNemar significance probability = 0.0000
Proportion with factor
Cases .45
Controls .41 [95% Conf. Interval]
--------- --------------------
difference .04 .0206589 .0593411
ratio 1.097561 1.050514 1.146715
rel. diff. .0677966 .0370011 .0985921
odds ratio 1.744186 1.329228 2.300979 (exact)
Section 9.2.2 A Logit Model for Matched-Pairs Data on page 231.
expand count
drop count
gen id = _n
reshape long r, i(id) j(m)
recode m 2=0
recode r 0 = 1 1=0
clogit r m, or group(id)
note: multiple positive outcomes within groups encountered.
note: 1364 groups (2728 obs) dropped due to all positive or
all negative outcomes.
Conditional (fixed-effects) logistic regression Number of obs = 472
LR chi2(1) = 17.58
Prob > chi2 = 0.0000
Log likelihood = -154.79514 Pseudo R2 = 0.0537
------------------------------------------------------------------------------
r | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m | 1.744186 .2359133 4.11 0.000 1.338018 2.273651
------------------------------------------------------------------------------
Section 9.2.3 Logistic Regression for Matched Case-Control Studies
The following code for creating a data set can be copied to Stata Do-file Editor and be executed within the Do-file Editor.
* TABLE 9.3
clear
input c1 c2 count
1 1 9
1 0 16
0 1 37
0 0 119
end
expand count
gen id = _n
reshape long c, i(id) j(m)
clogit c m, group(id)
note: multiple positive outcomes within groups encountered.
note: 128 groups (256 obs) dropped due to all positive or
all negative outcomes.
Conditional (fixed-effects) logistic regression Number of obs = 106
LR chi2(1) = 8.55
Prob > chi2 = 0.0034
Log likelihood = -32.460089 Pseudo R2 = 0.1164
------------------------------------------------------------------------------
c | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m | .8383292 .2992107 2.80 0.005 .251887 1.424771
------------------------------------------------------------------------------
clogit c m, group(id) or
note: multiple positive outcomes within groups encountered.
note: 128 groups (256 obs) dropped due to all positive or
all negative outcomes.
Conditional (fixed-effects) logistic regression Number of obs = 106
LR chi2(1) = 8.55
Prob > chi2 = 0.0034
Log likelihood = -32.460089 Pseudo R2 = 0.1164
------------------------------------------------------------------------------
c | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
m | 2.3125 .6919247 2.80 0.005 1.286451 4.156907
------------------------------------------------------------------------------
Section 9.3.2 Coffee Market Share Example. Test on symmetry models. The list command displays all the observations and we can see how the variable for symmetry is constructed. The other variable qs will be used later for quasi-independence models. We ran both the glm model and Stata’s symmetry command to show two ways in Stata to test on a symmetry model.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/coffee, clear
list
+---------------------------------------------+
| p1 p2 count qs symm |
|---------------------------------------------|
1. | High Point High Point 93 1 1 |
2. | High Point Taster's 17 6 2 |
3. | High Point Sanka 44 6 3 |
4. | High Point Nescafe 7 6 4 |
5. | High Point Brim 10 6 5 |
|---------------------------------------------|
6. | Taster's High Point 9 6 2 |
7. | Taster's Taster's 46 2 6 |
8. | Taster's Sanka 11 6 7 |
9. | Taster's Nescafe 0 6 8 |
10. | Taster's Brim 9 6 9 |
|---------------------------------------------|
11. | Sanka High Point 17 6 3 |
12. | Sanka Taster's 11 6 7 |
13. | Sanka Sanka 155 3 10 |
14. | Sanka Nescafe 9 6 11 |
15. | Sanka Brim 12 6 12 |
|---------------------------------------------|
16. | Nescafe High Point 6 6 4 |
17. | Nescafe Taster's 4 6 8 |
18. | Nescafe Sanka 9 6 11 |
19. | Nescafe Nescafe 15 4 13 |
20. | Nescafe Brim 2 6 14 |
|---------------------------------------------|
21. | Brim High Point 10 6 5 |
22. | Brim Taster's 4 6 9 |
23. | Brim Sanka 12 6 12 |
24. | Brim Nescafe 2 6 14 |
25. | Brim Brim 27 5 15 |
+---------------------------------------------+
xi: glm count i.symm, fam(poi) nolog
i.symm _Isymm_1-15 (naturally coded; _Isymm_1 omitted)
Generalized linear models No. of obs = 25
Optimization : ML: Newton-Raphson Residual df = 10
Scale parameter = 1
Deviance = 22.47293283 (1/df) Deviance = 2.247293
Pearson = 20.41235813 (1/df) Pearson = 2.041236
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -63.50502298 AIC = 6.280402
BIC = -9.715825421
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isymm_2 | -1.96765 .2218428 -8.87 0.000 -2.402454 -1.532846
_Isymm_3 | -1.114873 .1647608 -6.77 0.000 -1.437798 -.7919475
_Isymm_4 | -2.660797 .2961009 -8.99 0.000 -3.241144 -2.08045
_Isymm_5 | -2.230014 .2464806 -9.05 0.000 -2.713108 -1.746921
_Isymm_6 | -.7039581 .1802549 -3.91 0.000 -1.057251 -.350665
_Isymm_7 | -2.134704 .2370806 -9.00 0.000 -2.599374 -1.670035
_Isymm_8 | -3.839452 .5106395 -7.52 0.000 -4.840287 -2.838617
_Isymm_9 | -2.660797 .2961009 -8.99 0.000 -3.241144 -2.08045
_Isymm_10 | .5108256 .1311652 3.89 0.000 .2537466 .7679046
_Isymm_11 | -2.335375 .2575039 -9.07 0.000 -2.840073 -1.830677
_Isymm_12 | -2.047693 .2289527 -8.94 0.000 -2.496432 -1.598954
_Isymm_13 | -1.824549 .2782433 -6.56 0.000 -2.369896 -1.279202
_Isymm_14 | -3.839452 .5106395 -7.52 0.000 -4.840287 -2.838617
_Isymm_15 | -1.236763 .2186086 -5.66 0.000 -1.665228 -.8082976
_cons | 4.532599 .1036952 43.71 0.000 4.329361 4.735838
------------------------------------------------------------------------------
symmetry p1 p2 [fw=count], notable
chi2 df Prob>chi2
------------------------------------------------------------------------
Symmetry (asymptotic) | 20.41 10 0.0256
Marginal homogeneity (Stuart-Maxwell) | 12.29 4 0.0153
------------------------------------------------------------------------
Section 9.3.3 Quasi Symmetry on page 236.
