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Stata Textbook Examples
Practical Multivariate Analysis, Fifth Edition, by Afifi, May and Clark
Chapter 12: Logistic Regression
Table 12.1, page 273.
use http://www.ats.ucla.edu/stat/stata/examples/pma5/depress, clear
tab sex cases
| depressed is cesd >=16
|
sex | normal depressed | Total
-----------+----------------------+----------
male | 101 10 | 111
female | 143 40 | 183
-----------+----------------------+----------
Total | 244 50 | 294
Page 274. The odds ratios at the top of the page.
logit cases i.sex, or
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -129.82684
Iteration 2: log likelihood = -129.69892
Iteration 3: log likelihood = -129.69883
Iteration 4: log likelihood = -129.69883
Logistic regression Number of obs = 294
LR chi2(1) = 8.73
Prob > chi2 = 0.0031
Log likelihood = -129.69883 Pseudo R2 = 0.0325
------------------------------------------------------------------------------
cases | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
2.sex | 2.825175 1.06421 2.76 0.006 1.35023 5.911299
_cons | .0990099 .0328231 -6.98 0.000 .0517004 .1896108
------------------------------------------------------------------------------
logit cases i.sex
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -129.82684
Iteration 2: log likelihood = -129.69892
Iteration 3: log likelihood = -129.69883
Iteration 4: log likelihood = -129.69883
Logistic regression Number of obs = 294
LR chi2(1) = 8.73
Prob > chi2 = 0.0031
Log likelihood = -129.69883 Pseudo R2 = 0.0325
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
2.sex | 1.03857 .3766882 2.76 0.006 .3002749 1.776866
_cons | -2.312535 .3315132 -6.98 0.000 -2.962289 -1.662782
------------------------------------------------------------------------------
Page 275. Top of the page.
logit cases age income i.sex
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -124.45941
Iteration 2: log likelihood = -123.7712
Iteration 3: log likelihood = -123.76979
Iteration 4: log likelihood = -123.76979
Logistic regression Number of obs = 294
LR chi2(3) = 20.58
Prob > chi2 = 0.0001
Log likelihood = -123.76979 Pseudo R2 = 0.0768
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0209575 .0090401 -2.32 0.020 -.0386759 -.0032392
income | -.0365635 .0140897 -2.60 0.009 -.0641787 -.0089482
2.sex | .9294487 .3858256 2.41 0.016 .1732444 1.685653
_cons | -.6764559 .5788124 -1.17 0.243 -1.810907 .4579956
------------------------------------------------------------------------------
Page 275. The coefficients at the bottom of the page.
logit cases age income
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -127.42024
Iteration 2: log likelihood = -127.01794
Iteration 3: log likelihood = -127.01305
Iteration 4: log likelihood = -127.01304
Logit estimates Number of obs = 294
LR chi2(2) = 14.10
Prob > chi2 = 0.0009
Log likelihood = -127.01304 Pseudo R2 = 0.0526
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0201671 .0088966 -2.27 0.023 -.0376041 -.0027301
income | -.0413479 .0140587 -2.94 0.003 -.0689025 -.0137933
_cons | .0279774 .4872007 0.06 0.954 -.9269184 .9828732
------------------------------------------------------------------------------
Page 276. Coefficients at the top.
logit cases age income
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -127.42024
Iteration 2: log likelihood = -127.01794
Iteration 3: log likelihood = -127.01305
Iteration 4: log likelihood = -127.01304
Logit estimates Number of obs = 294
LR chi2(2) = 14.10
Prob > chi2 = 0.0009
Log likelihood = -127.01304 Pseudo R2 = 0.0526
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0201671 .0088966 -2.27 0.023 -.0376041 -.0027301
income | -.0413479 .0140587 -2.94 0.003 -.0689025 -.0137933
_cons | .0279774 .4872007 0.06 0.954 -.9269184 .9828732
------------------------------------------------------------------------------
Page 277. These numbers are obtained from the output from page 276.
Page 278. Table at the top of the page.
gen duminc = income < 10
gen dumemp = employ == 2 | employ == 3
replace dumemp = . if employ == 7
logit cases duminc dumemp
Iteration 0: log likelihood = -131.73021
Iteration 1: log likelihood = -127.6761
Iteration 2: log likelihood = -127.42821
Iteration 3: log likelihood = -127.42796
Iteration 4: log likelihood = -127.42796
Logistic regression Number of obs = 290
LR chi2(2) = 8.60
Prob > chi2 = 0.0135
Log likelihood = -127.42796 Pseudo R2 = 0.0327
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
duminc | .2722943 .3376896 0.81 0.420 -.3895653 .9341538
dumemp | 1.028483 .3487121 2.95 0.003 .3450196 1.711946
_cons | -1.934537 .2259083 -8.56 0.000 -2.377309 -1.491765
------------------------------------------------------------------------------
Page 279. Table in the middle of the page.
