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Stata Textbook Examples
Applied Logistic Regression, Second Edition, by Hosmer and Lemeshow
Chapter 7: Logistic Regression for Matched Case-Control Studies
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 7.1, page 232.
Part 1: on variable lwt.
use lowbwt11, clear
clogit low lwt, group(pair)
(Intermediate results omitted)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 2.51
Prob > chi2 = 0.1131
Log likelihood = -37.561103 Pseudo R2 = 0.0323
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0093749 .0061654 -1.52 0.128 -.0214589 .0027091
------------------------------------------------------------------------------
gen lwt10 = lwt/10
clogit low lwt10, group(pair) or
(Intermediate results omitted)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 2.51
Prob > chi2 = 0.1131
Log likelihood = -37.561103 Pseudo R2 = 0.0323
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt10 | .9105114 .0561368 -1.52 0.128 .8068732 1.027461
------------------------------------------------------------------------------
Part 2: on variable smoke.
clogit low smoke, group(pair)
(Intermediate results omitted)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 6.79
Prob > chi2 = 0.0091
Log likelihood = -35.419282 Pseudo R2 = 0.0875
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke | 1.011601 .4128614 2.45 0.014 .2024075 1.820794
------------------------------------------------------------------------------
clogit low smoke, group(pair) or
(Intermediate results omitted)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 6.79
Prob > chi2 = 0.0091
Log likelihood = -35.419282 Pseudo R2 = 0.0875
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke | 2.75 1.135369 2.45 0.014 1.224347 6.176763
------------------------------------------------------------------------------
The code below shows how to compute the number of discordant pairs corresponding to the last column of the table.
sort pair
* Stata 8 code.
egen test = sum(smoke), by(pair)
* Stata 9 code.
egen test = total(smoke), by(pair)
list pair smoke test in 1/20
pair smoke test
1. 1 0 1
2. 1 1 1
3. 2 0 0
4. 2 0 0
5. 3 0 0
6. 3 0 0
7. 4 0 1
8. 4 1 1
9. 5 1 2
10. 5 1 2
11. 6 0 1
12. 6 1 1
13. 7 0 0
14. 7 0 0
15. 8 0 0
16. 8 0 0
17. 9 1 1
18. 9 0 1
19. 10 1 2
20. 10 1 2
tab low smoke if test == 1
| smoke
low | 0 1 | Total
-----------+----------------------+----------
0 | 22 8 | 30
1 | 8 22 | 30
-----------+----------------------+----------
Total | 30 30 | 60
Part 3: on variable race.
xi3: clogit low c.race, group(pair)
c.race _Irace_1-3 (naturally coded; _Irace_1 omitted)
Iteration 0: log likelihood = -38.801591
Iteration 1: log likelihood = -38.787243
Iteration 2: log likelihood = -38.787243
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(2) = 0.06
Prob > chi2 = 0.9714
Log likelihood = -38.787243 Pseudo R2 = 0.0007
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Irace_2 | .0870496 .5233129 0.17 0.868 -.9386249 1.112724
_Irace_3 | -.0290003 .396792 -0.07 0.942 -.8066982 .7486977
------------------------------------------------------------------------------
xi3: clogit low c.race, group(pair) or
c.race _Irace_1-3 (naturally coded; _Irace_1 omitted)
Iteration 0: log likelihood = -38.801591
Iteration 1: log likelihood = -38.787243
Iteration 2: log likelihood = -38.787243
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(2) = 0.06
Prob > chi2 = 0.9714
Log likelihood = -38.787243 Pseudo R2 = 0.0007
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Irace_2 | 1.090951 .5709087 0.17 0.868 .3911654 3.042636
_Irace_3 | .9714162 .3854501 -0.07 0.942 .4463293 2.114245
------------------------------------------------------------------------------
Part 4: on variable ptd.
clogit low ptd, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 6.78
Prob > chi2 = 0.0092
Log likelihood = -35.424856 Pseudo R2 = 0.0874
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptd | 1.321756 .56273 2.35 0.019 .2188253 2.424686
------------------------------------------------------------------------------
clogit low ptd, group(pair) or
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 6.78
Prob > chi2 = 0.0092
Log likelihood = -35.424856 Pseudo R2 = 0.0874
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ptd | 3.75 2.110237 2.35 0.019 1.244614 11.29869
------------------------------------------------------------------------------
The code below shows how to compute the number of discordant pairs corresponding to the last column of the table.