xi: glm count i.p1 i.p2 i.symm, fam(poi) nolog
i.p1 _Ip1_1-5 (naturally coded; _Ip1_1 omitted)
i.p2 _Ip2_1-5 (naturally coded; _Ip2_1 omitted)
i.symm _Isymm_1-15 (naturally coded; _Isymm_1 omitted)
note: _Isymm_6 dropped due to collinearity
note: _Isymm_10 dropped due to collinearity
note: _Isymm_13 dropped due to collinearity
note: _Isymm_15 dropped due to collinearity
Generalized linear models No. of obs = 25
Optimization : ML: Newton-Raphson Residual df = 6
Scale parameter = 1
Deviance = 9.974046925 (1/df) Deviance = 1.662341
Pearson = 8.530328477 (1/df) Pearson = 1.421721
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -57.25558002 AIC = 6.100446
BIC = -9.339208024
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ip1_2 | -.6517011 .1674134 -3.89 0.000 -.9798254 -.3235769
_Ip1_3 | -.0989566 .127788 -0.77 0.439 -.3494166 .1515033
_Ip1_4 | -1.058937 .2238647 -4.73 0.000 -1.497704 -.62017
_Ip1_5 | -.9161012 .183047 -5.00 0.000 -1.274867 -.5573356
_Ip2_2 | -.052257 .1674134 -0.31 0.755 -.3803812 .2758673
_Ip2_3 | .6097823 .127788 4.77 0.000 .3593223 .8602422
_Ip2_4 | -.7656124 .2238647 -3.42 0.001 -1.204379 -.3268456
_Ip2_5 | -.3206615 .183047 -1.75 0.080 -.6794271 .0381041
_Isymm_2 | -1.659931 .2197059 -7.56 0.000 -2.090547 -1.229315
_Isymm_3 | -1.431803 .1486171 -9.63 0.000 -1.723087 -1.140519
_Isymm_4 | -1.759239 .3113361 -5.65 0.000 -2.369447 -1.149032
_Isymm_5 | -1.655312 .2524893 -6.56 0.000 -2.150182 -1.160442
_Isymm_7 | -2.03963 .2292631 -8.90 0.000 -2.488978 -1.590283
_Isymm_8 | -2.586867 .5225077 -4.95 0.000 -3.610963 -1.562771
_Isymm_9 | -1.690439 .3026834 -5.58 0.000 -2.283687 -1.09719
_Isymm_11 | -1.699931 .2739694 -6.20 0.000 -2.236901 -1.162961
_Isymm_12 | -1.686328 .2293554 -7.35 0.000 -2.135856 -1.2368
_Isymm_14 | -2.320162 .5261484 -4.41 0.000 -3.351394 -1.288931
_cons | 4.532599 .1036952 43.71 0.000 4.329361 4.735838
------------------------------------------------------------------------------
predict p
(option mu assumed; predicted mean count)
table p1 p2, contents(sum count sum p)
-----------------------------------------------------------------------
| p2
p1 | High Point Taster's Sanka Nescafe Brim
-----------+-----------------------------------------------------------
High Point | 93 17 44 7 10
| 93 16.78376 40.87747 7.446527 12.89225
|
Taster's | 9 46 11 0 9
| 9.216243 46 11.60052 1.696249 6.486985
|
Sanka | 17 11 155 9 12
| 20.12253 10.39948 155 7.157062 11.32093
|
Nescafe | 6 4 9 15 2
| 5.553473 2.303751 10.84294 15 2.299838
|
Brim | 10 4 12 2 27
| 7.107754 6.513015 12.67907 1.700162 27
-----------------------------------------------------------------------
Section 9.3.5 Premarital and Extramarital Sex Example on page 238.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/marital, clear
xi: glm count i.symm, fam(poi) nolog /*symmetry*/
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 6
Scale parameter = 1
Deviance = 402.2028677 (1/df) Deviance = 67.03381
Pearson = 297.610989 (1/df) Pearson = 49.60183
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -229.8458217 AIC = 29.98073
BIC = 385.5673354
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isymm_2 | -2.107612 .1884566 -11.18 0.000 -2.47698 -1.738244
_Isymm_3 | -1.232144 .1372924 -8.97 0.000 -1.501232 -.9630555
_Isymm_4 | -.8266786 .1219875 -6.78 0.000 -1.06577 -.5875874
_Isymm_5 | -3.583519 .5068969 -7.07 0.000 -4.577019 -2.590019
_Isymm_6 | -2.890372 .2635231 -10.97 0.000 -3.406868 -2.373876
_Isymm_7 | -2.295665 .2035367 -11.28 0.000 -2.694589 -1.89674
_Isymm_8 | -3.178054 .4166667 -7.63 0.000 -3.994705 -2.361402
_Isymm_9 | -2.404864 .2130868 -11.29 0.000 -2.822506 -1.987221
_Isymm_10 | -3.360375 .4549115 -7.39 0.000 -4.251985 -2.468765
_cons | 4.969813 .0833333 59.64 0.000 4.806483 5.133144
------------------------------------------------------------------------------
xi: glm count i.p1 i.p2 i.symm, fam(poi) nolog /*quasi-symmetry*/
i.p1 _Ip1_1-4 (naturally coded; _Ip1_1 omitted)
i.p2 _Ip2_1-4 (naturally coded; _Ip2_1 omitted)
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
note: _Isymm_5 dropped due to collinearity
note: _Isymm_8 dropped due to collinearity
note: _Isymm_10 dropped due to collinearity