logit cases duminc##dumemp
Iteration 0: log likelihood = -131.73021
Iteration 1: log likelihood = -125.18993
Iteration 2: log likelihood = -123.52872
Iteration 3: log likelihood = -123.31292
Iteration 4: log likelihood = -123.31287
Iteration 5: log likelihood = -123.31287
Logistic regression Number of obs = 290
LR chi2(3) = 16.83
Prob > chi2 = 0.0008
Log likelihood = -123.31287 Pseudo R2 = 0.0639
-------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------+----------------------------------------------------------------
1.duminc | -.3756121 .4349381 -0.86 0.388 -1.228075 .4768508
1.dumemp | .317535 .4520206 0.70 0.482 -.5684091 1.203479
|
duminc#dumemp |
1 1 | 2.198143 .7888295 2.79 0.005 .6520659 3.744221
|
_cons | -1.734601 .2214037 -7.83 0.000 -2.168544 -1.300658
-------------------------------------------------------------------------------
Page 280
di 2.198143/.7888294
2.7865886
di (2.7865886)^2
7.765076
* for likelihood ratio chi square
logit cases duminc dumemp
Iteration 0: log likelihood = -131.73021
Iteration 1: log likelihood = -127.6761
Iteration 2: log likelihood = -127.42821
Iteration 3: log likelihood = -127.42796
Logit estimates Number of obs = 290
LR chi2(2) = 8.60
Prob > chi2 = 0.0135
Log likelihood = -127.42796 Pseudo R2 = 0.0327
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
duminc | .2722943 .3376895 0.81 0.420 -.3895651 .9341536
dumemp | 1.028483 .3487117 2.95 0.003 .3450204 1.711945
_cons | -1.934537 .2259083 -8.56 0.000 -2.377309 -1.491765
------------------------------------------------------------------------------
di 16.83-8.6
8.23
Page 287. Middle of the page.
egen cage = cut(age), at(0, 28, 43, 59, 90)
logit cases i.cage income sex
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -124.32078
Iteration 2: log likelihood = -123.5791
Iteration 3: log likelihood = -123.57661
Iteration 4: log likelihood = -123.57661
Logistic regression Number of obs = 294
LR chi2(5) = 20.97
Prob > chi2 = 0.0008
Log likelihood = -123.57661 Pseudo R2 = 0.0782
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cage |
28 | .0747259 .4318019 0.17 0.863 -.7715902 .9210421
43 | -.5706276 .4743977 -1.20 0.229 -1.50043 .3591748
59 | -.8853103 .456306 -1.94 0.052 -1.779654 .0090329
|
income | -.0379521 .014852 -2.56 0.011 -.0670616 -.0088426
sex | .9238035 .3864416 2.39 0.017 .1663918 1.681215
_cons | -2.159495 .7830425 -2.76 0.006 -3.69423 -.62476
------------------------------------------------------------------------------
Figure 12.2, page 289.
gen female = (sex == 2)
logit cases i.cage income female
matrix b = e(b)
gen b0 = 0 in 1
svmat b
list b0 - b6 in 1
* The point of the next two commands is to drop all of the
* unnecessary variables and observations. You may need to
* modify the variable names on the drop command to match
* your variables.
drop sex - b1 b6 b7
keep in 1
reshape long b, i(id)
list
gen newage = 22.5
replace newage = 35 if _j == 2
replace newage = 50.5 if _j == 3
replace newage = 74 if _j == 4
sort newage
* You need to calculate the midpoint of each interval based on the
* table on page 287. The minimum of age is 18.
graph twoway scatter b newage in 1/4, msymbol(O) connect(L) ylabel(-1(.5)0, nogrid) ///
ytitle(Coefficient b) xlabel(20(10)80) xtitle(Age)
Figure 12.3, page 291.
use http://www.ats.ucla.edu/stat/stata/examples/pma5/depress, clear logit cases sex income age predict p predict db, db graph twoway scatter db p
Table 12.2, page 292.