sort pair
* Stata 8 code.
egen test = sum(ptd), by(pair)
* Stata 9 code.
egen test = total(ptd), by(pair)
list pair ptd test in 1/20
pair ptd test
1. 1 0 1
2. 1 1 1
3. 2 0 0
4. 2 0 0
5. 3 0 0
6. 3 0 0
7. 4 0 1
8. 4 1 1
9. 5 0 0
10. 5 0 0
11. 6 0 0
12. 6 0 0
13. 7 0 0
14. 7 0 0
15. 8 0 0
16. 8 0 0
17. 9 0 0
18. 9 0 0
19. 10 0 1
20. 10 1 1
tab low ptd if test == 1
| ptd
low | 0 1 | Total
-----------+----------------------+----------
0 | 15 4 | 19
1 | 4 15 | 19
-----------+----------------------+----------
Total | 19 19 | 38
Part 5: on variable ht.
clogit low ht, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 1.65
Prob > chi2 = 0.1996
Log likelihood = -37.993413 Pseudo R2 = 0.0212
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ht | .8472979 .6900656 1.23 0.220 -.5052058 2.199801
-----------------------------------------------------------------------------
clogit low ht, group(pair) or
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 1.65
Prob > chi2 = 0.1996
Log likelihood = -37.993413 Pseudo R2 = 0.0212
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ht | 2.333333 1.610153 1.23 0.220 .6033814 9.023222
------------------------------------------------------------------------------
Part 6: on variable ui.
clogit low ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 4.19
Prob > chi2 = 0.0408
Log likelihood = -36.72325 Pseudo R2 = 0.0539
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ui | 1.098612 .5773502 1.90 0.057 -.0329732 2.230198
------------------------------------------------------------------------------
clogit low ui, group(pair) or
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(1) = 4.19
Prob > chi2 = 0.0408
Log likelihood = -36.72325 Pseudo R2 = 0.0539
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ui | 3 1.73205 1.90 0.057 .9675645 9.301706
------------------------------------------------------------------------------
Table 7.2, page 232.
xi: clogit low lwt i.race smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(7) = 26.04
Prob > chi2 = 0.0005
Log likelihood = -25.794271 Pseudo R2 = 0.3355
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0183757 .0100806 -1.82 0.068 -.0381333 .0013819
_Irace_2 | .5713643 .6896449 0.83 0.407 -.7803149 1.923044
_Irace_3 | -.0253148 .6992044 -0.04 0.971 -1.39573 1.345101
smoke | 1.400656 .6278396 2.23 0.026 .1701131 2.631199
ptd | 1.808009 .7886502 2.29 0.022 .2622829 3.353735
ht | 2.361152 1.086128 2.17 0.030 .2323797 4.489924
ui | 1.401929 .6961585 2.01 0.044 .0374836 2.766375
------------------------------------------------------------------------------
Table 7.3, page 233.
clogit low lwt smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0150834 .0081465 -1.85 0.064 -.0310503 .0008834
smoke | 1.479564 .5620191 2.63 0.008 .3780272 2.581102
ptd | 1.670594 .7468062 2.24 0.025 .206881 3.134308
ht | 2.329361 1.002549 2.32 0.020 .3644009 4.294322
ui | 1.344895 .693843 1.94 0.053 -.0150127 2.704802
------------------------------------------------------------------------------
Table 7.4, page 233.
fracpoly clogit low lwt smoke ptd ht ui, degree(2) compare group(pair)
-> gen double Ilwt__1 = X^3-2.057 if e(sample)
-> gen double Ilwt__2 = X^3*ln(X)-.4943 if e(sample)
(where: X = lwt/100)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(6) = 26.39
Prob > chi2 = 0.0002
Log likelihood = -25.619273 Pseudo R2 = 0.3400
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Ilwt__1 | .1293646 .7216141 0.18 0.858 -1.284973 1.543702
Ilwt__2 | -.4866156 .9224357 -0.53 0.598 -2.294556 1.321325
smoke | 1.587445 .5772395 2.75 0.006 .4560765 2.718814
ptd | 1.482725 .7515386 1.97 0.049 .0097367 2.955714
ht | 2.776714 1.174591 2.36 0.018 .4745582 5.07887
ui | 1.441683 .7313612 1.97 0.049 .0082417 2.875125
------------------------------------------------------------------------------
Deviance: 51.23855. Best powers of lwt among 44 models fit: 3 3.