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 3
Scale parameter = 1
Deviance = 1.364550248 (1/df) Deviance = .4548501
Pearson = .8683363489 (1/df) Pearson = .2894454
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -29.42666302 AIC = 5.303333
BIC = -6.953215918
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ip1_2 | -.2652152 .4479877 -0.59 0.554 -1.143255 .6128245
_Ip1_3 | 1.080925 .5104393 2.12 0.034 .0804828 2.081368
_Ip1_4 | 2.667576 .7041824 3.79 0.000 1.287403 4.047748
_Ip2_2 | -3.318304 .4479877 -7.41 0.000 -4.196343 -2.440264
_Ip2_3 | -4.258979 .5104393 -8.34 0.000 -5.259422 -3.258537
_Ip2_4 | -6.027951 .7041824 -8.56 0.000 -7.408123 -4.647779
_Isymm_2 | -1.195382 .4536139 -2.64 0.008 -2.084449 -.3063153
_Isymm_3 | -1.624707 .5180026 -3.14 0.002 -2.639973 -.6094404
_Isymm_4 | -2.801274 .709586 -3.95 0.000 -4.192037 -1.410511
_Isymm_6 | -.0566003 .5112585 -0.11 0.912 -1.058649 .945448
_Isymm_7 | -.9553273 .7136538 -1.34 0.181 -2.354063 .4434084
_Isymm_9 | -.154606 .5967923 -0.26 0.796 -1.324297 1.015085
_cons | 4.969813 .0833333 59.64 0.000 4.806483 5.133144
------------------------------------------------------------------------------
xi: glm count p1 i.symm, fam(poi) nolog /*ordinal quasi-symmetry*/
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 5
Scale parameter = 1
Deviance = 2.097209206 (1/df) Deviance = .4194418
Pearson = 2.084385929 (1/df) Pearson = .4168772
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -29.7929925 AIC = 5.099124
BIC = -11.7657344
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p1 | 2.856564 .4205179 6.79 0.000 2.032364 3.680764
_Isymm_2 | -4.326905 .4400612 -9.83 0.000 -5.189409 -3.4644
_Isymm_3 | -6.255421 .8494362 -7.36 0.000 -7.920286 -4.590557
_Isymm_4 | -8.703413 1.2672 -6.87 0.000 -11.18708 -6.219747
_Isymm_5 | -6.440083 .6586196 -9.78 0.000 -7.730954 -5.149212
_Isymm_6 | -7.966228 .8595749 -9.27 0.000 -9.650964 -6.281492
_Isymm_7 | -10.17551 1.275135 -7.98 0.000 -12.67472 -7.676288
_Isymm_8 | -8.891182 .9385907 -9.47 0.000 -10.73079 -7.051578
_Isymm_9 | -10.33728 1.256896 -8.22 0.000 -12.80076 -7.873813
_Isymm_10 | -11.93007 1.341068 -8.90 0.000 -14.55851 -9.301623
_cons | 2.113249 .4286954 4.93 0.000 1.273022 2.953477
------------------------------------------------------------------------------
predict p
(option mu assumed; predicted mean count)
format p %5.2f
table p1 p2, c(mean count mean p)
------------------------------------------
| p2
p1 | 1 2 3 4
----------+-------------------------------
1 | 144 2 0 0
| 144.00 1.90 0.28 0.02
|
2 | 33 4 2 0
| 33.10 4.00 0.87 0.10
|
3 | 84 14 6 1
| 83.72 15.13 6.00 1.41
|
4 | 126 29 25 5
| 125.98 28.90 24.59 5.00
------------------------------------------
Section 9.4.1 Testing Marginal Homogeneity on page 239.
The fitstat command needs to be downloaded prior to its use, which can be done by typing search fitstat in the command line (see How can I use the search command to search for programs and get additional help? for more information about using search).
use https://stats.idre.ucla.edu/stat/stata/examples/icda/coffee, clear
quietly xi: poisson count i.p1 i.p2 i.symm
fitstat, saving(m0)
Measures of Fit for poisson of count
Log-Lik Intercept Only: -436.541 Log-Lik Full Model: -57.256
D(6): 114.511 LR(18): 758.570
Prob > LR: 0.000
McFadden's R2: 0.869 McFadden's Adj R2: 0.825
Maximum Likelihood R2: 1.000 Cragg & Uhler's R2: 1.000
AIC: 6.100 AIC*n: 152.511
BIC: 95.198 BIC': -700.631
(Indices saved in matrix fs_m0)
quietly xi: poisson count i.symm
fitstat, using(m0)
Measures of Fit for poisson of count
Current Saved Difference
Model: poisson poisson
N: 25 25 0
Log-Lik Intercept Only: -436.541 -436.541 0.000
Log-Lik Full Model: -63.505 -57.256 -6.249
D: 127.010(10) 114.511(6) 12.499(4)
LR: 746.071(14) 758.570(18) 12.499(4)
Prob > LR: 0.000 0.000 0.014
McFadden's R2: 0.855 0.869 -0.014
McFadden's Adj R2: 0.820 0.825 -0.005
Maximum Likelihood R2: 1.000 1.000 -0.000
Cragg & Uhler's R2: 1.000 1.000 -0.000
AIC: 6.280 6.100 0.180
AIC*n: 157.010 152.511 4.499
BIC: 94.821 95.198 -0.377
BIC': -701.007 -700.631 -0.377
Difference of 0.377 in BIC' provides weak support for current model.
