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
(113 real changes made)
replace symptd = 1 if sympt == 3| sympt == 4
(299 real changes made)
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
(143 real changes made)
replace bwt4 = 2 if 2500 > bwt | bwt<=3000
(97 real changes made)
replace bwt4 = 3 if bwt<=2500
(59 real changes made)
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
(92 real changes made)
replace bwc2 = 1 if bwt4 == 2
(38 real changes made)
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
(59 real changes made)
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 search command to search for programs and get additional help? for more information about using search).
gen bwt4_rec = bwt4 recode bwt4_rec 0 = 3 1 = 2 2 = 1 3 = 0 (189 changes made) 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
(38 real changes made)
replace bwt4n = 2 if 3000 < bwt & bwt <=3500
(46 real changes made)
replace bwt4n = 3 if bwt > 3500
(46 real changes made)
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
(159 real changes made)
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
------------------------------------------------------------------------------