Stata Textbook Examples Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow Chapter 8: Special Topics

The data files used for the examples in this text can be downloaded in a .zip file from the Wiley Publications website.  You can then use a program such as zip to unzip the data files.  If you need assistance getting data into Stata, please see our Stata Class Notes, especially the unit on Entering Data.  (NOTE:  The *.dat files are the data files, and the *.txt files contain the codebook information.)
Table 8.2, page 266.
use mammog.dta, clear
(Hosmer and Lemeshow - modified from appendix 6)

tab2 me hist

-> tabulation of me by hist

|         hist
me |         0          1 |     Total
-----------+----------------------+----------
0 |       220         14 |       234
1 |        85         19 |       104
2 |        63         11 |        74
-----------+----------------------+----------
Total |       368         44 |       412
NOTE: The text just above this table (on page 266) shows how the odds ratios were calculated.
Table 8.3, page 267.
mlogit me hist

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood =   -396.214
Iteration 2:   log likelihood =    -396.17
Iteration 3:   log likelihood = -396.16997

Multinomial regression                            Number of obs   =        412
LR chi2(2)      =      12.86
Prob > chi2     =     0.0016
Log likelihood = -396.16997                       Pseudo R2       =     0.0160

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
hist |   1.256358   .3746603     3.35   0.001     .5220372    1.990679
_cons |  -.9509763   .1277112    -7.45   0.000    -1.201286   -.7006669
-------------+----------------------------------------------------------------
2            |
hist |   1.009331   .4274998     2.36   0.018     .1714466    1.847215
_cons |  -1.250493   .1428932    -8.75   0.000    -1.530558   -.9704273
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.4, page 269. Estimated covariance matrix for the fitted model in Table 8.3.
* Stata 8 code.
vce

* Stata 9 code and output.
estat vce

Covariance matrix of coefficients of mlogit model

| 1                      | 2
e(V) |       hist       _cons |       hist       _cons
-------------+------------------------+------------------------
1            |                        |
hist |  .14037035             |
_cons | -.01631016   .01631016 |
-------------+------------------------+------------------------
2            |                        |
hist |  .07597403  -.00454545 |  .18275604
_cons | -.00454545   .00454545 | -.02041847   .02041847
Table 8.5, page 271.
tab2 me detc

-> tabulation of me by detc

|               detc
me |         1          2          3 |     Total
-----------+---------------------------------+----------
0 |        13         77        144 |       234
1 |         1         12         91 |       104
2 |         4         16         54 |        74
-----------+---------------------------------+----------
Total |        18        105        289 |       412 
Table 8.6, page 271.
xi: mlogit me i.detc

i.detc            _Idetc_1-3          (naturally coded; _Idetc_1 omitted)

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood = -389.76354
Iteration 2:   log likelihood = -389.21625
Iteration 3:   log likelihood = -389.20061
Iteration 4:   log likelihood = -389.20054

Multinomial regression                            Number of obs   =        412
LR chi2(4)      =      26.80
Prob > chi2     =     0.0000
Log likelihood = -389.20054                       Pseudo R2       =     0.0333

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
_Idetc_2 |   .7060506   1.083136     0.65   0.514    -1.416856    2.828958
_Idetc_3 |   2.105996   1.046325     2.01   0.044     .0552361    4.156755
_cons |  -2.564949    1.03772    -2.47   0.013    -4.598843   -.5310556
-------------+----------------------------------------------------------------
2            |
_Idetc_2 |  -.3925617   .6343589    -0.62   0.536    -1.635882     .850759
_Idetc_3 |   .1978257   .5936221     0.33   0.739    -.9656522    1.361304
_cons |  -1.178655   .5717729    -2.06   0.039    -2.299309   -.0580007
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)

xi: mlogit me i.detc, rrr

i.detc            _Idetc_1-3          (naturally coded; _Idetc_1 omitted)

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood = -389.76354
Iteration 2:   log likelihood = -389.21625
Iteration 3:   log likelihood = -389.20061
Iteration 4:   log likelihood = -389.20054

Multinomial regression                            Number of obs   =        412
LR chi2(4)      =      26.80
Prob > chi2     =     0.0000
Log likelihood = -389.20054                       Pseudo R2       =     0.0333

------------------------------------------------------------------------------
me |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
_Idetc_2 |   2.025974   2.194405     0.65   0.514     .2424751    16.92781
_Idetc_3 |   8.215278   8.595851     2.01   0.044      1.05679    63.86395
-------------+----------------------------------------------------------------
2            |
_Idetc_2 |   .6753247   .4283982    -0.62   0.536     .1947804    2.341423
_Idetc_3 |    1.21875   .7234769     0.33   0.739     .3807348    3.901276
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.7, page 274.
xi: mlogit me i.sympt pb hist bse i.detc

i.sympt           _Isympt_1-4         (naturally coded; _Isympt_1 omitted)
i.detc            _Idetc_1-3          (naturally coded; _Idetc_1 omitted)

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood = -351.59713
Iteration 2:   log likelihood = -347.26545
Iteration 3:   log likelihood = -346.95451
Iteration 4:   log likelihood = -346.95096
Iteration 5:   log likelihood = -346.95096

Multinomial regression                            Number of obs   =        412
LR chi2(16)     =     111.30
Prob > chi2     =     0.0000
Log likelihood = -346.95096                       Pseudo R2       =     0.1382

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
_Isympt_2 |   .1100372   .9227608     0.12   0.905    -1.698541    1.918615
_Isympt_3 |   1.924708   .7775975     2.48   0.013     .4006449    3.448771
_Isympt_4 |   2.456993   .7753323     3.17   0.002     .9373693    3.976616
pb |  -.2194368   .0755139    -2.91   0.004    -.3674414   -.0714323
hist |   1.366239   .4375196     3.12   0.002     .5087163    2.223762
bse |   1.291666    .529891     2.44   0.015     .2530992    2.330234
_Idetc_2 |   .0170207   1.161896     0.01   0.988    -2.260254    2.294296
_Idetc_3 |   .9041379   1.126822     0.80   0.422    -1.304393    3.112668
_cons |   -2.99875    1.53922    -1.95   0.051    -6.015566    .0180663
-------------+----------------------------------------------------------------
2            |
_Isympt_2 |  -.2900833   .6440636    -0.45   0.652    -1.552425    .9722582
_Isympt_3 |   .8173136   .5397922     1.51   0.130    -.2406596    1.875287
_Isympt_4 |   1.132239   .5476704     2.07   0.039     .0588252    2.205654
pb |  -.1482068   .0763686    -1.94   0.052    -.2978866    .0014729
hist |   1.065436    .459396     2.32   0.020     .1650366    1.965836
bse |   1.052144   .5149894     2.04   0.041     .0427838    2.061505
_Idetc_2 |  -.9243928   .7137382    -1.30   0.195    -2.323294    .4745083
_Idetc_3 |  -.6905329   .6871078    -1.00   0.315    -2.037239    .6561736
_cons |  -.9860915   1.111832    -0.89   0.375    -3.165242    1.193059
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.8, page 275.
gen symptd = .
(412 missing values generated)

replace symptd = 0 if sympt == 1 | sympt == 2

replace symptd = 1 if sympt == 3| sympt == 4

xi: mlogit me symptd pb hist bse i.detc

i.detc            _Idetc_1-3          (naturally coded; _Idetc_1 omitted)