Note: p-value for difference in LR is only valid if models are nested.
tab p1 p2 [fw=count], row col
+-------------------+
| Key |
|-------------------|
| frequency |
| row percentage |
| column percentage |
+-------------------+
| p2
p1 | High Poin Taster's Sanka Nescafe Brim | Total
-----------+-------------------------------------------------------+----------
High Point | 93 17 44 7 10 | 171
| 54.39 9.94 25.73 4.09 5.85 | 100.00
| 68.89 20.73 19.05 21.21 16.67 | 31.61
-----------+-------------------------------------------------------+----------
Taster's | 9 46 11 0 9 | 75
| 12.00 61.33 14.67 0.00 12.00 | 100.00
| 6.67 56.10 4.76 0.00 15.00 | 13.86
-----------+-------------------------------------------------------+----------
Sanka | 17 11 155 9 12 | 204
| 8.33 5.39 75.98 4.41 5.88 | 100.00
| 12.59 13.41 67.10 27.27 20.00 | 37.71
-----------+-------------------------------------------------------+----------
Nescafe | 6 4 9 15 2 | 36
| 16.67 11.11 25.00 41.67 5.56 | 100.00
| 4.44 4.88 3.90 45.45 3.33 | 6.65
-----------+-------------------------------------------------------+----------
Brim | 10 4 12 2 27 | 55
| 18.18 7.27 21.82 3.64 49.09 | 100.00
| 7.41 4.88 5.19 6.06 45.00 | 10.17
-----------+-------------------------------------------------------+----------
Total | 135 82 231 33 60 | 541
| 24.95 15.16 42.70 6.10 11.09 | 100.00
| 100.00 100.00 100.00 100.00 100.00 | 100.00
gen p1hi = (p1==1)
gen p2hi = (p2 ==1)
mcc p1hi p2hi [fw=count]
| Controls |
Cases | Exposed Unexposed | Total
-----------------+------------------------+----------
Exposed | 93 78 | 171
Unexposed | 42 328 | 370
-----------------+------------------------+----------
Total | 135 406 | 541
McNemar's chi2(1) = 10.80 Prob > chi2 = 0.0010
Exact McNemar significance probability = 0.0013
Proportion with factor
Cases .3160813
Controls .2495379 [95% Conf. Interval]
--------- --------------------
difference .0665434 .0254068 .1076801
ratio 1.266667 1.099745 1.458924
rel. diff. .08867 .0381863 .1391536
odds ratio 1.857143 1.260425 2.770706 (exact)
di sqrt(r(chi2))
3.2863353
Section 9.4.2 Marginal Homogeneity and Ordered Categories on page 241.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/marital, clear
xi: poisson count p1 i.symm /*ordinal quasi-symmetry*/
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
Poisson regression Number of obs = 16
LR chi2(10) = 886.28
Prob > chi2 = 0.0000
Log likelihood = -29.792992 Pseudo R2 = 0.9370
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p1 | 2.856564 .420518 6.79 0.000 2.032364 3.680764
_Isymm_2 | -4.326905 .4400613 -9.83 0.000 -5.189409 -3.4644
_Isymm_3 | -6.255422 .8494362 -7.36 0.000 -7.920286 -4.590557
_Isymm_4 | -8.703413 1.2672 -6.87 0.000 -11.18708 -6.219748
_Isymm_5 | -6.440083 .6586196 -9.78 0.000 -7.730954 -5.149212
_Isymm_6 | -7.966228 .8595749 -9.27 0.000 -9.650964 -6.281492
_Isymm_7 | -10.17551 1.275135 -7.98 0.000 -12.67472 -7.676289
_Isymm_8 | -8.891182 .9385907 -9.47 0.000 -10.73079 -7.051578
_Isymm_9 | -10.33728 1.256896 -8.22 0.000 -12.80076 -7.873813
_Isymm_10 | -11.93007 1.341068 -8.90 0.000 -14.55851 -9.301623
_cons | 2.113249 .4286955 4.93 0.000 1.273022 2.953477
------------------------------------------------------------------------------
fitstat, saving(moqs)
Measures of Fit for poisson of count
Log-Lik Intercept Only: -472.933 Log-Lik Full Model: -29.793
D(5): 59.586 LR(10): 886.281
Prob > LR: 0.000
McFadden's R2: 0.937 McFadden's Adj R2: 0.914
Maximum Likelihood R2: 1.000 Cragg & Uhler's R2: 1.000
AIC: 5.099 AIC*n: 81.586
BIC: 45.723 BIC': -858.555
(Indices saved in matrix fs_moqs)
xi: poisson count i.symm /*symmetry*/
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
Poisson regression Number of obs = 16
LR chi2(9) = 486.17
Prob > chi2 = 0.0000
Log likelihood = -229.84582 Pseudo R2 = 0.5140
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isymm_2 | -2.107612 .1884566 -11.18 0.000 -2.47698 -1.738244
_Isymm_3 | -1.232144 .1372924 -8.97 0.000 -1.501232 -.9630555
_Isymm_4 | -.8266786 .1219875 -6.78 0.000 -1.06577 -.5875874
_Isymm_5 | -3.583519 .5068969 -7.07 0.000 -4.577019 -2.590019
_Isymm_6 | -2.890372 .2635231 -10.97 0.000 -3.406868 -2.373876
_Isymm_7 | -2.295665 .2035367 -11.28 0.000 -2.694589 -1.89674
_Isymm_8 | -3.178054 .4166667 -7.63 0.000 -3.994705 -2.361402
_Isymm_9 | -2.404864 .2130868 -11.29 0.000 -2.822506 -1.987221
_Isymm_10 | -3.360375 .4549115 -7.39 0.000 -4.251985 -2.468765
_cons | 4.969813 .0833333 59.64 0.000 4.806483 5.133144
------------------------------------------------------------------------------
fitstat, using(moqs)
Measures of Fit for poisson of count
Current Saved Difference
Model: poisson poisson
N: 16 16 0
Log-Lik Intercept Only: -472.933 -472.933 0.000
Log-Lik Full Model: -229.846 -29.793 -200.053
D: 459.692(6) 59.586(5) 400.106(1)
LR: 486.175(9) 886.281(10) 400.106(1)
Prob > LR: 0.000 0.000 0.000
McFadden's R2: 0.514 0.937 -0.423
McFadden's Adj R2: 0.493 0.914 -0.421
Maximum Likelihood R2: 1.000 1.000 -0.000
Cragg & Uhler's R2: 1.000 1.000 -0.000
AIC: 29.981 5.099 24.882
AIC*n: 479.692 81.586 398.106
BIC: 443.056 45.723 397.333
BIC': -461.222 -858.555 397.333
Difference of 397.333 in BIC' provides very strong support for saved model.