Fractional polynomial model comparisons:
---------------------------------------------------------------
lwt df Deviance Gain P(term) Powers
---------------------------------------------------------------
Not in model 0 56.299 -- --
Linear 1 52.474 0.000 0.050 1
m = 1 2 51.541 0.933 0.334 3
m = 2 4 51.239 1.235 0.860 3 3
---------------------------------------------------------------
Table 7.5, page 234.
sum lwt, de
lwt
-------------------------------------------------------------
Percentiles Smallest
1% 85 80
5% 91 85
10% 95 89 Obs 112
25% 106.5 90 Sum of Wgt. 112
50% 120 Mean 127.1696
Largest Std. Dev. 30.46986
75% 136.5 200
90% 168 215 Variance 928.4124
95% 190 235 Skewness 1.434646
99% 235 241 Kurtosis 5.353944
di (80+106.5)/2
93.25
di (106.5+120)/2
113.25
di (120+136.5)/2
128.25
di (136.5 + 241)/2
188.75
gen lwt1 = (lwt <= 106.5)
gen lwt2 = (lwt >106.5 & lwt <=120)
gen lwt3 = (lwt >120 & lwt <=136.5)
gen lwt4 = (lwt >136.5 )
clogit low lwt2-lwt4 smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(7) = 23.55
Prob > chi2 = 0.0014
Log likelihood = -27.040323 Pseudo R2 = 0.3034
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt2 | -.3990522 .6634445 -0.60 0.548 -1.69938 .9012751
lwt3 | -.4430378 .6717904 -0.66 0.510 -1.759723 .8736472
lwt4 | -.8887328 .6254553 -1.42 0.155 -2.114603 .3371371
smoke | 1.352736 .5567867 2.43 0.015 .2614543 2.444018
ptd | 1.739829 .7461841 2.33 0.020 .2773346 3.202323
ht | 1.892555 .9646519 1.96 0.050 .0018721 3.783238
ui | 1.316209 .688568 1.91 0.056 -.0333594 2.665777
------------------------------------------------------------------------------
Figure 7.1, page 234.
preserve clear input coef2go lwt2go 0 93.25 -.399 113.25 -.433 128.25 -.889 188.75 end graph twoway scatter coef2go lwt2go, /// connect(l) ylabel(-1(.25)0) xlabel(93.25 113.5 128.5 188.75)
restore
Table 7.6, page 235. This is fairly long table comparing a lot of possible interaction terms with model presented in Table 7.3. We only present code for the first row of the table testing interaction term on age and lwt. The other rows of the table can be generated exactly the same way and we omit them here.
gen agelwt = age*lwt
clogit low lwt smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0150834 .0081465 -1.85 0.064 -.0310503 .0008834
smoke | 1.479564 .5620191 2.63 0.008 .3780272 2.581102
ptd | 1.670594 .7468062 2.24 0.025 .206881 3.134308
ht | 2.329361 1.002549 2.32 0.020 .3644009 4.294322
ui | 1.344895 .693843 1.94 0.053 -.0150127 2.704802
------------------------------------------------------------------------------
fitstat, saving(m0)
Measures of Fit for clogit of low
Log-Lik Intercept Only: -38.816 Log-Lik Full Model: -26.237
D(51): 52.474 LR(5): 25.159
Prob > LR: 0.000
McFadden's R2: 0.324 McFadden's Adj R2: 0.195
Maximum Likelihood R2: 0.362 Cragg & Uhler's R2: 0.483
Count R2: 0.750
AIC: 1.116 AIC*n: 62.474
BIC: -152.819 BIC': -5.032
(Indices saved in matrix fs_m0)
clogit low lwt smoke ptd ht ui agelwt, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(6) = 25.66
Prob > chi2 = 0.0003
Log likelihood = -25.984088 Pseudo R2 = 0.3306
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | .0226658 .0541908 0.42 0.676 -.0835461 .1288778
smoke | 1.502073 .5683783 2.64 0.008 .3880719 2.616074
ptd | 1.633939 .751427 2.17 0.030 .1611697 3.106709
ht | 2.289793 1.004234 2.28 0.023 .3215311 4.258056
ui | 1.391004 .709504 1.96 0.050 .0004015 2.781606
agelwt | -.0016997 .0024358 -0.70 0.485 -.0064739 .0030744
------------------------------------------------------------------------------
fitstat, using(m0)
Measures of Fit for clogit of low
Current Saved Difference
Model: clogit clogit
N: 56 56 0
Log-Lik Intercept Only: -38.816 -38.816 0.000
Log-Lik Full Model: -25.984 -26.237 0.253
D: 51.968(50) 52.474(51) 0.506(1)
LR: 25.664(6) 25.159(5) 0.506(1)
Prob > LR: 0.000 0.000 0.477
McFadden's R2: 0.331 0.324 0.007
McFadden's Adj R2: 0.176 0.195 -0.019
Maximum Likelihood R2: 0.368 0.362 0.006
Cragg & Uhler's R2: 0.490 0.483 0.008
Count R2: 0.768 0.750 0.018
AIC: 1.142 1.116 0.027
AIC*n: 63.968 62.474 1.494
BIC: -149.299 -152.819 3.520
BIC': -1.512 -5.032 3.520
Difference of 3.520 in BIC' provides positive support for saved model.