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood = -353.37799
Iteration 2:   log likelihood = -349.07042
Iteration 3:   log likelihood = -348.75167
Iteration 4:   log likelihood = -348.74797
Iteration 5:   log likelihood = -348.74797

Multinomial regression                            Number of obs   =        412
LR chi2(12)     =     107.70
Prob > chi2     =     0.0000
Log likelihood = -348.74797                       Pseudo R2       =     0.1338

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |   2.095341   .4573977     4.58   0.000     1.198858    2.991824
pb |  -.2510121   .0729327    -3.44   0.001    -.3939575   -.1080667
hist |   1.293281   .4335351     2.98   0.003     .4435676    2.142994
bse |   1.243974   .5263057     2.36   0.018      .212434    2.275514
_Idetc_2 |   .0902755   1.161025     0.08   0.938    -2.185291    2.365842
_Idetc_3 |   .9728148   1.126271     0.86   0.388    -1.234636    3.180266
_cons |   -2.70375   1.434414    -1.88   0.059     -5.51515    .1076495
-------------+----------------------------------------------------------------
2            |
symptd |   1.121365   .3571979     3.14   0.002     .4212698     1.82146
pb |  -.1681062   .0741724    -2.27   0.023    -.3134815    -.022731
hist |   1.014055   .4538042     2.23   0.025     .1246154    1.903495
bse |    1.02859   .5139737     2.00   0.045     .0212205    2.035961
_Idetc_2 |  -.9021325   .7146177    -1.26   0.207    -2.302758    .4984924
_Idetc_3 |  -.6698221    .687579    -0.97   0.330    -2.017452    .6778079
_cons |  -.9987682   1.071963    -0.93   0.351    -3.099778    1.102242
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.9, page 276.
mlogit me symptd pb hist bse

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood = -356.82062
Iteration 2:   log likelihood = -353.22809
Iteration 3:   log likelihood = -353.02058
Iteration 4:   log likelihood = -353.01904
Iteration 5:   log likelihood = -353.01904

Multinomial regression                            Number of obs   =        412
LR chi2(8)      =      99.16
Prob > chi2     =     0.0000
Log likelihood = -353.01904                       Pseudo R2       =     0.1231

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |   2.230432    .451959     4.94   0.000     1.344609    3.116255
pb |  -.2825439   .0713491    -3.96   0.000    -.4223855   -.1427024
hist |    1.29663   .4293033     3.02   0.003     .4552113    2.138049
bse |   1.220961   .5210422     2.34   0.019     .1997369    2.242185
_cons |  -1.788769   .8470723    -2.11   0.035       -3.449   -.1285377
-------------+----------------------------------------------------------------
2            |
symptd |   1.153122   .3513753     3.28   0.001     .4644391    1.841805
pb |  -.1577922   .0711783    -2.22   0.027     -.297299   -.0182853
hist |   1.061324   .4526774     2.34   0.019     .1740929    1.948556
bse |   .9603822   .5072023     1.89   0.058    -.0337161     1.95448
_cons |   -1.74214   .8086823    -2.15   0.031    -3.327128   -.1571521
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.10, page 277.
rename  _Idetc_3 detcd
mlogit me symptd pb hist bse detcd

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood =  -354.2052
Iteration 2:   log likelihood = -349.86452
Iteration 3:   log likelihood = -349.56908
Iteration 4:   log likelihood =  -349.5663
Iteration 5:   log likelihood =  -349.5663

Multinomial regression                            Number of obs   =        412
LR chi2(10)     =     106.07
Prob > chi2     =     0.0000
Log likelihood =  -349.5663                       Pseudo R2       =     0.1317

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |    2.09475   .4574302     4.58   0.000     1.198203    2.991297
pb |  -.2494746    .072579    -3.44   0.001    -.3917269   -.1072224
hist |   1.309864   .4336022     3.02   0.003     .4600195    2.159709
bse |   1.237011   .5254241     2.35   0.019      .207199    2.266824
detcd |   .8851839   .3562379     2.48   0.013     .1869705    1.583397
_cons |  -2.623759   .9263964    -2.83   0.005    -4.439462   -.8080551
-------------+----------------------------------------------------------------
2            |
symptd |   1.127417   .3563621     3.16   0.002     .4289603    1.825874
pb |  -.1543182   .0726206    -2.12   0.034     -.296652   -.0119845
hist |   1.063179   .4528412     2.35   0.019     .1756263    1.950731
bse |   .9560104   .5073366     1.88   0.060    -.0383511    1.950372
detcd |   .1141572   .3182122     0.36   0.720    -.5095272    .7378416
_cons |  -1.823882   .8550928    -2.13   0.033    -3.499833   -.1479306
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Figure 8.1, page 278.
preserve

clear
input elogit1 elogit2 percb
0         0    5
-.1592353 -.3348183  6.5
-.6278501 -.5585917  8.5
-1.482975 -.8304334 13.5
end

graph twoway scatter elogit1 elogit2 percb, ///
xlabel(5 6.5 8.5 13.5) ylabel(-1.5(.5)0) connect(l l) 
restore
Table 8.11, page 280.
NOTE: This gives the values for the columns labeled MLE.
mlogit me symptd pb hist bse detcd

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood =  -354.2052
Iteration 2:   log likelihood = -349.86452
Iteration 3:   log likelihood = -349.56908
Iteration 4:   log likelihood =  -349.5663
Iteration 5:   log likelihood =  -349.5663

Multinomial regression                            Number of obs   =        412
LR chi2(10)     =     106.07
Prob > chi2     =     0.0000
Log likelihood =  -349.5663                       Pseudo R2       =     0.1317

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |    2.09475   .4574302     4.58   0.000     1.198203    2.991297
pb |  -.2494746    .072579    -3.44   0.001    -.3917269   -.1072224
hist |   1.309864   .4336022     3.02   0.003     .4600195    2.159709
bse |   1.237011   .5254241     2.35   0.019      .207199    2.266824
detcd |   .8851839   .3562379     2.48   0.013     .1869705    1.583397
_cons |  -2.623759   .9263964    -2.83   0.005    -4.439462   -.8080551
-------------+----------------------------------------------------------------
2            |
symptd |   1.127417   .3563621     3.16   0.002     .4289603    1.825874
pb |  -.1543182   .0726206    -2.12   0.034     -.296652   -.0119845
hist |   1.063179   .4528412     2.35   0.019     .1756263    1.950731
bse |   .9560104   .5073366     1.88   0.060    -.0383511    1.950372
detcd |   .1141572   .3182122     0.36   0.720    -.5095272    .7378416
_cons |  -1.823882   .8550928    -2.13   0.033    -3.499833   -.1479306
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
NOTE: This gives the values for the columns labeled ILR.
mlogit me symptd pb hist bse detcd if me != 2

Iteration 0:   log likelihood = -208.62772
Iteration 1:   log likelihood = -167.49587
Iteration 2:   log likelihood = -162.26366
Iteration 3:   log likelihood = -161.78826
Iteration 4:   log likelihood = -161.78146
Iteration 5:   log likelihood = -161.78145