Note: p-value for difference in LR is only valid if models are nested.
xi: poisson count p1 i.symm /*ordinal quasi-symmetry*/
Poisson regression Number of obs = 16
LR chi2(10) = 886.28
Prob > chi2 = 0.0000
Log likelihood = -29.792992 Pseudo R2 = 0.9370
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
p1 | 2.856564 .420518 6.79 0.000 2.032364 3.680764
_Isymm_2 | -4.326905 .4400613 -9.83 0.000 -5.189409 -3.4644
_Isymm_3 | -6.255422 .8494362 -7.36 0.000 -7.920286 -4.590557
_Isymm_4 | -8.703413 1.2672 -6.87 0.000 -11.18708 -6.219748
_Isymm_5 | -6.440083 .6586196 -9.78 0.000 -7.730954 -5.149212
_Isymm_6 | -7.966228 .8595749 -9.27 0.000 -9.650964 -6.281492
_Isymm_7 | -10.17551 1.275135 -7.98 0.000 -12.67472 -7.676289
_Isymm_8 | -8.891182 .9385907 -9.47 0.000 -10.73079 -7.051578
_Isymm_9 | -10.33728 1.256896 -8.22 0.000 -12.80076 -7.873813
_Isymm_10 | -11.93007 1.341068 -8.90 0.000 -14.55851 -9.301623
_cons | 2.113249 .4286955 4.93 0.000 1.273022 2.953477
------------------------------------------------------------------------------
test p1
( 1) [count]p1 = 0
chi2( 1) = 46.14
Prob > chi2 = 0.0000
Section 9.4.3 A Proportional Odds Comparison of Margins on page 241-242.
clear
input score below above trials
1 33 2 35
1 14 2 16
1 25 1 26
2 84 0 84
2 29 0 29
3 126 0 126
end
glm above [fw=score], fam(bin trials)
Generalized linear models No. of obs = 10
Optimization : ML: Newton-Raphson Residual df = 9
Scale parameter = 1
Deviance = 23.23829262 (1/df) Deviance = 2.582033
Pearson = 50.22291971 (1/df) Pearson = 5.580324
Variance function: V(u) = u*(1-u/trials) [Binomial]
Link function : g(u) = ln(u/(trials-u)) [Logit]
Standard errors : OIM
Log likelihood = -15.11807183 AIC = 3.223614
BIC = 2.515026785
------------------------------------------------------------------------------
above | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons | -4.906755 .4488644 -10.93 0.000 -5.786513 -4.026997
------------------------------------------------------------------------------
di exp(-4.906755)
.00739645
Section 9.5.1 Quasi Independence and Table 9.7 on page 242.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/carcinoma, clear
xi: glm count i.px i.py, fam(poi)
i.px _Ipx_1-4 (naturally coded; _Ipx_1 omitted)
i.py _Ipy_1-4 (naturally coded; _Ipy_1 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 9
Scale parameter = 1
Deviance = 117.9568605 (1/df) Deviance = 13.10632
Pearson = 120.2634516 (1/df) Pearson = 13.36261
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -79.38776817 AIC = 10.79847
BIC = 93.00356204
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ipx_2 | -4.07e-08 .2773501 -0.00 1.000 -.5435962 .5435962
_Ipx_3 | .3794896 .2545139 1.49 0.136 -.1193485 .8783277
_Ipx_4 | .0741079 .2723524 0.27 0.786 -.4596929 .6079088
_Ipy_2 | -.8109302 .3469443 -2.34 0.019 -1.490929 -.1309318
_Ipy_3 | .9382696 .2270017 4.13 0.000 .4933544 1.383185
_Ipy_4 | -.9932518 .3701851 -2.68 0.007 -1.718801 -.2677022
_cons | 1.783249 .2588899 6.89 0.000 1.275834 2.290664
------------------------------------------------------------------------------
The tabchi command needs to be downloaded prior to its use, which can be done by typing search tabchi in the command line (see How can I use the search command to search for programs and get additional help? for more information about using search).