Note: p-value for difference in LR is only valid if models are nested.
Figure 7.2, page 237.
clogit low lwt smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0150834 .0081465 -1.85 0.064 -.0310503 .0008834
smoke | 1.479564 .5620191 2.63 0.008 .3780272 2.581102
ptd | 1.670594 .7468062 2.24 0.025 .206881 3.134308
ht | 2.329361 1.002549 2.32 0.020 .3644009 4.294322
ui | 1.344895 .693843 1.94 0.053 -.0150127 2.704802
------------------------------------------------------------------------------
You can download clfit from within Stata by typing findit clfit (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
clfit predict p (option pc1 assumed; conditional probability for single outcome within group) graph twoway scatter _dx2 p if low == 1, ylabel(0(2)10) xlabel(0(.25)1)
Figure 7.3, page 238.
graph twoway scatter _dbeta p if low == 1, ylabel(0(.25)1.25) xlabel(0(.25)1)
Figure 7.4, page 249.
graph twoway scatter _dx2 p if low==1 [w=_dbeta], /// msymbol(oh) ylabel(0(2)10) xlabel(0(.25)1)
Table 7.7, page 240. We first use summarize command to find out the extreme cases using _dbeta.
sum _dbeta, de
Delta-Beta influence statistics
-------------------------------------------------------------
Percentiles Smallest
1% 2.06e-08 1.06e-09
5% 8.24e-07 2.06e-08
10% .0000229 2.90e-08 Obs 112
25% .0004128 1.39e-07 Sum of Wgt. 112
50% .0047458 Mean .0326452
Largest Std. Dev. .0904789
75% .0285309 .3247977
90% .0711812 .3630173 Variance .0081864
95% .0850838 .4022526 Skewness 5.396415
99% .4022526 .7241585 Kurtosis 36.17471
format _hat _dx2 _dbeta p %4.2f
list pair low lwt smoke ptd ht ui p _dbeta _dx2 _hat ///
if pair==9 | pair == 16 | pair==27 | pair==34
pair low lwt smoke ptd ht ui p _db~a _dx2 _hat
17. 9 0 100 1 0 0 0 0.90 0.00 0.91 0.00
18. 9 1 148 0 0 0 0 0.10 0.40 8.54 0.04
31. 16 0 169 0 1 0 1 0.69 0.06 0.74 0.07
32. 16 1 120 1 0 0 0 0.31 0.36 1.83 0.17
53. 27 0 95 0 0 1 0 0.80 0.04 0.83 0.04
54. 27 1 130 1 0 0 0 0.20 0.72 3.77 0.16
67. 34 0 90 1 1 0 0 0.89 0.00 0.89 0.01
68. 34 1 128 0 1 0 0 0.11 0.32 7.21 0.04
Table 7.8, page 241. We will only perform analysis on deleting pair number 9. The other analyses are the same.