Multinomial regression                            Number of obs   =        338
LR chi2(5)      =      93.69
Prob > chi2     =     0.0000
Log likelihood = -161.78145                       Pseudo R2       =     0.2245

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |   2.091002   .4651287     4.50   0.000     1.179366    3.002638
pb |  -.2426146    .073756    -3.29   0.001    -.3871737   -.0980554
hist |   1.385025   .4682596     2.96   0.003     .4672527    2.302796
bse |   1.363308   .5338994     2.55   0.011     .3168847    2.409732
detcd |    .852694   .3654564     2.33   0.020     .1364125    1.568975
_cons |  -2.765088   .9421802    -2.93   0.003    -4.611727   -.9184483
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)

mlogit me symptd pb hist bse detcd if me != 1

Iteration 0:   log likelihood = -169.82478
Iteration 1:   log likelihood = -154.48353
Iteration 2:   log likelihood = -153.48912
Iteration 3:   log likelihood = -153.47233
Iteration 4:   log likelihood = -153.47232

Multinomial regression                            Number of obs   =        308
LR chi2(5)      =      32.70
Prob > chi2     =     0.0000
Log likelihood = -153.47232                       Pseudo R2       =     0.0963

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
2            |
symptd |    1.15299   .3565788     3.23   0.001     .4541082    1.851871
pb |  -.1537696   .0726013    -2.12   0.034    -.2960655   -.0114736
hist |   1.097696   .4593413     2.39   0.017     .1974035    1.997988
bse |   .9534998   .5097419     1.87   0.061    -.0455759    1.952576
detcd |   .0987046   .3190788     0.31   0.757    -.5266785    .7240876
_cons |    -1.8381    .860046    -2.14   0.033     -3.52376   -.1524412
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.12, page 281.
logit me symptd pb hist bse detcd if me != 2

Iteration 0:   log likelihood = -208.62772
Iteration 1:   log likelihood = -167.49587
Iteration 2:   log likelihood = -162.26366
Iteration 3:   log likelihood = -161.78826
Iteration 4:   log likelihood = -161.78146
Iteration 5:   log likelihood = -161.78145

Logit estimates                                   Number of obs   =        338
LR chi2(5)      =      93.69
Prob > chi2     =     0.0000
Log likelihood = -161.78145                       Pseudo R2       =     0.2245

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
symptd |   2.091002   .4651287     4.50   0.000     1.179366    3.002638
pb |  -.2426146    .073756    -3.29   0.001    -.3871737   -.0980554
hist |   1.385025   .4682596     2.96   0.003     .4672527    2.302796
bse |   1.363308   .5338994     2.55   0.011     .3168847    2.409732
detcd |    .852694   .3654564     2.33   0.020     .1364125    1.568975
_cons |  -2.765088   .9421802    -2.93   0.003    -4.611727   -.9184483
------------------------------------------------------------------------------

* Stata 8 code.
lfit, group(10)

* Stata 9 code and output.
estat gof, group(10)

Logistic model for me, goodness-of-fit test
(Table collapsed on quantiles of estimated probabilities)

number of observations =       338
number of groups =        10
Hosmer-Lemeshow chi2(8) =        12.20
Prob > chi2 =         0.1424

* Stata 8 code.
lfit

* Stata 9 code and output.
estat gof

Logistic model for me, goodness-of-fit test

number of observations =       338
number of covariate patterns =        74
Pearson chi2(68) =        67.84
Prob > chi2 =         0.4828

* We thank Silvano Andorno for providing the following code for the Stukel test
generate me1=0
replace me1=1 if me==1
replace me1=. if me==2
generate me2=0
replace me2=1 if me==2
replace me2=. if me==1
quietly logit me1 symptd pb hist bse detcd
predict p1
generate g1=ln(p1/(1-p1))
generate z11=0.5*g1^2
replace z11=0 if p1<0.5
generate z12=-0.5*g1^2
replace z12=0 if p1>=0.5

quietly logit me1 symptd pb hist bse detcd
estimates store reduced
quietly logit me1 symptd pb hist bse detcd z11 z12
estimates store full
lrtest reduced full
Likelihood-ratio test                                 LR chi2(2)  =      1.02
(Assumption: reduced nested in full)                  Prob > chi2 =    0.6006
logit me symptd pb hist bse detcd if me != 1

Iteration 0:   log likelihood = -169.82478
Iteration 1:   log likelihood = -154.48353
Iteration 2:   log likelihood = -153.48912
Iteration 3:   log likelihood = -153.47233
Iteration 4:   log likelihood = -153.47232

Logit estimates                                   Number of obs   =        308
LR chi2(5)      =      32.70
Prob > chi2     =     0.0000
Log likelihood = -153.47232                       Pseudo R2       =     0.0963

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
symptd |    1.15299   .3565788     3.23   0.001     .4541082    1.851871
pb |  -.1537696   .0726013    -2.12   0.034    -.2960655   -.0114736
hist |   1.097696   .4593413     2.39   0.017     .1974035    1.997988
bse |   .9534998   .5097419     1.87   0.061    -.0455759    1.952576
detcd |   .0987046   .3190788     0.31   0.757    -.5266785    .7240876
_cons |    -1.8381    .860046    -2.14   0.033     -3.52376   -.1524412
------------------------------------------------------------------------------

* Stata 8 code.
lfit, group(10)

* Stata 9 code and output.
estat gof, group(10)

Logistic model for me, goodness-of-fit test
(Table collapsed on quantiles of estimated probabilities)

number of observations =       308
number of groups =        10
Hosmer-Lemeshow chi2(8) =         9.62
Prob > chi2 =         0.2929

* Stata 8 code.
lfit

* Stata 9 code and output.
estat gof

Logistic model for me, goodness-of-fit test

number of observations =       308
number of covariate patterns =        75
Pearson chi2(69) =        63.83
Prob > chi2 =         0.6535
* We thank Silvano Andorno for providing the following code for the Stukel test
quietly logit me2 symptd pb hist bse detcd
predict p2
generate g2=ln(p2/(1-p2))
generate z21=0.5*g2^2
replace z21=0 if p2<0.5
generate z22=-0.5*g2^2
replace z22=0 if p2>=0.5
quietly logit me2 symptd pb hist bse detcd
estimates store reduced
quietly logit me2 symptd pb hist bse detcd z21 z22
estimates store full
lrtest reduced full
Likelihood-ratio test LR chi2(2) = 1.86
(Assumption: reduced nested in full) Prob > chi2 = 0.3937

Table 8.13, page 283.