tabchi px py [fw=count], a noe
observed frequency
adjusted residual
------------------------------------------
| py
px | 1 2 3 4
----------+-------------------------------
1 | 22 2 2 0
| 8.487 -0.473 -5.951 -1.757
|
2 | 5 7 14 0
| -0.502 3.201 -0.542 -1.757
|
3 | 0 2 36 0
| -4.078 -1.215 5.509 -2.278
|
4 | 0 1 17 10
| -3.300 -1.323 0.275 5.926
------------------------------------------
8 cells with expected frequency < 5
Pearson chi2(9) = 120.2635 Pr = 0.000
likelihood-ratio chi2(9) = . Pr = .
xi: glm count i.px i.py i.qs, fam(poi)
i.px _Ipx_1-4 (naturally coded; _Ipx_1 omitted)
i.py _Ipy_1-4 (naturally coded; _Ipy_1 omitted)
i.qs _Iqs_1-5 (naturally coded; _Iqs_1 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 5
Scale parameter = 1
Deviance = 13.17806287 (1/df) Deviance = 2.635613
Pearson = 11.52236291 (1/df) Pearson = 2.304473
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -26.99836934 AIC = 4.749796
BIC = -.6848807377
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ipx_2 | 1.631969 .560423 2.91 0.004 .5335598 2.730377
_Ipx_3 | .5016421 .9260906 0.54 0.588 -1.313462 2.316746
_Ipx_4 | 1.394444 .5550495 2.51 0.012 .3065673 2.482321
_Ipy_2 | .4796116 .655163 0.73 0.464 -.8044843 1.763707
_Ipy_3 | 1.949173 .4970561 3.92 0.000 .9749608 2.923385
_Ipy_4 | -16.2392 1771.65 -0.01 0.993 -3488.609 3456.13
_Iqs_2 | -3.256746 1.033483 -3.15 0.002 -5.282336 -1.231157
_Iqs_3 | -1.958314 1.188863 -1.65 0.100 -4.288441 .3718142
_Iqs_4 | 14.05626 1771.65 0.01 0.994 -3458.314 3486.426
_Iqs_5 | -3.860885 .7296819 -5.29 0.000 -5.291036 -2.430735
_cons | 3.091077 .2131971 14.50 0.000 2.673218 3.508935
------------------------------------------------------------------------------
use https://stats.idre.ucla.edu/stat/stata/examples/icda/coffee, clear
xi: glm count i.p1 i.p2 i.qs, fam(poi)
i.p1 _Ip1_1-5 (naturally coded; _Ip1_1 omitted)
i.p2 _Ip2_1-5 (naturally coded; _Ip2_1 omitted)
i.qs _Iqs_1-6 (naturally coded; _Iqs_1 omitted)
Generalized linear models No. of obs = 25
Optimization : ML: Newton-Raphson Residual df = 11
Scale parameter = 1
Deviance = 13.78562612 (1/df) Deviance = 1.253239
Pearson = 12.24792024 (1/df) Pearson = 1.113447
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -59.16136962 AIC = 5.85291
BIC = -21.62200795
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ip1_2 | -1.110158 .22572 -4.92 0.000 -1.552561 -.6677549
_Ip1_3 | -.2471955 .2080429 -1.19 0.235 -.6549521 .160561
_Ip1_4 | -1.521394 .2515045 -6.05 0.000 -2.014333 -1.028454
_Ip1_5 | -1.161002 .2280781 -5.09 0.000 -1.608026 -.7139767
_Ip2_2 | -.4965487 .2381542 -2.08 0.037 -.9633223 -.0297751
_Ip2_3 | .4678636 .2187364 2.14 0.032 .0391481 .8965791
_Ip2_4 | -1.236619 .2896265 -4.27 0.000 -1.804277 -.6689617
_Ip2_5 | -.5905986 .2431813 -2.43 0.015 -1.067225 -.1139721
_Iqs_2 | .9027485 .4100027 2.20 0.028 .0991581 1.706339
_Iqs_3 | .2901575 .3893074 0.75 0.456 -.472871 1.053186
_Iqs_4 | .9334636 .50043 1.87 0.062 -.0473612 1.914288
_Iqs_5 | .5148376 .4318692 1.19 0.233 -.3316104 1.361286
_Iqs_6 | -1.29089 .2460296 -5.25 0.000 -1.773099 -.8086812
_cons | 4.532599 .1036952 43.71 0.000 4.329361 4.735838
------------------------------------------------------------------------------
xi: glm count i.p1 i.p2 , fam(poi)
i.p1 _Ip1_1-5 (naturally coded; _Ip1_1 omitted)
i.p2 _Ip2_1-5 (naturally coded; _Ip2_1 omitted)
Generalized linear models No. of obs = 25
Optimization : ML: Newton-Raphson Residual df = 16
Scale parameter = 1
Deviance = 346.3809793 (1/df) Deviance = 21.64881
Pearson = 463.3043939 (1/df) Pearson = 28.95652
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -225.4590462 AIC = 18.75672
BIC = 294.8789661
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ip1_2 | -.8241754 .1384965 -5.95 0.000 -1.095624 -.5527273
_Ip1_3 | .1764564 .1036818 1.70 0.089 -.0267561 .379669
_Ip1_4 | -1.558145 .1833732 -8.50 0.000 -1.917549 -1.19874
_Ip1_5 | -1.13433 .1550154 -7.32 0.000 -1.438155 -.8305058
_Ip2_2 | -.4985555 .140009 -3.56 0.000 -.7729682 -.2241429
_Ip2_3 | .5371429 .1083347 4.96 0.000 .3248108 .7494751
_Ip2_4 | -1.408767 .1941917 -7.25 0.000 -1.789376 -1.028158
_Ip2_5 | -.8109302 .1551582 -5.23 0.000 -1.115035 -.5068257
_cons | 3.753519 .1068032 35.14 0.000 3.544189 3.96285
------------------------------------------------------------------------------