clogit low lwt smoke ptd ht ui , group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0150834 .0081465 -1.85 0.064 -.0310503 .0008834
smoke | 1.479564 .5620191 2.63 0.008 .3780272 2.581102
ptd | 1.670594 .7468062 2.24 0.025 .206881 3.134308
ht | 2.329361 1.002549 2.32 0.020 .3644009 4.294322
ui | 1.344895 .693843 1.94 0.053 -.0150127 2.704802
------------------------------------------------------------------------------
matrix all=e(b)
clogit low lwt smoke ptd ht ui if pair~=9, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 110
LR chi2(5) = 28.91
Prob > chi2 = 0.0000
Log likelihood = -23.665784 Pseudo R2 = 0.3792
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt | -.0196132 .009098 -2.16 0.031 -.037445 -.0017814
smoke | 1.878073 .6545208 2.87 0.004 .5952357 3.16091
ptd | 1.883064 .8279104 2.27 0.023 .2603895 3.505739
ht | 2.719296 1.118355 2.43 0.015 .5273607 4.911231
ui | 1.497879 .731723 2.05 0.041 .063728 2.932029
------------------------------------------------------------------------------
matrix del9 = e(b)
matrix diff = J(1,5,0)
local i = 1
while `i' <= 5 {
matrix diff[1,`i']= 100*abs((all[1,`i']-del9[1,`i'])/all[1,`i'])
local i = `i' + 1
}
matrix list diff
diff[1,5]
c1 c2 c3 c4 c5
r1 30.031356 26.934178 12.718221 16.739972 11.375172
Table 7.9, page 242.
gen lwt10 = lwt/10
clogit low lwt10 smoke ptd ht ui, group(pair)
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt10 | -.1508343 .0814652 -1.85 0.064 -.3105031 .0088345
smoke | 1.479564 .5620191 2.63 0.008 .3780272 2.581102
ptd | 1.670594 .7468062 2.24 0.025 .206881 3.134307
ht | 2.329361 1.002549 2.32 0.020 .3644009 4.294322
ui | 1.344895 .693843 1.94 0.053 -.0150127 2.704802
------------------------------------------------------------------------------
clogit low lwt10 smoke ptd ht ui, group(pair) or
Conditional (fixed-effects) logistic regression Number of obs = 112
LR chi2(5) = 25.16
Prob > chi2 = 0.0001
Log likelihood = -26.236872 Pseudo R2 = 0.3241
------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lwt10 | .8599902 .0700592 -1.85 0.064 .7330781 1.008874
smoke | 4.391033 2.467844 2.63 0.008 1.459403 13.21168
ptd | 5.315325 3.969518 2.24 0.025 1.229836 22.97272
ht | 10.27138 10.29757 2.32 0.020 1.439651 73.28251
ui | 3.837782 2.662818 1.94 0.053 .9850994 14.95135
------------------------------------------------------------------------------
use http://www.ats.ucla.edu/stat/stata/examples/alr2/bbdm13, clear
Table 7.11, page 246.
clogit fndx chk , group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 12.99
Prob > chi2 = 0.0003
Log likelihood = -62.817366 Pseudo R2 = 0.0937
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.245445 .38154 -3.26 0.001 -1.99325 -.4976404
------------------------------------------------------------------------------
clogit fndx chk , group(str) or
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 12.99
Prob > chi2 = 0.0003
Log likelihood = -62.817366 Pseudo R2 = 0.0937
------------------------------------------------------------------------------
fndx | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | .2878128 .1098121 -3.26 0.001 .1362519 .6079635
------------------------------------------------------------------------------
clogit fndx agmn, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 21.76
Prob > chi2 = 0.0000
Log likelihood = -58.432931 Pseudo R2 = 0.1570
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
agmn | .4717591 .1109862 4.25 0.000 .2542301 .689288
------------------------------------------------------------------------------
gen agmn2 = agmn/2
clogit fndx agmn2, group(str) or
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 21.76
Prob > chi2 = 0.0000
Log likelihood = -58.432931 Pseudo R2 = 0.1570
------------------------------------------------------------------------------
fndx | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
agmn2 | 2.569004 .5702478 4.25 0.000 1.662729 3.969245
------------------------------------------------------------------------------
clogit fndx wt, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 25.53
Prob > chi2 = 0.0000
Log likelihood = -56.551372 Pseudo R2 = 0.1841
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wt | -.035159 .0085993 -4.09 0.000 -.0520132 -.0183047
------------------------------------------------------------------------------
gen wt10 = wt/10
clogit fndx wt10, group(str) or
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(1) = 25.53
Prob > chi2 = 0.0000
Log likelihood = -56.551373 Pseudo R2 = 0.1841
------------------------------------------------------------------------------
fndx | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wt10 | .7035688 .0605018 -4.09 0.000 .5944419 .8327291
------------------------------------------------------------------------------
recode mst 2 3 = 2
(6 changes made)
xi: clogit fndx i.mst, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(3) = 7.28
Prob > chi2 = 0.0635
Log likelihood = -65.674935 Pseudo R2 = 0.0525
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Imst_2 | -.3584355 .5605431 -0.64 0.523 -1.45708 .7402089
_Imst_4 | -.7510264 .7904422 -0.95 0.342 -2.300265 .7982119
_Imst_5 | 1.248429 .6058547 2.06 0.039 .0609759 2.435883
------------------------------------------------------------------------------
xi: clogit fndx i.mst, group(str) or
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(3) = 7.28
Prob > chi2 = 0.0635
Log likelihood = -65.674935 Pseudo R2 = 0.0525
------------------------------------------------------------------------------
fndx | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_Imst_2 | .6987687 .39169 -0.64 0.523 .2329154 2.096373
_Imst_4 | .471882 .3729954 -0.95 0.342 .1002323 2.221565
_Imst_5 | 3.484865 2.111322 2.06 0.039 1.062873 11.4259
------------------------------------------------------------------------------
Table 7.12, page 247. Notice that variable mst has been recoded in the previous example.