NOTE: mj = the number of observation that share the pattern.
logit me symptd pb hist bse detcd if me != 2

Iteration 0:   log likelihood = -208.62772
Iteration 1:   log likelihood = -167.49587
Iteration 2:   log likelihood = -162.26366
Iteration 3:   log likelihood = -161.78826
Iteration 4:   log likelihood = -161.78146
Iteration 5:   log likelihood = -161.78145

Logit estimates                                   Number of obs   =        338
LR chi2(5)      =      93.69
Prob > chi2     =     0.0000
Log likelihood = -161.78145                       Pseudo R2       =     0.2245

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
symptd |   2.091002   .4651287     4.50   0.000     1.179366    3.002638
pb |  -.2426146    .073756    -3.29   0.001    -.3871737   -.0980554
hist |   1.385025   .4682596     2.96   0.003     .4672527    2.302796
bse |   1.363308   .5338994     2.55   0.011     .3168847    2.409732
detcd |    .852694   .3654564     2.33   0.020     .1364125    1.568975
_cons |  -2.765088   .9421802    -2.93   0.003    -4.611727   -.9184483
------------------------------------------------------------------------------

predict p1
(option p assumed; Pr(me))

predict dx1, dx2
(74 missing values generated)

predict db1, db
(74 missing values generated)

predict dd1, dd
(74 missing values generated)

predict h1, h
(74 missing values generated)

predict n1, n
(74 missing values generated)

format n1 symptd pb hist bse detcd %2.0f
list n1 symptd pb hist bse detcd p1 db1 dx1 dd1 h1 if n1 == 4 | n1 == 63

n1  sym~d  pb  hist  bse  detcd         p1        db1        dx1        dd1         h1
319. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
320. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
321. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
322. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
323. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
324. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
325. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
326. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
327. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
328. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
329. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
330. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
331. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
332. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
333. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
334. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
335. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
336. 63   1   9   0   1   1   .3448817   1.732725   7.037074   6.585556   .1975787
337.  4   0   6   0   0   0   .0144747   .5432962    33.5851   5.819932   .0159192
338.  4   0   6   0   0   0   .0144747   .5432962    33.5851   5.819932   .0159192

logit me symptd pb hist bse detcd if me != 1

Iteration 0:   log likelihood = -169.82478
Iteration 1:   log likelihood = -154.48353
Iteration 2:   log likelihood = -153.48912
Iteration 3:   log likelihood = -153.47233
Iteration 4:   log likelihood = -153.47232

Logit estimates                                   Number of obs   =        308
LR chi2(5)      =      32.70
Prob > chi2     =     0.0000
Log likelihood = -153.47232                       Pseudo R2       =     0.0963

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
symptd |    1.15299   .3565788     3.23   0.001     .4541082    1.851871
pb |  -.1537696   .0726013    -2.12   0.034    -.2960655   -.0114736
hist |   1.097696   .4593413     2.39   0.017     .1974035    1.997988
bse |   .9534998   .5097419     1.87   0.061    -.0455759    1.952576
detcd |   .0987046   .3190788     0.31   0.757    -.5266785    .7240876
_cons |    -1.8381    .860046    -2.14   0.033     -3.52376   -.1524412
------------------------------------------------------------------------------

predict p2
(option p assumed; Pr(me))

predict dx2, dx2
(104 missing values generated)

predict db2, db
(104 missing values generated)

predict dd2, dd
(104 missing values generated)

predict h2, h
(104 missing values generated)

predict n2, n
(104 missing values generated)

list n2 symptd pb hist bse detcd p2 db2 dx2 dd2 h2 if n2 == 62 | n2 == 63 | n2 == 66

n2  sym~d  pb  hist  bse  detcd         p2        db2        dx2        dd2         h2
237.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
238.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
239.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
240.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
241.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
242.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
243.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
244.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
245.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
247.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
248.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
249.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
251.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
253.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
254.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
255.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
256.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
347.        62   1   9   1   1   0   .4955399   .9564146   3.818863    5.26768   .2002846
360.        62   1   9   1   1   0   .4955399   .9564146   3.818863    5.26768   .2002846
363.        63   1  10   0   0   0   .0977211   .2639904   9.490052   4.780663   .0270647
365.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
371.        66   1  10   0   1   1   .2367462   .9990091    2.53433   3.013997    .282738
399.        62   1   9   1   1   0   .4955399   .9564146   3.818863    5.26768   .2002846
Table 8.14, page 285.
mlogit me symptd pb hist bse detcd if n2 != 62 & n1 != 63 & n2 != 66

Iteration 0:   log likelihood = -365.25083
Iteration 1:   log likelihood = -318.11909
Iteration 2:   log likelihood = -314.01421
Iteration 3:   log likelihood = -313.74957
Iteration 4:   log likelihood = -313.74728
Iteration 5:   log likelihood = -313.74728

Multinomial regression                            Number of obs   =        372
LR chi2(10)     =     103.01
Prob > chi2     =     0.0000
Log likelihood = -313.74728                       Pseudo R2       =     0.1410

------------------------------------------------------------------------------
me |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |   2.124646   .4633131     4.59   0.000     1.216569    3.032723
pb |  -.2162733   .0854258    -2.53   0.011    -.3837048   -.0488418
hist |   1.243508   .4417728     2.81   0.005     .3776495    2.109367
bse |   1.271312    .531037     2.39   0.017     .2304986    2.312125
detcd |    .883019   .3691392     2.39   0.017     .1595194    1.606519
_cons |  -2.891975   1.041649    -2.78   0.005    -4.933569   -.8503814
-------------+----------------------------------------------------------------
2            |
symptd |   1.190628   .3609934     3.30   0.001     .4830943    1.898162
pb |  -.0803882    .078619    -1.02   0.307    -.2344787    .0737023
hist |   .6058955   .4952242     1.22   0.221    -.3647261    1.576517
bse |   1.081212   .5122946     2.11   0.035     .0771333    2.085291
detcd |   .4767587   .3403687     1.40   0.161    -.1903518    1.143869
_cons |  -2.663662   .9556489    -2.79   0.005    -4.536699   -.7906244
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)
Table 8.15, page 286.
mlogit me symptd pb hist bse detcd, rrr

Iteration 0:   log likelihood = -402.59901
Iteration 1:   log likelihood =  -354.2052
Iteration 2:   log likelihood = -349.86452
Iteration 3:   log likelihood = -349.56908
Iteration 4:   log likelihood =  -349.5663
Iteration 5:   log likelihood =  -349.5663

Multinomial regression                            Number of obs   =        412
LR chi2(10)     =     106.07
Prob > chi2     =     0.0000
Log likelihood =  -349.5663                       Pseudo R2       =     0.1317

------------------------------------------------------------------------------
me |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
symptd |   8.123411   3.715893     4.58   0.000     3.314157    19.91149
pb |   .7792101   .0565543    -3.44   0.001     .6758887    .8983259
hist |   3.705671   1.606787     3.02   0.003     1.584105    8.668614
bse |   3.445301   1.810244     2.35   0.019     1.230227    9.648703
detcd |    2.42343   .8633175     2.48   0.013     1.205592    4.871477
-------------+----------------------------------------------------------------
2            |
symptd |   3.087671   1.100329     3.16   0.002      1.53566    6.208219
pb |   .8569993   .0622358    -2.12   0.034     .7433027    .9880871
hist |    2.89556   1.311229     2.35   0.019     1.191993    7.033828
bse |   2.601298   1.319734     1.88   0.060      .962375    7.031302
detcd |   1.120928   .3566931     0.36   0.720     .6007795    2.091417
------------------------------------------------------------------------------
(Outcome me==0 is the comparison group)

lincom [1]pb*-2, rrr

( 1) - 2.0 [1]pb = 0.0

------------------------------------------------------------------------------
me |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |    1.64699   .2390738     3.44   0.001     1.239174    2.189019
------------------------------------------------------------------------------

lincom [2]pb*-2, rrr

( 1) - 2.0 [2]pb = 0.0

------------------------------------------------------------------------------
me |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |   1.361567   .1977557     2.12   0.034     1.024258    1.809959
------------------------------------------------------------------------------
Table 8.16, page 293.
use lowbwt.dta, clear
(Hosmer and Lemeshow - from appendix 1)

gen bwt4 = 0
replace bwt4 = 1 if 3000 > bwt | bwt<=3500

replace bwt4 = 2 if 2500 > bwt | bwt<=3000

replace bwt4 = 3 if bwt<=2500

tab2 bwt4 smoke

-> tabulation of bwt4 by smoke

|         smoke
bwt4 |         0          1 |     Total
-----------+----------------------+----------
0 |        35         11 |        46
1 |        29         17 |        46
2 |        22         16 |        38
3 |        29         30 |        59
-----------+----------------------+----------
Total |       115         74 |       189 
Middle of page.
logistic bwt4 smoke if bwt4 == 0 | bwt4 == 1