Section 9.5.2 Summarizing Agreement on page 244.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/carcinoma, clear
char qs[omit]
xi: glm count i.px i.py i.qs, fam(poi)
i.px _Ipx_1-4 (naturally coded; _Ipx_1 omitted)
i.py _Ipy_1-4 (naturally coded; _Ipy_1 omitted)
i.qs _Iqs_1-5 (naturally coded; _Iqs_5 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 5
Scale parameter = 1
Deviance = 13.17806287 (1/df) Deviance = 2.635613
Pearson = 11.52236291 (1/df) Pearson = 2.304473
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -26.99836934 AIC = 4.749796
BIC = -.6848807377
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ipx_2 | 1.631969 .560423 2.91 0.004 .5335598 2.730377
_Ipx_3 | .5016421 .9260906 0.54 0.588 -1.313462 2.316746
_Ipx_4 | 1.394444 .5550495 2.51 0.012 .3065673 2.482321
_Ipy_2 | .4796116 .655163 0.73 0.464 -.8044843 1.763707
_Ipy_3 | 1.949173 .4970561 3.92 0.000 .9749608 2.923385
_Ipy_4 | -16.2392 1771.65 -0.01 0.993 -3488.609 3456.13
_Iqs_1 | 3.860885 .7296819 5.29 0.000 2.430735 5.291036
_Iqs_2 | .6041388 .6899838 0.88 0.381 -.7482046 1.956482
_Iqs_3 | 1.902572 .8367 2.27 0.023 .2626698 3.542473
_Iqs_4 | 17.91715 1771.65 0.01 0.992 -3454.452 3490.287
_cons | -.7698087 .6978414 -1.10 0.270 -2.137553 .5979354
------------------------------------------------------------------------------
Section 9.5.3 Quasi Symmetry and Agreement Modeling on page 245.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/carcinoma, clear
xi: glm count i.px i.py i.symm, fam(poi) nolog
i.px _Ipx_1-4 (naturally coded; _Ipx_1 omitted)
i.py _Ipy_1-4 (naturally coded; _Ipy_1 omitted)
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
note: _Isymm_5 dropped due to collinearity
note: _Isymm_8 dropped due to collinearity
note: _Isymm_10 dropped due to collinearity
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 3
Scale parameter = 1
Deviance = .978304658 (1/df) Deviance = .3261016
Pearson = .621982784 (1/df) Pearson = .2073276
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -20.89849023 AIC = 4.237311
BIC = -7.339461509
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ipx_2 | -.2360635 .430017 -0.55 0.583 -1.078881 .6067543
_Ipx_3 | -.5038594 .5050534 -1.00 0.318 -1.493746 .486027
_Ipx_4 | 8.229144 1131.109 0.01 0.994 -2208.703 2225.161
_Ipy_2 | -.9090505 .430017 -2.11 0.035 -1.751868 -.0662327
_Ipy_3 | .9963219 .5050534 1.97 0.049 .0064355 1.986208
_Ipy_4 | -9.017585 1131.109 -0.01 0.994 -2225.95 2207.915
_Isymm_2 | -1.321299 .4521483 -2.92 0.003 -2.207493 -.4351046
_Isymm_3 | -3.595678 .783512 -4.59 0.000 -5.131334 -2.060023
_Isymm_4 | -27.11437 2775.396 -0.01 0.992 -5466.791 5412.562
_Isymm_6 | -1.186505 .4441345 -2.67 0.008 -2.056992 -.3160173
_Isymm_7 | -10.41121 1131.109 -0.01 0.993 -2227.344 2206.522
_Isymm_9 | -9.48327 1131.109 -0.01 0.993 -2226.415 2207.449
_cons | 3.091024 .2132027 14.50 0.000 2.673155 3.508894
------------------------------------------------------------------------------
predict psymm
(option mu assumed; predicted mean count)
xi: glm count i.px i.py i.qs, fam(poi) nolog
i.px _Ipx_1-4 (naturally coded; _Ipx_1 omitted)
i.py _Ipy_1-4 (naturally coded; _Ipy_1 omitted)
i.qs _Iqs_1-5 (naturally coded; _Iqs_5 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 5
Scale parameter = 1
Deviance = 13.17806287 (1/df) Deviance = 2.635613
Pearson = 11.52236291 (1/df) Pearson = 2.304473
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -26.99836934 AIC = 4.749796
BIC = -.6848807377
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Ipx_2 | 1.631969 .560423 2.91 0.004 .5335598 2.730377
_Ipx_3 | .5016421 .9260906 0.54 0.588 -1.313462 2.316746
_Ipx_4 | 1.394444 .5550495 2.51 0.012 .3065673 2.482321
_Ipy_2 | .4796116 .655163 0.73 0.464 -.8044843 1.763707
_Ipy_3 | 1.949173 .4970561 3.92 0.000 .9749608 2.923385
_Ipy_4 | -16.2392 1771.65 -0.01 0.993 -3488.609 3456.13
_Iqs_1 | 3.860885 .7296819 5.29 0.000 2.430735 5.291036
_Iqs_2 | .6041388 .6899838 0.88 0.381 -.7482046 1.956482
_Iqs_3 | 1.902572 .8367 2.27 0.023 .2626698 3.542473
_Iqs_4 | 17.91715 1771.65 0.01 0.992 -3454.452 3490.287
_cons | -.7698087 .6978414 -1.10 0.270 -2.137553 .5979354
------------------------------------------------------------------------------
predict pqs
(option mu assumed; predicted mean count)
table px py, con(sum count sum pqs sum psymm)
--------------------------------------------------
