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Statistical Computing Seminars
Logistic Regression with Stata
This page has been updated to Stata 12.
The purpose of this seminar is to help you increase your skills in using logistic regression analysis with Stata. The seminar does not teach logistic regression, per se, but focuses on how to perform logistic regression analyses and interpret the results using Stata. It is assumed that you are familiar with Logistic Regression (e.g., have had a class in logistic regression or have read about logistic regression, see our Statistics Books for Loan for books you can borrow on logistic regression).
In addition to the built-in Stata commands we will be demonstrating the use of a number on user-written ados, in particular, listcoef, fitstat, prchange, prtab, prgen, etc. To find out more about these programs or to download them type findit followed by the program name in the Stata command window (example: findit listcoef). These add-on programs ease the running and interpretation of ordinal logistic models. Or, you can download the complete spostado package by typing the following in the Stata command window:
net from http://www.indiana.edu/~jslsoc/stata/ net install spost9_ado
We will use the hsbdemo dataset with the binary response variable honors (enrolled in an honors program). We will looks at some descriptive statistics before we begin our first logistic regression model.
use http://www.ats.ucla.edu/stat/data/hsbdemo, clear
describe honors read female prog
storage display value
variable name type format label variable label
---------------------------------------------------------------------------------
honors float %19.0g honlab honors english
read float %9.0g reading score
female float %9.0g fl
prog float %9.0g sel type of program
summarize honors read female prog
Variable | Obs Mean Std. Dev. Min Max
-------------+--------------------------------------------------------
honors | 200 .265 .4424407 0 1
read | 200 52.23 10.25294 28 76
female | 200 .545 .4992205 0 1
prog | 200 2.025 .6904772 1 3
tab1 honors female prog
-> tabulation of honors
honors |
english | Freq. Percent Cum.
-------------+-----------------------------------
not enrolled | 147 73.50 73.50
enrolled | 53 26.50 100.00
-------------+-----------------------------------
Total | 200 100.00
-> tabulation of female
female | Freq. Percent Cum.
------------+-----------------------------------
male | 91 45.50 45.50
female | 109 54.50 100.00
------------+-----------------------------------
Total | 200 100.00
-> tabulation of prog
type of |
program | Freq. Percent Cum.
------------+-----------------------------------
general | 45 22.50 22.50
academic | 105 52.50 75.00
vocation | 50 25.00 100.00
------------+-----------------------------------
Total | 200 100.00
logit honors read i.female i.prog
Iteration 0: log likelihood = -115.64441
Iteration 1: log likelihood = -86.845312
Iteration 2: log likelihood = -84.560995
Iteration 3: log likelihood = -84.542357
Iteration 4: log likelihood = -84.542348
Iteration 5: log likelihood = -84.542348
Logistic regression Number of obs = 200
LR chi2(4) = 62.20
Prob > chi2 = 0.0000
Log likelihood = -84.542348 Pseudo R2 = 0.2689
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .1352861 .0242218 5.59 0.000 .0878123 .18276
1.female | 1.08343 .4094357 2.65 0.008 .2809511 1.885909
|
prog |
2 | .5559416 .5053125 1.10 0.271 -.4344527 1.546336
3 | .0016408 .6611702 0.00 0.998 -1.294229 1.29751
|
_cons | -9.41691 1.481922 -6.35 0.000 -12.32142 -6.512397
------------------------------------------------------------------------------
contrast prog // multi degree of freedom test
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
prog | 2 1.78 0.4101
------------------------------------------------
estimates store m1
/* alternative to contrast: Wald test */
test 2.prog 3.prog
( 1) [honors]2.prog = 0
( 2) [honors]3.prog = 0
chi2( 2) = 1.78
Prob > chi2 = 0.4101
/* Likelihood ratio-test */
logit honors read i.female, nolog
Logistic regression Number of obs = 200
LR chi2(2) = 60.40
Prob > chi2 = 0.0000
Log likelihood = -85.44372 Pseudo R2 = 0.2612
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .1443657 .0233338 6.19 0.000 .0986322 .1900991
1.female | 1.120926 .4081043 2.75 0.006 .3210558 1.920795
_cons | -9.603364 1.426412 -6.73 0.000 -12.39908 -6.807647
------------------------------------------------------------------------------
lrtest m1 .