Logit estimates                                   Number of obs   =         92
LR chi2(1)      =       1.86
Prob > chi2     =     0.1727
Log likelihood = -62.840008                       Pseudo R2       =     0.0146

------------------------------------------------------------------------------
bwt4 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |   1.865204   .8603962     1.35   0.177     .7552265    4.606546
------------------------------------------------------------------------------

logistic bwt4 smoke if bwt4 == 0 | bwt4 == 2

Logit estimates                                   Number of obs   =         84
LR chi2(1)      =       3.16
Prob > chi2     =     0.0755
Log likelihood = -56.263134                       Pseudo R2       =     0.0273

------------------------------------------------------------------------------
bwt4 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |    2.31405   1.103574     1.76   0.079     .9087269    5.892667
------------------------------------------------------------------------------

logistic bwt4 smoke if bwt4 == 0 | bwt4 == 3

Logit estimates                                   Number of obs   =        105
LR chi2(1)      =       8.10
Prob > chi2     =     0.0044
Log likelihood = -67.923441                       Pseudo R2       =     0.0563

------------------------------------------------------------------------------
bwt4 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |   3.291536   1.424504     2.75   0.006     1.409346    7.687404
------------------------------------------------------------------------------

* Stata 8 code.
mlogit bwt4 smoke, basecategory(0) rrr

* Stata 9 code and output.
mlogit bwt4 smoke, baseoutcome(0) rrr

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -255.53804
Iteration 2:   log likelihood = -255.48595
Iteration 3:   log likelihood = -255.48592

Multinomial regression                            Number of obs   =        189
LR chi2(3)      =       8.33
Prob > chi2     =     0.0396
Log likelihood = -255.48592                       Pseudo R2       =     0.0160

------------------------------------------------------------------------------
bwt4 |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
smoke |   1.865204   .8603963     1.35   0.177     .7552264    4.606546
-------------+----------------------------------------------------------------
2            |
smoke |    2.31405   1.103573     1.76   0.079      .908727    5.892667
-------------+----------------------------------------------------------------
3            |
smoke |   3.291536   1.424503     2.75   0.006     1.409346    7.687402
------------------------------------------------------------------------------
(Outcome bwt4==0 is the comparison group)
Table 8.17, page 294.
* Stata 8 code.
mlogit bwt4 smoke, basecategory(0) rrr

* Stata 9 code and output.
mlogit bwt4 smoke, baseoutcome(0) rrr

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -255.53804
Iteration 2:   log likelihood = -255.48595
Iteration 3:   log likelihood = -255.48592

Multinomial regression                            Number of obs   =        189
LR chi2(3)      =       8.33
Prob > chi2     =     0.0396
Log likelihood = -255.48592                       Pseudo R2       =     0.0160

------------------------------------------------------------------------------
bwt4 |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
smoke |   1.865204   .8603963     1.35   0.177     .7552264    4.606546
-------------+----------------------------------------------------------------
2            |
smoke |    2.31405   1.103573     1.76   0.079      .908727    5.892667
-------------+----------------------------------------------------------------
3            |
smoke |   3.291536   1.424503     2.75   0.006     1.409346    7.687402
------------------------------------------------------------------------------
(Outcome bwt4==0 is the comparison group)

constraint define 1 [2]smoke=2*[1]smoke
constraint define 2 [3]smoke=3*[1]smoke

* Stata 8 code.
mlogit bwt4 smoke, constraint(1 2) basecategory(0)

* Stata 9 code and outcome.
mlogit bwt4 smoke, constraint(1 2) baseoutcome(0)

( 1) - 2.0 [1]smoke + [2]smoke = 0.0
( 2) - 3.0 [1]smoke + [3]smoke = 0.0

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -255.67704
Iteration 2:   log likelihood = -255.65281
Iteration 3:   log likelihood = -255.65281

Multinomial regression                            Number of obs   =        189
LR chi2(1)      =       8.00
Prob > chi2     =     0.0047
Log likelihood = -255.65281                       Pseudo R2       =     0.0154

------------------------------------------------------------------------------
bwt4 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
1            |
smoke |   .3695792   .1332141     2.77   0.006     .1084844     .630674
_cons |  -.1099797   .2106498    -0.52   0.602    -.5228458    .3028864
-------------+----------------------------------------------------------------
2            |
smoke |   .7391584   .2664281     2.77   0.006     .2169689    1.261348
_cons |  -.4414182   .2333447    -1.89   0.059    -.8987655     .015929
-------------+----------------------------------------------------------------
3            |
smoke |   1.108738   .3996422     2.77   0.006     .3254533    1.892022
_cons |  -.1750312   .2494677    -0.70   0.483    -.6639789    .3139164
------------------------------------------------------------------------------
(Outcome bwt4==0 is the comparison group)
Middle of page 295.
display exp(.3695792)
1.4471255
lrtest in middle of page 295
* Stata 8 code.
quietly mlogit  bwt4 smoke, basecategory(0)

* Stata 9 code.
quietly mlogit  bwt4 smoke, baseoutcome(0)

lrtest, saving(0)

* Stata 8 code.
quietly mlogit  bwt4 smoke, constraint(1 2) basecategory(0)

* Stata 9 code.
quietly mlogit  bwt4 smoke, constraint(1 2) baseoutcome(0)

lrtest, using(0)

Mlogit:  likelihood-ratio test                        chi2(2)     =       0.33
Prob > chi2 =     0.8463
Table 8.18, page 296.
NOTE: Logit 1:
logit bwt4 smoke if bwt4 == 0 | bwt4 == 1

Iteration 0:   log likelihood = -63.769541
Iteration 1:   log likelihood = -62.840162
Iteration 2:   log likelihood = -62.840008

Logit estimates                                   Number of obs   =         92
LR chi2(1)      =       1.86
Prob > chi2     =     0.1727
Log likelihood = -62.840008                       Pseudo R2       =     0.0146