xi: clogit fndx chk agmn wt i.mst, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(6) = 48.20
Prob > chi2 = 0.0000
Log likelihood = -45.214824 Pseudo R2 = 0.3477
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.121849 .4474471 -2.51 0.012 -1.998829 -.2448688
agmn | .3561333 .1291722 2.76 0.006 .1029605 .6093061
wt | -.0283565 .0099776 -2.84 0.004 -.0479122 -.0088009
_Imst_2 | -.2030472 .6472909 -0.31 0.754 -1.471714 1.06562
_Imst_4 | -.4915826 .8173094 -0.60 0.548 -2.09348 1.110314
_Imst_5 | 1.472195 .7582064 1.94 0.052 -.0138621 2.958252
------------------------------------------------------------------------------
Table 7.13, page 247.
gen nvmr = (mst==5)
clogit fndx chk agmn wt nvmr, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(4) = 47.75
Prob > chi2 = 0.0000
Log likelihood = -45.439011 Pseudo R2 = 0.3445
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.161303 .4469763 -2.60 0.009 -2.037361 -.285246
agmn | .3592472 .1278849 2.81 0.005 .1085973 .609897
wt | -.0282355 .0099785 -2.83 0.005 -.047793 -.0086781
nvmr | 1.593384 .7360284 2.16 0.030 .1507946 3.035973
------------------------------------------------------------------------------
We use clfit command to generate the diagnostic statistics and graph them against the predicted probability. As we mentioned before, you can download the program from the internet within Stata.
Figure 7.5, page 253.
clogit fndx chk agmn wt nvmr, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(4) = 47.75
Prob > chi2 = 0.0000
Log likelihood = -45.439011 Pseudo R2 = 0.3445
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.161303 .4469763 -2.60 0.009 -2.037361 -.285246
agmn | .3592472 .1278849 2.81 0.005 .1085973 .609897
wt | -.0282355 .0099785 -2.83 0.005 -.047793 -.0086781
nvmr | 1.593384 .7360284 2.16 0.030 .1507946 3.035973
------------------------------------------------------------------------------
clfit predict p (option pc1 assumed; conditional probability for single outcome within group) graph twoway scatter _dx2 p if _dx2 <= 20, ylabel(0(3)18) xlabel(0(.25)1)
Figure 7.6, page 254.
graph twoway scatter _dbeta p if _dx2 <= 20, ylabel(0(.25).75) xlabel(0(.25)1)
Figure 7.7, page 255.
graph twoway scatter _dx2 p [weight = _dbeta] if _dx2 <= 20 /// , msymbol(oh) ylabel(0(3)18) xlabel(0(.25)1)
Table 7.14, page 256. You can download hilo from within Stata by typing findit hilo to get the extreme values for variable _dx2 (see How can I use the findit command to search for programs and get additional help? for more information about using findit).
hilo _dx2, show(5) high
5 highest observations on _dx2
_dx2
4.3509183
7.2066903
13.215487
17.962026
84.545673
tab str if _dx2 >=4.3
str | Freq. Percent Cum.