Likelihood-ratio test LR chi2(2) = 1.80
(Assumption: . nested in m1) Prob > chi2 = 0.4060
/* rerun full model */
logit honors read i.female i.prog, nolog /* displays coefficients */
Logistic regression Number of obs = 200
LR chi2(4) = 62.20
Prob > chi2 = 0.0000
Log likelihood = -84.542348 Pseudo R2 = 0.2689
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .1352861 .0242218 5.59 0.000 .0878123 .18276
1.female | 1.08343 .4094357 2.65 0.008 .2809511 1.885909
|
prog |
2 | .5559416 .5053125 1.10 0.271 -.4344527 1.546336
3 | .0016408 .6611702 0.00 0.998 -1.294229 1.29751
|
_cons | -9.41691 1.481922 -6.35 0.000 -12.32142 -6.512397
------------------------------------------------------------------------------
logit, or /* display odds ratios */
Logistic regression Number of obs = 200
LR chi2(4) = 62.20
Prob > chi2 = 0.0000
Log likelihood = -84.542348 Pseudo R2 = 0.2689
------------------------------------------------------------------------------
honors | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | 1.144864 .0277307 5.59 0.000 1.091783 1.200526
1.female | 2.954798 1.2098 2.65 0.008 1.324389 6.592347
|
prog |
2 | 1.743582 .8810538 1.10 0.271 .647619 4.694239
3 | 1.001642 .6622559 0.00 0.998 .2741091 3.660173
|
_cons | .0000813 .0001205 -6.35 0.000 4.46e-06 .0014849
------------------------------------------------------------------------------
Now we will demonstrate some of the utilities developed by J. Scott Long & Jeremy Freese.
listcoef
logit (N=200): Factor Change in Odds
Odds of: enrolled vs not_enro
----------------------------------------------------------------------
honors | b z P>|z| e^b e^bStdX SDofX
-------------+--------------------------------------------------------
read | 0.13529 5.585 0.000 1.1449 4.0031 10.2529
1.female | 1.08343 2.646 0.008 2.9548 1.7175 0.4992
2.prog | 0.55594 1.100 0.271 1.7436 1.3209 0.5006
3.prog | 0.00164 0.002 0.998 1.0016 1.0007 0.4341
----------------------------------------------------------------------
listcoef, percent
logit (N=200): Percentage Change in Odds
Odds of: enrolled vs not_enro
----------------------------------------------------------------------
honors | b z P>|z| % %StdX SDofX
-------------+--------------------------------------------------------
read | 0.13529 5.585 0.000 14.5 300.3 10.2529
1.female | 1.08343 2.646 0.008 195.5 71.8 0.4992
2.prog | 0.55594 1.100 0.271 74.4 32.1 0.5006
3.prog | 0.00164 0.002 0.998 0.2 0.1 0.4341
----------------------------------------------------------------------
fitstat
Measures of Fit for logit of honors
Log-Lik Intercept Only: -115.644 Log-Lik Full Model: -84.542
D(193): 169.085 LR(4): 62.204
Prob > LR: 0.000
McFadden's R2: 0.269 McFadden's Adj R2: 0.208
ML (Cox-Snell) R2: 0.267 Cragg-Uhler(Nagelkerke) R2: 0.390
McKelvey & Zavoina's R2: 0.435 Efron's R2: 0.284
Variance of y*: 5.820 Variance of error: 3.290
Count R2: 0.800 Adj Count R2: 0.245
AIC: 0.915 AIC*n: 183.085
BIC: -853.491 BIC': -41.011
BIC used by Stata: 195.576 AIC used by Stata: 179.085
Another fit indicator is the Hosmer & Lemeshow goodness-of-fit given by the lfit command which is part of Stata.
estat gof, group(10)
Logistic model for honors, goodness-of-fit test
(Table collapsed on quantiles of estimated probabilities)
number of observations = 200
number of groups = 10
Hosmer-Lemeshow chi2(8) = 15.12
Prob > chi2 = 0.0568
Next, let's look at some logistic regression diagnostics.