------------------------------------------------------------------------------
bwt4 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |   .6233703    .461288     1.35   0.177    -.2807376    1.527478
_cons |  -.1880522   .2511059    -0.75   0.454    -.6802108    .3041063
------------------------------------------------------------------------------
NOTE: Logit 2:
gen bwc2 = .
(189 missing values generated)

replace bwc2 = 0 if bwt4 == 0 | bwt4 == 1

replace bwc2 = 1 if bwt4 == 2

logit bwc2 smoke

Iteration 0:   log likelihood = -78.546655
Iteration 1:   log likelihood = -77.746128
Iteration 2:   log likelihood = -77.743614

Logit estimates                                   Number of obs   =        130
LR chi2(1)      =       1.61
Prob > chi2     =     0.2050
Log likelihood = -77.743614                       Pseudo R2       =     0.0102

------------------------------------------------------------------------------
bwc2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |   .5082248    .399114     1.27   0.203    -.2740243    1.290474
_cons |  -1.067841    .247142    -4.32   0.000     -1.55223   -.5834512
------------------------------------------------------------------------------

gen bwc3 = 0
replace bwc3 = 1 if bwt4 == 3

logit bwc3 smoke

Iteration 0:   log likelihood =   -117.336
Iteration 1:   log likelihood =  -114.9123
Iteration 2:   log likelihood =  -114.9023

Logit estimates                                   Number of obs   =        189
LR chi2(1)      =       4.87
Prob > chi2     =     0.0274
Log likelihood =  -114.9023                       Pseudo R2       =     0.0207

------------------------------------------------------------------------------
bwc3 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |   .7040592   .3196386     2.20   0.028     .0775791    1.330539
_cons |  -1.087051   .2147299    -5.06   0.000    -1.507914   -.6661886
------------------------------------------------------------------------------
Table 8.19, page 297.

NOTE: In order to get the result using Wolfe's program ocratio mentioned in the book on page 290, we need to recode the variable in reverse order. The Stata program ocratio can be downloaded from the internet (see How can I use the findit command to search for programs and get additional help? for more information about using findit).

gen bwt4_rec = bwt4
recode bwt4_rec 0 = 3 1 = 2 2 = 1 3 = 0

ocratio bwt4_rec smoke
Continuation-ratio logit Estimates                     Number of obs =     411
chi2(1)       =    8.19
Prob > chi2   =  0.0042
Log Likelihood = -255.5594                             Pseudo R2     =  0.0158
------------------------------------------------------------------------------
bwc3_rec |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |  -.6265962   .2192267    -2.86   0.004    -1.056273   -.1969197
------------------------------------------------------------------------------
_cut1   |  -1.052336   .1862181             (Ancillary parameters)
_cut2   |  -1.113813   .2129495
_cut3   |  -.1890080   .2204464
-----------------------------------------------------------------------------
Table 8.20, page 303.
gen bwt4n = 0
replace bwt4n = 1 if 2500 < bwt & bwt <=3000

replace bwt4n = 2 if 3000 < bwt & bwt <=3500

replace bwt4n = 3 if bwt > 3500

ologit  bwt4n lwt

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -255.15519
Iteration 2:   log likelihood = -255.14768

Ordered logit estimates                           Number of obs   =        189
LR chi2(1)      =       9.01
Prob > chi2     =     0.0027
Log likelihood = -255.14768                       Pseudo R2       =     0.0173

------------------------------------------------------------------------------
bwt4n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt |   .0127375   .0043168     2.95   0.003     .0042767    .0211982
-------------+----------------------------------------------------------------
_cut1 |   .8316033   .5686351          (Ancillary parameters)
_cut2 |    1.70695   .5781657
_cut3 |   2.831112    .602725
------------------------------------------------------------------------------
Table 8.21, page 304.
ologit bwt4n smoke

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -255.67803
Iteration 2:   log likelihood =  -255.6725

Ordered logit estimates                           Number of obs   =        189
LR chi2(1)      =       7.96
Prob > chi2     =     0.0048
Log likelihood =  -255.6725                       Pseudo R2       =     0.0153

------------------------------------------------------------------------------
bwt4n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |  -.7607847   .2718672    -2.80   0.005    -1.293635   -.2279348
-------------+----------------------------------------------------------------
_cut1 |  -1.116297   .1984448          (Ancillary parameters)
_cut2 |  -.2476773   .1819248
_cut3 |   .8667339   .1937335
------------------------------------------------------------------------------
Table 8.22, page 306.
gen ptd = 1
replace ptd = 0 if ptl == 0

xi: ologit bwt4n age lwt i.race smoke ht ui ptd

i.race            _Irace_1-3          (naturally coded; _Irace_1 omitted)

Iteration 0:   log likelihood = -259.65219
Iteration 1:   log likelihood = -235.91069
Iteration 2:   log likelihood = -235.65121
Iteration 3:   log likelihood = -235.65042

Ordered logit estimates                           Number of obs   =        189
LR chi2(8)      =      48.00
Prob > chi2     =     0.0000
Log likelihood = -235.65042                       Pseudo R2       =     0.0924

------------------------------------------------------------------------------
bwt4n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .0006257   .0274693     0.02   0.982    -.0532131    .0544645
lwt |   .0128958   .0048733     2.65   0.008     .0033442    .0224473
_Irace_2 |  -1.470897   .4346912    -3.38   0.001    -2.322876   -.6189183
_Irace_3 |   -.869222   .3344913    -2.60   0.009    -1.524813   -.2136312
smoke |  -.9877202   .3149779    -3.14   0.002    -1.605066   -.3703748
ht |     -1.194   .6122466    -1.95   0.051    -2.393982    .0059809
ui |  -.9129658   .4044862    -2.26   0.024    -1.705744   -.1201874
ptd |  -.8219579   .4173644    -1.97   0.049    -1.639977   -.0039387
-------------+----------------------------------------------------------------
_cut1 |  -.4952642     .87984          (Ancillary parameters)
_cut2 |   .5160991   .8816949
_cut3 |   1.803489   .8913835
------------------------------------------------------------------------------

lincom age*10

( 1)  10.0 age = 0.0

------------------------------------------------------------------------------
bwt4n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |    .006257   .2746928     0.02   0.982     -.532131     .544645
------------------------------------------------------------------------------

lincom lwt*10

( 1)  10.0 lwt = 0.0

------------------------------------------------------------------------------
bwt4n |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |   .1289576   .0487331     2.65   0.008     .0334424    .2244728
------------------------------------------------------------------------------
Table 8.23, page 307.
di exp(-.006257)
.99376253

di exp(-.1289576)
.87901123

di exp(1.470897)
4.3531382

di exp(.869222)
2.3850546

di exp(.9877202)
2.685106

di exp(1.194)
3.3002559

di exp(.9129658)
2.4917015

di exp(.8219579)
2.2749496
Table 8.24, page 319.
use clslowbwt.dta, clear

list id smoke race age lwt bwt low if id == 1 | id == 2 |id == 43

Observation 1

id            1       smoke            1        race            3
age           28         lwt          120         bwt         2865
low            0

Observation 2

id            1       smoke            1        race            3
age           33         lwt          141         bwt         2609
low            0

Observation 3

id            2       smoke            0        race            1
age           29         lwt          130         bwt         2613
low            0

Observation 4

id            2       smoke            0        race            1
age           34         lwt          151         bwt         3125
low            0

Observation 5

id            2       smoke            0        race            1
age           37         lwt          144         bwt         2481
low            1