logit cases age income sex
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -124.45941
Iteration 2: log likelihood = -123.78013
Iteration 3: log likelihood = -123.76979
Iteration 4: log likelihood = -123.76979
Logit estimates Number of obs = 294
LR chi2(3) = 20.58
Prob > chi2 = 0.0001
Log likelihood = -123.76979 Pseudo R2 = 0.0768
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0209575 .0090401 -2.32 0.020 -.0386758 -.0032392
income | -.0365635 .0140897 -2.60 0.009 -.0641787 -.0089482
sex | .9294487 .3858256 2.41 0.016 .1732444 1.685653
_cons | -1.605905 .8465372 -1.90 0.058 -3.265087 .0532779
------------------------------------------------------------------------------
list db in -4/l
+----------+
| db |
|----------|
291. | .0004829 |
292. | .0001442 |
293. | .0006498 |
294. | .0111896 |
+----------+
gen x = 0
replace x = 3 if db > .1637310
(5 real changes made)
replace x = 2 if db > .1789604
(4 real changes made)
replace x = 1 if db > .2084397
(3 real changes made)
logit cases age income sex if x ~= 1
Iteration 0: log likelihood = -131.91495
Iteration 1: log likelihood = -121.29438
Iteration 2: log likelihood = -120.39934
Iteration 3: log likelihood = -120.3796
Iteration 4: log likelihood = -120.37958
Logit estimates Number of obs = 291
LR chi2(3) = 23.07
Prob > chi2 = 0.0000
Log likelihood = -120.37958 Pseudo R2 = 0.0874
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0215037 .0091147 -2.36 0.018 -.0393683 -.0036391
income | -.0416866 .0149928 -2.78 0.005 -.071072 -.0123013
sex | 1.022995 .4007114 2.55 0.011 .2376152 1.808375
_cons | -1.692541 .8721181 -1.94 0.052 -3.401861 .016779
------------------------------------------------------------------------------
logit cases age income sex if x ~= 2
Iteration 0: log likelihood = -132.28233
Iteration 1: log likelihood = -121.82603
Iteration 2: log likelihood = -121.03222
Iteration 3: log likelihood = -121.01885
Iteration 4: log likelihood = -121.01885
Logit estimates Number of obs = 293
LR chi2(3) = 22.53
Prob > chi2 = 0.0001
Log likelihood = -121.01885 Pseudo R2 = 0.0851
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.023414 .0092536 -2.53 0.011 -.0415507 -.0052774
income | -.0357778 .0141515 -2.53 0.011 -.0635142 -.0080415
sex | 1.050539 .4007857 2.62 0.009 .2650138 1.836065
_cons | -1.756961 .871175 -2.02 0.044 -3.464433 -.0494895
------------------------------------------------------------------------------
logit cases age income sex if x ~= 3
Iteration 0: log likelihood = -132.28233
Iteration 1: log likelihood = -121.54471
Iteration 2: log likelihood = -120.67498
Iteration 3: log likelihood = -120.65779
Iteration 4: log likelihood = -120.65778
Logit estimates Number of obs = 293
LR chi2(3) = 23.25
Prob > chi2 = 0.0000
Log likelihood = -120.65778 Pseudo R2 = 0.0879
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0228888 .0092002 -2.49 0.013 -.0409209 -.0048567
income | -.0389067 .0145405 -2.68 0.007 -.0674056 -.0104078
sex | 1.04192 .4008515 2.60 0.009 .2562651 1.827574
_cons | -1.71381 .8720871 -1.97 0.049 -3.423069 -.0045506
------------------------------------------------------------------------------
logit cases age income sex if x == 0
Iteration 0: log likelihood = -128.31745
Iteration 1: log likelihood = -115.44875
Iteration 2: log likelihood = -114.1166
Iteration 3: log likelihood = -114.074
Iteration 4: log likelihood = -114.07392
Logit estimates Number of obs = 289
LR chi2(3) = 28.49
Prob > chi2 = 0.0000
Log likelihood = -114.07392 Pseudo R2 = 0.1110
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | -.0262663 .0095311 -2.76 0.006 -.0449469 -.0075856
income | -.0439743 .015642 -2.81 0.005 -.074632 -.0133166
sex | 1.30267 .4406845 2.96 0.003 .4389443 2.166396
_cons | -2.018118 .9403468 -2.15 0.032 -3.861163 -.1750718
------------------------------------------------------------------------------
Table 12.3, page 293.
list age income sex cases p if id == 288 | id==99 | id==143 | id == 232 | id == 68
+---------------------------------------+
| age income sex cases p |
|---------------------------------------|
68. | 40 45 1 1 .0406946 |
99. | 72 11 1 1 .069941 |
143. | 40 45 1 0 .0406946 |
232. | 40 45 1 0 .0406946 |
288. | 61 28 1 1 .0484001 |
+---------------------------------------+
Figure 12.4, page 294.
logit cases sex income age
Iteration 0: log likelihood = -134.06225
Iteration 1: log likelihood = -124.45941
Iteration 2: log likelihood = -123.78013
Iteration 3: log likelihood = -123.76979
Iteration 4: log likelihood = -123.76979
Logit estimates Number of obs = 294
LR chi2(3) = 20.58
Prob > chi2 = 0.0001
Log likelihood = -123.76979 Pseudo R2 = 0.0768
------------------------------------------------------------------------------
cases | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sex | .9294487 .3858256 2.41 0.016 .1732444 1.685653
income | -.0365635 .0140897 -2.60 0.009 -.0641787 -.0089482
age | -.0209575 .0090401 -2.32 0.020 -.0386758 -.0032392
_cons | -1.605905 .8465372 -1.90 0.058 -3.265087 .0532779
------------------------------------------------------------------------------
predict dx2, dx2
graph twoway scatter dx2 p [w = db], msymbol(Oh) ylabel(0(5)25, nogrid) xlabel(0(.1).5)
Figure 12.5, page 296.
lsens
Figure 12.6, page 297.
lroc
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