predict pprob // predicted probabilities predict r, resid // pearson residulas predict h, hat // leverage predict db, dbeta // pregobon dbeta predict dx2, dx2 // hosmer & lemeshow influence scatter h r, xline(0) msym(Oh) jitter(2) // leverage vs residual plottwoway (scatter dx2 pprob if honors==1, msym(Oh) jitter(2)) /// (scatter dx2 pprob if honors==0, msym(Oh) jitter(2))
scatter dx2 pprob if honors==1 [w=db], msym(Oh) jitter(2)
summarize pprob Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pprob | 200 .265 .2444744 .0053708 .9244364 histogram pprob (bin=14, start=.01473261, width=.0701496)
Some researchers find log-odds and odds ratios difficult to interpret and prefer to interpret their results in terms of predicted probabilities.
list honors pprob in 110/125
+-------------------+
| honors pprob |
|-------------------|
110. | 0 .2405516 |
111. | 1 .1948044 |
112. | 0 .2405516 |
113. | 0 .416587 |
114. | 0 .1387049 |
|-------------------|
115. | 0 .1948044 |
116. | 0 .0449239 |
117. | 1 .1946255 |
118. | 0 .6781951 |
119. | 0 .4834491 |
|-------------------|
120. | 1 .5841008 |
121. | 1 .3496613 |
122. | 0 .3224231 |
123. | 1 .1948044 |
124. | 1 .1948044 |
|-------------------|
125. | 0 .0756818 |
+-------------------+
Here is another utility (leastlikely) by Jeremy Freese that is not part of the spostado package (findit leastlikely).
leastlikely honors read female prog
Outcome: 0 (not enrolled)
+----------------------------------------------------+
| Prob honors read female prog |
|----------------------------------------------------|
134. | .2657953 not enrolled 65 female academic |
157. | .2657953 not enrolled 65 female academic |
165. | .1943608 not enrolled 68 female academic |
166. | .29575 not enrolled 68 female vocation |
180. | .1945395 not enrolled 76 male academic |
+----------------------------------------------------+
Outcome: 1 (enrolled)
+------------------------------------------------+
| Prob honors read female prog |
|------------------------------------------------|
59. | .1220252 enrolled 47 female vocation |
135. | .1387049 enrolled 52 male academic |
145. | .1556703 enrolled 53 male academic |
155. | .1723344 enrolled 50 female general |
160. | .0756818 enrolled 47 male academic |
+------------------------------------------------+
margins, dydx(read female prog) // as observed
Average marginal effects Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
dy/dx w.r.t. : read 1.female 2.prog 3.prog
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .018305 .0022549 8.12 0.000 .0138856 .0227245
1.female | .1456766 .051693 2.82 0.005 .0443602 .2469929
|
prog |
2 | .0768896 .0680412 1.13 0.258 -.0564686 .2102479
3 | .0002073 .0835493 0.00 0.998 -.1635463 .163961
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
margins, dydx(read female prog) atmeans // holding variables at their mean value
Conditional marginal effects Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
dy/dx w.r.t. : read 1.female 2.prog 3.prog
at : read = 52.23 (mean)
0.female = .455 (mean)
1.female = .545 (mean)
1.prog = .225 (mean)
2.prog = .525 (mean)
3.prog = .25 (mean)
------------------------------------------------------------------------------
| Delta-method
| dy/dx Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .0205865 .0035592 5.78 0.000 .0136105 .0275624
1.female | .1606615 .0586157 2.74 0.006 .0457769 .2755462
|
prog |
2 | .0839404 .071436 1.18 0.240 -.0560715 .2239524
3 | .0002055 .0828337 0.00 0.998 -.1621455 .1625566
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.