Observation 109

id           43       smoke            1        race            2
age           24         lwt          105         bwt         2679
low            0

Observation 110

id           43       smoke            1        race            2
age           30         lwt          131         bwt         2240
low            1

Observation 111

id           43       smoke            1        race            2
age           35         lwt          121         bwt         2172
low            1

Observation 112

id           43       smoke            1        race            2
age           41         lwt          141         bwt         1853
low            1
Table 8.25, page 320.
NOTE: See text at the bottom of page 319.
xtlogit low age lwt smoke, i(id) pa robust

Iteration 1: tolerance = .09292774
Iteration 2: tolerance = .00535895
Iteration 3: tolerance = .00003964
Iteration 4: tolerance = 9.801e-07

GEE population-averaged model                   Number of obs      =       488
Group variable:                         id      Number of groups   =       188
Link:                                logit      Obs per group: min =         2
Family:                           binomial                     avg =       2.6
Correlation:                  exchangeable                     max =         4
Wald chi2(3)       =     13.46
Scale parameter:                         1      Prob > chi2        =    0.0037

(standard errors adjusted for clustering on id)
------------------------------------------------------------------------------
|             Semi-robust
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .0583975   .0195492     2.99   0.003     .0200818    .0967132
lwt |  -.0091427   .0040935    -2.23   0.026    -.0171658   -.0011196
smoke |   .7017452   .2829116     2.48   0.013     .1472486    1.256242
_cons |  -1.342052   .5895171    -2.28   0.023    -2.497484   -.1866194
------------------------------------------------------------------------------
Table 8.26, page 321.
NOTE: The computation of rho has been changed in Stata 7 as of April 6, 2001.
xtlogit low age lwt smoke, i(id) re

Fitting comparison model:

Iteration 0:   log likelihood = -301.89672
Iteration 1:   log likelihood = -288.88873
Iteration 2:   log likelihood = -288.76222
Iteration 3:   log likelihood = -288.76218

Fitting full model:

rho =  0.0     log likelihood = -288.76218
rho =  0.1     log likelihood =  -283.8448
rho =  0.2     log likelihood = -278.75435
rho =  0.3     log likelihood = -273.49059
rho =  0.4     log likelihood = -268.05351
rho =  0.5     log likelihood = -262.44808
rho =  0.6     log likelihood = -256.69965
rho =  0.7     log likelihood = -250.90472
rho =  0.8     log likelihood = -245.44398
Iteration 0:   log likelihood = -250.90472
Iteration 1:   log likelihood = -244.98109
Iteration 2:   log likelihood = -236.66884
Iteration 3:   log likelihood = -233.69517
Iteration 4:   log likelihood = -233.03016
Iteration 5:   log likelihood = -232.98816
Iteration 6:   log likelihood = -232.98805

Random-effects logit                            Number of obs      =       488
Group variable (i) : id                         Number of groups   =       188

Random effects u_i ~ Gaussian                   Obs per group: min =         2
avg =       2.6
max =         4

Wald chi2(3)       =     13.77
Log likelihood  = -232.98805                    Prob > chi2        =    0.0032

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .1409224   .0493303     2.86   0.004     .0442368    .2376079
lwt |  -.0152739     .00824    -1.85   0.064    -.0314241    .0008762
smoke |   1.860842   .6391547     2.91   0.004      .608122    3.113562
_cons |  -4.642465   1.677828    -2.77   0.006    -7.930948   -1.353982
-------------+----------------------------------------------------------------
/lnsig2u |   2.775743   .3674805                      2.055495    3.495992
-------------+----------------------------------------------------------------
sigma_u |   4.006314   .7361212                      2.794763    5.743081
rho |   .8298968   .0157686                      .7036307    .9093022
------------------------------------------------------------------------------
Likelihood ratio test of rho=0: chibar2(01) =   111.55 Prob >= chibar2 = 0.000
Table 8.27, page 322.
NOTE: The values in this table are given in the two outputs above and with the above equation (on page 317).
Bottom of page 320.
loneway low id

One-way Analysis of Variance for low:

Number of obs =       488
R-squared =    0.7571

Source                SS         df      MS            F     Prob > F
-------------------------------------------------------------------------
Between id             78.943306    187    .42215672      5.00     0.0000
Within id              25.333333    300    .08444444
-------------------------------------------------------------------------
Total                  104.27664    487    .21412041

Intraclass       Asy.
correlation      S.E.       [95% Conf. Interval]
------------------------------------------------
0.60648     0.03975       0.52856     0.68439

Estimated SD of id effect               .3607527
Estimated SD within id                  .2905933
Est. reliability of a id mean            .799969
(evaluated at n=2.59)
Table 8.28, page 322.
quietly xtlogit low age lwt smoke, i(id) re
lincom age*5

( 1)  5.0 [low]age = 0.0

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |    .704612   .2466513     2.86   0.004     .2211842     1.18804
------------------------------------------------------------------------------

lincom lwt*10

( 1)  10.0 [low]lwt = 0.0

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |  -.1527394   .0824004    -1.85   0.064    -.3142413    .0087624
------------------------------------------------------------------------------

quietly xtlogit low age lwt smoke, i(id) pa robust
lincom age*5

( 1)  5.0 age = 0.0

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |   .2919875   .0977459     2.99   0.003     .1004091     .483566
------------------------------------------------------------------------------

lincom lwt*10

( 1)  10.0 lwt = 0.0

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |  -.0914273   .0409349    -2.23   0.026    -.1716582   -.0111964
------------------------------------------------------------------------------

di exp(.704612)
2.0230616

di exp(-.1527394)
.85835338

di exp(1.861)
6.4301637

di exp(.2919875)
1.3390863

di exp(-.0914273)
.91262766

di exp(.702)
2.0177842
Table 8.29, page 326.
xtlogit low age lwt smoke, i(id)

Fitting comparison model:

Iteration 0:   log likelihood = -301.89672
Iteration 1:   log likelihood = -288.88873
Iteration 2:   log likelihood = -288.76222
Iteration 3:   log likelihood = -288.76218

Fitting full model:

tau =  0.0     log likelihood = -288.76218
tau =  0.1     log likelihood =  -283.8448
tau =  0.2     log likelihood = -278.75435
tau =  0.3     log likelihood = -273.49059
tau =  0.4     log likelihood = -268.05351
tau =  0.5     log likelihood = -262.44808
tau =  0.6     log likelihood = -256.69965
tau =  0.7     log likelihood = -250.90472
tau =  0.8     log likelihood = -245.44398
Iteration 0:   log likelihood = -250.90472
Iteration 1:   log likelihood = -244.98109
Iteration 2:   log likelihood = -236.66884
Iteration 3:   log likelihood = -233.69517
Iteration 4:   log likelihood = -233.03016
Iteration 5:   log likelihood = -232.98816
Iteration 6:   log likelihood = -232.98805

Random-effects logistic regression              Number of obs      =       488
Group variable (i): id                          Number of groups   =       188

Random effects u_i ~ Gaussian                   Obs per group: min =         2
avg =       2.6
max =         4

Wald chi2(3)       =     13.77
Log likelihood  = -232.98805                    Prob > chi2        =    0.0032