| py
px | 1 2 3 4
----------+---------------------------------------
1 | 22 2 2 0
| 22.00075 .7481161 3.252306 4.10e-08
| 21.9996 2.364755 1.63504 4.47e-15
|
2 | 5 7 14 0
| 2.36827 7.000001 16.63207 2.10e-07
| 4.635118 7 14.36476 6.34e-08
|
3 | 0 2 36 0
| .7647803 1.235462 36.00212 6.78e-08
| .3647607 1.634945 35.99884 1.23e-07
|
4 | 0 1 17 10
| 1.867565 3.016952 13.11568 10.00003
| 1.38e-07 .9999095 17.00012 9.999983
--------------------------------------------------
xi: glm count i.symm, fam(poi) nolog
i.symm _Isymm_1-10 (naturally coded; _Isymm_1 omitted)
Generalized linear models No. of obs = 16
Optimization : ML: Newton-Raphson Residual df = 6
Scale parameter = 1
Deviance = 39.17823839 (1/df) Deviance = 6.529706
Pearson = 30.2854683 (1/df) Pearson = 5.047578
Variance function: V(u) = u [Poisson]
Link function : g(u) = ln(u) [Log]
Standard errors : OIM
Log likelihood = -39.9984571 AIC = 6.249807
BIC = 22.54270606
------------------------------------------------------------------------------
count | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Isymm_2 | -1.838279 .4339457 -4.24 0.000 -2.688797 -.9877615
_Isymm_3 | -3.091058 .7385487 -4.19 0.000 -4.538587 -1.643529
_Isymm_4 | -20.03611 3381.085 -0.01 0.995 -6646.842 6606.769
_Isymm_5 | -1.145147 .4339482 -2.64 0.008 -1.99567 -.2946244
_Isymm_6 | -1.011603 .3285621 -3.08 0.002 -1.655573 -.3676328
_Isymm_7 | -3.78444 1.02259 -3.70 0.000 -5.788679 -1.780201
_Isymm_8 | .4924818 .2706124 1.82 0.069 -.0379088 1.022872
_Isymm_9 | -.950971 .3229183 -2.94 0.003 -1.583879 -.3180628
_Isymm_10 | -.7884702 .3813839 -2.07 0.039 -1.535969 -.0409715
_cons | 3.091057 .2131991 14.50 0.000 2.673195 3.50892
------------------------------------------------------------------------------
Section 9.5.4 Kappa Measure of Agreement on page 246.
use https://stats.idre.ucla.edu/stat/stata/examples/icda/carcinoma, clear
kap px py [fw=count]
Expected
Agreement Agreement Kappa Std. Err. Z Prob>Z
-----------------------------------------------------------------
63.56% 28.12% 0.4930 0.0501 9.83 0.0000
Section 9.6.1 The Bradley-Terry Model on page 247.
clear
input wins matches seles graf sabat navrat sanchez
2 5 1 -1 0 0 0
1 1 1 0 -1 0 0
3 6 1 0 0 -1 0
2 2 1 0 0 0 -1
6 9 0 1 -1 0 0
3 3 0 1 0 -1 0
7 8 0 1 0 0 -1
1 3 0 0 1 -1 0
3 5 0 0 1 0 -1
3 4 0 0 0 1 -1
end
glm wins seles graf sabat navrat sanchez, fam(bin matches) nocons
note: sanchez dropped due to collinearity
Generalized linear models No. of obs = 10
Optimization : ML: Newton-Raphson Residual df = 6
Scale parameter = 1
Deviance = 4.649258673 (1/df) Deviance = .7748764
Pearson = 3.204827193 (1/df) Pearson = .5341379
Variance function: V(u) = u*(1-u/matches) [Binomial]
Link function : g(u) = ln(u/(matches-u)) [Logit]
Standard errors : OIM
Log likelihood = -9.519233528 AIC = 2.703847
BIC = -9.166251885
------------------------------------------------------------------------------
wins | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
seles | 1.533144 .7870659 1.95 0.051 -.0094769 3.075765
graf | 1.932784 .6783673 2.85 0.004 .6032082 3.262359
sabat | .7308542 .6771022 1.08 0.280 -.5962416 2.05795
navrat | 1.087506 .7236525 1.50 0.133 -.3308268 2.505839
------------------------------------------------------------------------------
lincom graf-seles
( 1) - [wins]seles + [wins]graf = 0
------------------------------------------------------------------------------
wins | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | .3996396 .6689474 0.60 0.550 -.9114732 1.710752
------------------------------------------------------------------------------
predict pwins
(option mu assumed; predicted mean wins)
list
+---------------------------------------------------------------------+
| wins matches seles graf sabat navrat sanchez pwins |
|---------------------------------------------------------------------|
1. | 2 5 1 -1 0 0 0 2.006995 |
2. | 1 1 1 0 -1 0 0 .6904641 |
3. | 3 6 1 0 0 -1 0 3.65761 |
4. | 2 2 1 0 0 0 -1 1.644932 |
5. | 6 9 0 1 -1 0 0 6.91981 |
|---------------------------------------------------------------------|
6. | 3 3 0 1 0 -1 0 2.098727 |
7. | 7 8 0 1 0 0 -1 6.988458 |
8. | 1 3 0 0 1 -1 0 1.235311 |
9. | 3 5 0 0 1 0 -1 3.374964 |
10. | 3 4 0 0 0 1 -1 2.991647 |
+---------------------------------------------------------------------+