margins female prog
Predictive margins Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
female |
0 | .1888093 .0345352 5.47 0.000 .1211215 .2564971
1 | .3344859 .0382269 8.75 0.000 .2595625 .4094092
|
prog |
1 | .2181091 .0562519 3.88 0.000 .1078574 .3283608
2 | .2949988 .0364807 8.09 0.000 .223498 .3664996
3 | .2183165 .0636938 3.43 0.001 .093479 .3431539
------------------------------------------------------------------------------
margins female, at(read=(30 50 70) prog=1) vsquish // for prog equal 1
lAdjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
1._at : read = 30
prog = 1
2._at : read = 50
prog = 1
3._at : read = 70
prog = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at#female |
1 0 | .0046867 .0038796 1.21 0.227 -.0029172 .0122906
1 1 | .0137226 .009905 1.39 0.166 -.0056908 .033136
2 0 | .0658288 .0322765 2.04 0.041 .002568 .1290896
2 1 | .1723344 .0683062 2.52 0.012 .0384568 .3062121
3 0 | .513277 .14321 3.58 0.000 .2325905 .7939635
3 1 | .7570458 .1152195 6.57 0.000 .5312198 .9828718
------------------------------------------------------------------------------
margins female, at(read=(30 50 70) prog=2) vsquish // for prog equal 2
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
1._at : read = 30
prog = 2
2._at : read = 50
prog = 2
3._at : read = 70
prog = 2
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at#female |
1 0 | .0081433 .0066016 1.23 0.217 -.0047956 .0210822
1 1 | .0236848 .0160775 1.47 0.141 -.0078265 .055196
2 0 | .1094218 .0412597 2.65 0.008 .0285542 .1902894
2 1 | .2663481 .0632006 4.21 0.000 .1424772 .390219
3 0 | .6477268 .0912298 7.10 0.000 .4689197 .8265339
3 1 | .8445516 .0579974 14.56 0.000 .7308788 .9582245
------------------------------------------------------------------------------
margins female, at(read=(30 50 70) prog=3) vsquish // for prog equal 3
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
1._at : read = 30
prog = 3
2._at : read = 50
prog = 3
3._at : read = 70
prog = 3
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at#female |
1 0 | .0046944 .0038948 1.21 0.228 -.0029393 .012328
1 1 | .0137448 .0096791 1.42 0.156 -.0052258 .0327154
2 0 | .0659298 .0353531 1.86 0.062 -.003361 .1352205
2 1 | .1725686 .0720298 2.40 0.017 .0313927 .3137445
3 0 | .5136869 .164499 3.12 0.002 .1912747 .836099
3 1 | .7573474 .1257846 6.02 0.000 .5108141 1.003881
------------------------------------------------------------------------------
margins prog, at(read=(20(10)70) female==1) vsquish // for females
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(honors), predict()
1._at : read = 20
female = 1
2._at : read = 30
female = 1
3._at : read = 40
female = 1
4._at : read = 50
female = 1
5._at : read = 60
female = 1
6._at : read = 70
female = 1
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
_at#prog |
1 1 | .0035837 .0033206 1.08 0.280 -.0029246 .0100921
1 2 | .0062319 .0057058 1.09 0.275 -.0049512 .0174151
1 3 | .0035896 .003226 1.11 0.266 -.0027332 .0099124
2 1 | .0137226 .009905 1.39 0.166 -.0056908 .033136
2 2 | .0236848 .0160775 1.47 0.141 -.0078265 .055196
2 3 | .0137448 .0096791 1.42 0.156 -.0052258 .0327154
3 1 | .051075 .0275788 1.85 0.064 -.0029784 .1051285
3 2 | .0857952 .0380499 2.25 0.024 .0112186 .1603717
3 3 | .0511546 .0276057 1.85 0.064 -.0029516 .1052608
4 1 | .1723344 .0683062 2.52 0.012 .0384568 .3062121
4 2 | .2663481 .0632006 4.21 0.000 .1424772 .390219
4 3 | .1725686 .0720298 2.40 0.017 .0313927 .3137445
5 1 | .4461322 .124094 3.60 0.000 .2029123 .689352
5 2 | .5841008 .0733682 7.96 0.000 .4403019 .7278998
5 3 | .4465376 .1359971 3.28 0.001 .1799882 .7130871
6 1 | .7570458 .1152195 6.57 0.000 .5312198 .9828718
6 2 | .8445516 .0579974 14.56 0.000 .7308788 .9582245
6 3 | .7573474 .1257846 6.02 0.000 .5108141 1.003881
------------------------------------------------------------------------------
marginsplot
Let's rerun our model.