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .1409224   .0493303     2.86   0.004     .0442368    .2376079
lwt |  -.0152739     .00824    -1.85   0.064    -.0314241    .0008762
smoke |   1.860842   .6391547     2.91   0.004      .608122    3.113562
_cons |  -4.642465   1.677828    -2.77   0.006    -7.930948   -1.353982
-------------+----------------------------------------------------------------
/lnsig2u |   2.775743   .3674805                      2.055495    3.495992
-------------+----------------------------------------------------------------
sigma_u |   4.006314   .7361212                      2.794763    5.743081
rho |   .8298968   .0518765                      .7036307    .9093022
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) =   111.55 Prob >= chibar2 = 0.000
Table 8.30, page 329.
tsset id birth

panel variable:  id, 1 to 188
time variable:  birth, 1 to 4

gen prevlow = l.low
(188 missing values generated)

logit low age lwt smoke prevlow

Iteration 0:   log likelihood = -189.53785
Iteration 1:   log likelihood = -118.72848
Iteration 2:   log likelihood = -114.25647
Iteration 3:   log likelihood = -113.99221
Iteration 4:   log likelihood = -113.99062

Logit estimates                                   Number of obs   =        300
LR chi2(4)      =     151.09
Prob > chi2     =     0.0000
Log likelihood = -113.99062                       Pseudo R2       =     0.3986

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
age |   .0801916   .0337502     2.38   0.017     .0140425    .1463408
lwt |  -.0166757   .0065635    -2.54   0.011      -.02954   -.0038113
smoke |   1.687073   .3612794     4.67   0.000     .9789783    2.395167
prevlow |   3.414563   .3892281     8.77   0.000     2.651689    4.177436
_cons |  -2.490903   1.259569    -1.98   0.048    -4.959614   -.0221929
------------------------------------------------------------------------------
Table 8.31, page 333.
use lowbwt.dta, clear
(Hosmer and Lemeshow - from appendix 1)
tab2 low ptl if age >=30

-> tabulation of low by ptl if age >=30

| history of premature
|         labor
< 2500g |         0          1 |     Total
-----------+----------------------+----------
0 |        19          4 |        23
1 |         2          2 |         4
-----------+----------------------+----------
Total |        21          6 |        27 
Table 8.32, page 334.  We thank Silvano Andorno for providing the code for this example.
quietly: exlogistic low ptl if age >=30, saving(distrib)
use distrib, clear
egen sum1=total(_f_)
generate p = _f_/ sum1
list ptl _f_ p, noobs sum(_f_ p)
      +------------------------+
| ptl     _f_          p |
|------------------------|
|   0    5985   .3410257 |
|   1    7980   .4547009 |
|   2    3150   .1794872 |
|   3     420   .0239316 |
|   4      15   .0008547 |
|------------------------|
Sum |       17550          1 |
+------------------------+
Table 8.33, page 335.
MLE:
logit low ptl if age >=30

Iteration 0:   log likelihood = -11.326051
Iteration 1:   log likelihood = -10.547126
Iteration 2:   log likelihood = -10.423619
Iteration 3:   log likelihood = -10.423421

Logit estimates                                   Number of obs   =         27
LR chi2(1)      =       1.81
Prob > chi2     =     0.1791
Log likelihood = -10.423421                       Pseudo R2       =     0.0797

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptl |   1.558145   1.141323     1.37   0.172    -.6788077    3.795097
_cons |  -2.251292   .7433911    -3.03   0.002    -3.708312   -.7942721
------------------------------------------------------------------------------
Table 8.34, page 336.
tab2 low smoke if age >=30

-> tabulation of low by smoke if age >=30

|         smoke
< 2500g |         0          1 |     Total
-----------+----------------------+----------
0 |        17          6 |        23
1 |         0          4 |         4
-----------+----------------------+----------
Total |        17         10 |        27 
Table 8.35, page 336.
NOTE: LogExact is needed to make this table.
Table 8.36, page 338.
gen ptd = 1
replace ptd = 0 if ptl == 0
logit low lwt smoke ptd if age >=25
Iteration 0:   log likelihood = -40.607858
Iteration 1:   log likelihood = -35.561288
Iteration 2:   log likelihood = -35.277974
Iteration 3:   log likelihood = -35.276275
Iteration 4:   log likelihood = -35.276275

Logistic regression                               Number of obs   =         69
LR chi2(3)      =      10.66
Prob > chi2     =     0.0137
Log likelihood = -35.276275                       Pseudo R2       =     0.1313

------------------------------------------------------------------------------
low |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt |  -.0193155    .011657    -1.66   0.098    -.0421628    .0035318
smoke |   .2489932   .6086556     0.41   0.682    -.9439498    1.441936
ptd |   1.392705   .6687296     2.08   0.037     .0820189    2.703391
_cons |   1.096696   1.559898     0.70   0.482    -1.960647     4.15404
------------------------------------------------------------------------------
exlogistic low lwt smoke ptd if age>=25, mem(1000m) coef
Enumerating sample-space combinations:
observation 1: enumerations = 2
observation 2: enumerations = 4
observation 3: enumerations = 8
observation 4: enumerations = 16
observation 5: enumerations = 32
observation 6: enumerations = 64
...
observation 65:  enumerations =     969120
observation 66:  enumerations =     813626
observation 67:  enumerations =     639700
observation 68:  enumerations =     479915
observation 69:  enumerations =     250420

Exact logistic regression                        Number of obs =         69
Model score   =   10.29496
Pr >= score   =     0.0130
---------------------------------------------------------------------------
low |      Coef.       Suff.  2*Pr(Suff.)     [95% Conf. Interval]
-------------+-------------------------------------------------------------
lwt |  -.0184291        2309      0.0833       -.04257    .0021023
smoke |   .2563555           9      0.8825     -1.111262    1.567583
pt101 |   1.310344           8      0.0806       -.13651    2.798213
---------------------------------------------------------------------------

Table 8.37, page 344.
use uis.dta, clear

gen ages = (age-32)/6
gen  ndrugtxs = (ndrugtx-5)/5
logit dfree  ages ndrugtxs ivhx2 ivhx3 race treat

Iteration 0:   log likelihood = -326.86446
Iteration 1:   log likelihood = -310.42821
Iteration 2:   log likelihood = -309.86176
Iteration 3:   log likelihood =  -309.8567
Iteration 4:   log likelihood =  -309.8567

Logit estimates                                   Number of obs   =        575
LR chi2(6)      =      34.02
Prob > chi2     =     0.0000
Log likelihood =  -309.8567                       Pseudo R2       =     0.0520

------------------------------------------------------------------------------
dfree |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
ages |    .305763   .1038541     2.94   0.003     .1022126    .5093134
ndrugtxs |  -.3159991   .1282624    -2.46   0.014    -.5673889   -.0646094
ivhx2 |  -.5928725   .2864333    -2.07   0.038    -1.154272   -.0314735
ivhx3 |  -.7600441   .2489941    -3.05   0.002    -1.248064   -.2720245
race |   .2081089    .221453     0.94   0.347    -.2259309    .6421488
treat |    .438959   .1991429     2.20   0.028     .0486461     .829272
_cons |  -1.041049   .2097129    -4.96   0.000    -1.452079   -.6300195
------------------------------------------------------------------------------

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