------------+-----------------------------------
10 | 1 20.00 20.00
12 | 1 20.00 40.00
18 | 1 20.00 60.00
24 | 1 20.00 80.00
31 | 1 20.00 100.00
------------+-----------------------------------
Total | 5 100.00
format p _dbeta _dx2 _hat %4.2f
list str obs chk agmn wt nvmr p _dbeta _dx2 _hat if str == 10 | str == 12 | str ==18 | str == 24 | str ==31
str obs chk agmn wt nvmr p _db~a _dx2 _hat
37. 10 1 2 12 105 0 0.11 0.22 7.21 0.033
38. 10 2 1 13 115 0 0.39 0.01 0.40 0.02
39. 10 3 2 12 120 0 0.07 0.00 0.07 0.02
40. 10 4 1 16 150 0 0.42 0.02 0.45 0.05
45. 12 1 2 10 170 0 0.01 0.71 84.55 0.01
46. 12 2 1 13 140 0 0.26 0.02 0.27 0.06
47. 12 3 1 11 240 0 0.01 0.00 0.01 0.01
48. 12 4 2 16 100 0 0.73 0.02 0.75 0.03
69. 18 1 2 14 135 0 0.05 0.73 17.96 0.04
70. 18 2 1 14 132 1 0.89 0.01 0.90 0.01
71. 18 3 1 11 205 0 0.01 0.00 0.01 0.01
72. 18 4 1 10 127 0 0.05 0.00 0.05 0.03
93. 24 1 2 15 145 0 0.07 0.17 13.22 0.01
94. 24 2 1 13 140 0 0.12 0.00 0.12 0.01
95. 24 3 1 17 155 0 0.33 0.01 0.34 0.03
96. 24 4 1 15 116 0 0.48 0.01 0.49 0.02
121. 31 1 2 16 156 0 0.17 0.24 4.35 0.05
122. 31 2 2 12 161 0 0.03 0.00 0.03 0.01
123. 31 3 1 13 150 0 0.22 0.00 0.22 0.01
124. 31 4 1 13 115 0 0.58 0.01 0.60 0.02
Table 7.15, page 257. The analyses in this table is very similar to each other. We will perform the analysis corresponding to the first row and omit all the others.
clogit fndx chk agmn wt nvmr, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(4) = 47.75
Prob > chi2 = 0.0000
Log likelihood = -45.439011 Pseudo R2 = 0.3445
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.161303 .4469763 -2.60 0.009 -2.037361 -.285246
agmn | .3592472 .1278849 2.81 0.005 .1085973 .609897
wt | -.0282355 .0099785 -2.83 0.005 -.047793 -.0086781
nvmr | 1.593384 .7360284 2.16 0.030 .1507946 3.035973
------------------------------------------------------------------------------
matrix all=e(b)
clogit fndx chk agmn wt nvmr if str~=10, group(str)
Conditional (fixed-effects) logistic regression Number of obs = 196
LR chi2(4) = 49.65
Prob > chi2 = 0.0000
Log likelihood = -43.104413 Pseudo R2 = 0.3654
------------------------------------------------------------------------------
fndx | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | -1.342017 .4759564 -2.82 0.005 -2.274874 -.4091592
agmn | .4044 .1360889 2.97 0.003 .1376707 .6711294
wt | -.0254958 .0100782 -2.53 0.011 -.0452487 -.0057429
nvmr | 1.685185 .7548999 2.23 0.026 .2056084 3.164762
------------------------------------------------------------------------------
matrix del10 = e(b)
/*The following is from the do-file editor*/
matrix diff = J(1,4,0)
local i = 1
while `i' <= 4 {
matrix diff[1,`i']= 100*((del10[1,`i']-all[1,`i'])/all[1,`i'])
local i = `i' + 1
}
matrix list diff
diff[1,4]
c1 c2 c3 c4
r1 15.561224 12.568742 -9.7031755 5.761404
Table 7.16 on page 258.
clogit fndx chk agmn wt nvmr, group(str) or
Conditional (fixed-effects) logistic regression Number of obs = 200
LR chi2(4) = 47.75
Prob > chi2 = 0.0000
Log likelihood = -45.439011 Pseudo R2 = 0.3445
------------------------------------------------------------------------------
fndx | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
chk | .3130778 .1399384 -2.60 0.009 .1303723 .7518293
agmn | 1.432251 .1831633 2.81 0.005 1.114713 1.840242
wt | .9721594 .0097007 -2.83 0.005 .9533311 .9913594
nvmr | 4.92037 3.621532 2.16 0.030 1.162758 20.82123
------------------------------------------------------------------------------
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