logit honors read i.female i.prog
Iteration 0: log likelihood = -115.64441
Iteration 1: log likelihood = -86.845312
Iteration 2: log likelihood = -84.560995
Iteration 3: log likelihood = -84.542357
Iteration 4: log likelihood = -84.542348
Iteration 5: log likelihood = -84.542348
Logistic regression Number of obs = 200
LR chi2(4) = 62.20
Prob > chi2 = 0.0000
Log likelihood = -84.542348 Pseudo R2 = 0.2689
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read | .1352861 .0242218 5.59 0.000 .0878123 .18276
1.female | 1.08343 .4094357 2.65 0.008 .2809511 1.885909
|
prog |
2 | .5559416 .5053125 1.10 0.271 -.4344527 1.546336
3 | .0016408 .6611702 0.00 0.998 -1.294229 1.29751
|
_cons | -9.41691 1.481922 -6.35 0.000 -12.32142 -6.512397
------------------------------------------------------------------------------
Next, we will demonstrate some alternative coding systems.
logit honors i.ses
Iteration 0: log likelihood = -115.64441
Iteration 1: log likelihood = -108.69882
Iteration 2: log likelihood = -108.53558
Iteration 3: log likelihood = -108.53555
Iteration 4: log likelihood = -108.53555
Logistic regression Number of obs = 200
LR chi2(2) = 14.22
Prob > chi2 = 0.0008
Log likelihood = -108.53555 Pseudo R2 = 0.0615
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ses |
2 | -.4112355 .4402784 -0.93 0.350 -1.274165 .4516944
3 | .9779843 .4340489 2.25 0.024 .1272642 1.828704
|
_cons | -1.185624 .3445096 -3.44 0.001 -1.86085 -.5103972
------------------------------------------------------------------------------
contrast ses
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
ses | 2 13.94 0.0009
------------------------------------------------
contrast p.ses // orthogonal polynomials
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
ses |
(linear) | 1 5.08 0.0242
(quadratic) | 1 6.63 0.0100
Joint | 2 13.94 0.0009
------------------------------------------------
--------------------------------------------------------------
| Contrast Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
ses |
(linear) | .3992604 .1771997 .0519554 .7465655
(quadratic) | .4243714 .1648284 .1013136 .7474291
--------------------------------------------------------------
We continue with logistic regression models with multiple categorical predictors. These models are logistic equivalents of analysis of variance models. The next example is the logistic equivalent of a 3-by-2 factorial anova and is followed by the equivalent of a 3-by-2 factorial ancova.
logit honors i.prog##i.female
Iteration 0: log likelihood = -115.64441
Iteration 1: log likelihood = -105.80227
Iteration 2: log likelihood = -105.03687
Iteration 3: log likelihood = -105.01869
Iteration 4: log likelihood = -105.01869
Logistic regression Number of obs = 200
LR chi2(5) = 21.25
Prob > chi2 = 0.0007
Log likelihood = -105.01869 Pseudo R2 = 0.0919
------------------------------------------------------------------------------
honors | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
2 | 1.493604 .8065652 1.85 0.064 -.0872346 3.074443
3 | -.8397523 1.264154 -0.66 0.507 -3.317448 1.637944
|
1.female | .9162888 .8973641 1.02 0.307 -.8425125 2.67509
|
prog#female |
2 1 | -.4362348 .9866519 -0.44 0.658 -2.370037 1.497567
3 1 | .6931488 1.447816 0.48 0.632 -2.144518 3.530816
|
_cons | -2.25129 .7433913 -3.03 0.002 -3.70831 -.7942696
------------------------------------------------------------------------------
contrast r.prog r.female r.prog#r.female // reference group coding
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------------
| df chi2 P>chi2
-------------------+----------------------------------
prog |
(2 vs 1) | 1 6.68 0.0097
(3 vs 1) | 1 0.46 0.4957
Joint | 2 13.39 0.0012
|
female | 1 3.99 0.0458
|
prog#female |
(2 vs 1) (1 vs 0) | 1 0.20 0.6584
(3 vs 1) (1 vs 0) | 1 0.23 0.6321
Joint | 2 0.97 0.6150
------------------------------------------------------
--------------------------------------------------------------------
| Contrast Std. Err. [95% Conf. Interval]
-------------------+------------------------------------------------
prog |
(2 vs 1) | 1.275487 .4933259 .3085856 2.242388
(3 vs 1) | -.4931779 .723908 -1.912011 .9256557
|
female |
(1 vs 0) | 1.001927 .5015964 .0188158 1.985038
|
prog#female |
(2 vs 1) (1 vs 0) | -.4362348 .9866519 -2.370037 1.497567
(3 vs 1) (1 vs 0) | .6931488 1.447816 -2.144518 3.530816
--------------------------------------------------------------------
logit hiwrite i.prog##i.female read
Iteration 0: log likelihood = -131.79114
Iteration 1: log likelihood = -84.462377
Iteration 2: log likelihood = -82.994215
Iteration 3: log likelihood = -82.9704
Iteration 4: log likelihood = -82.970367
Iteration 5: log likelihood = -82.970367
Logistic regression Number of obs = 200
LR chi2(6) = 97.64
Prob > chi2 = 0.0000
Log likelihood = -82.970367 Pseudo R2 = 0.3704
------------------------------------------------------------------------------
hiwrite | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog |
2 | 1.479148 .6851452 2.16 0.031 .1362886 2.822008
3 | -1.543036 .9866088 -1.56 0.118 -3.476754 .3906817
|
1.female | 2.56807 .8096941 3.17 0.002 .9810989 4.155041
|
prog#female |
2 1 | -1.83987 .9600168 -1.92 0.055 -3.721468 .0417288
3 1 | .85677 1.194374 0.72 0.473 -1.484161 3.197701
|
read | .1637165 .0291826 5.61 0.000 .1065197 .2209134
_cons | -9.14064 1.699912 -5.38 0.000 -12.47241 -5.808874
------------------------------------------------------------------------------
contrast a.prog a.female r.prog#r.female // reference group coding
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------------
| df chi2 P>chi2
-------------------+----------------------------------
prog |
(2 vs 1) | 1 1.44 0.2296
(3 vs 1) | 1 3.48 0.0620
Joint | 2 9.68 0.0079
|
female | 1 20.72 0.0000
|
prog#female |
(2 vs 1) (1 vs 0) | 1 3.67 0.0553
(3 vs 1) (1 vs 0) | 1 0.51 0.4732
Joint | 2 7.32 0.0258
------------------------------------------------------
--------------------------------------------------------------------
| Contrast Std. Err. [95% Conf. Interval]
-------------------+------------------------------------------------
prog |
(2 vs 1) | .5592136 .4655076 -.3531646 1.471592
(3 vs 1) | -1.114651 .5972122 -2.285166 .0558634
|
female |
(1 vs 0) | 2.24037 .4921307 1.275812 3.204929
|
prog#female |
(2 vs 1) (1 vs 0) | -1.83987 .9600168 -3.721468 .0417288
(3 vs 1) (1 vs 0) | .85677 1.194374 -1.484161 3.197701
--------------------------------------------------------------------
contrast a.prog a.female a.prog#g.female // difference from adjacent group
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------------
| df chi2 P>chi2
-------------------+----------------------------------
prog |
(1 vs 2) | 1 1.44 0.2296
(2 vs 3) | 1 9.60 0.0019
Joint | 2 9.68 0.0079
|
female | 1 20.72 0.0000
|
prog#female |
(1 vs 2) (0 vs 1) | 1 3.67 0.0553
(2 vs 3) (0 vs 1) | 1 5.97 0.0146
Joint | 2 7.32 0.0258
------------------------------------------------------
--------------------------------------------------------------------
| Contrast Std. Err. [95% Conf. Interval]
-------------------+------------------------------------------------
prog |
(1 vs 2) | -.5592136 .4655076 -1.471592 .3531646
(2 vs 3) | 1.673865 .5401886 .6151145 2.732615
|
female |
(0 vs 1) | -2.24037 .4921307 -3.204929 -1.275812
|
prog#female |
(1 vs 2) (0 vs 1) | -1.83987 .9600168 -3.721468 .0417288
(2 vs 3) (0 vs 1) | 2.69664 1.103841 .5331519 4.860127
--------------------------------------------------------------------
contrast g.prog g.female g.prog#g.female // difference from grand mean; effect coding
Contrasts of marginal linear predictions
Margins : asbalanced
------------------------------------------------------------
| df chi2 P>chi2
-------------------------+----------------------------------
prog |
(1 vs mean) | 1 0.36 0.5480
(2 vs mean) | 1 7.55 0.0060
(3 vs mean) | 1 7.20 0.0073
Joint | 2 9.68 0.0079
|
female |
(0 vs mean) | 1 20.72 0.0000
(1 vs mean) | 1 20.72 0.0000
Joint | 1 20.72 0.0000
|
prog#female |
(1 vs mean) (0 vs mean) | 1 0.28 0.5981
(1 vs mean) (1 vs mean) | 1 0.28 0.5981
(2 vs mean) (0 vs mean) | 1 7.21 0.0072
(2 vs mean) (1 vs mean) | 1 7.21 0.0072
(3 vs mean) (0 vs mean) | 1 2.89 0.0891
(3 vs mean) (1 vs mean) | 1 2.89 0.0891
Joint | 2 7.32 0.0258
------------------------------------------------------------
--------------------------------------------------------------------------
| Contrast Std. Err. [95% Conf. Interval]
-------------------------+------------------------------------------------
prog |
(1 vs mean) | .1851458 .3082055 -.4189259 .7892176
(2 vs mean) | .7443595 .270871 .2134621 1.275257
(3 vs mean) | -.9295053 .3464478 -1.608531 -.25048
|
female |
(0 vs mean) | -1.120185 .2460653 -1.602464 -.6379059
(1 vs mean) | 1.120185 .2460653 .6379059 1.602464
|
prog#female |
(1 vs mean) (0 vs mean) | -.1638499 .3108171 -.7730402 .4453404
(1 vs mean) (1 vs mean) | .1638499 .3108171 -.4453404 .7730402
(2 vs mean) (0 vs mean) | .7560849 .2815464 .204264 1.307906
(2 vs mean) (1 vs mean) | -.7560849 .2815464 -1.307906 -.204264
(3 vs mean) (0 vs mean) | -.5922349 .3483436 -1.274976 .0905059
(3 vs mean) (1 vs mean) | .5922349 .3483436 -.0905059 1.274976
--------------------------------------------------------------------------
* plot interaction for three values of read (30 50 70)
* beginning with read = 30
margins prog#female, at(read=30) vsquish
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(hiwrite), predict()
at : read = 30
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog#female |
1 0 | .0143558 .0129815 1.11 0.269 -.0110874 .0397989
1 1 | .1596179 .0889452 1.79 0.073 -.0147114 .3339472
2 0 | .0600869 .0414002 1.45 0.147 -.0210559 .1412298
2 1 | .1169335 .069781 1.68 0.094 -.0198347 .2537018
3 0 | .0031033 .003399 0.91 0.361 -.0035585 .0097651
3 1 | .0872775 .0496422 1.76 0.079 -.0100194 .1845744
-----------------------------------------------------------------------------
marginsplot
* for read = 50
margins prog#female, at(read=50) vsquish
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(hiwrite), predict()
at : read = 50
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog#female |
1 0 | .2779179 .1149279 2.42 0.016 .0526635 .5031724
1 1 | .8338631 .0734785 11.35 0.000 .6898478 .9778784
2 0 | .628161 .0912562 6.88 0.000 .4493021 .8070199
2 1 | .7777385 .0677238 11.48 0.000 .6450023 .9104747
3 0 | .0760091 .0583469 1.30 0.193 -.0383488 .190367
3 1 | .7164644 .0946828 7.57 0.000 .5308896 .9020392
------------------------------------------------------------------------------
marginsplot
* for read = 70
margins prog#female, at(read=70) vsquish
Adjusted predictions Number of obs = 200
Model VCE : OIM
Expression : Pr(hiwrite), predict()
at : read = 70
------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
prog#female |
1 0 | .9104806 .0573769 15.87 0.000 .7980239 1.022937
1 1 | .9925168 .0066608 149.01 0.000 .979462 1.005572
2 0 | .9780902 .0143631 68.10 0.000 .9499391 1.006241
2 1 | .9893012 .0077172 128.19 0.000 .9741758 1.004427
3 0 | .6849213 .1994977 3.43 0.001 .2939129 1.07593
3 1 | .9852452 .0123986 79.46 0.000 .9609443 1.009546
------------------------------------------------------------------------------
marginsplot
Our last example shows how to do simple constrasts and simple main effects in a logistic regression model.
contrast female@prog, effects Contrasts of marginal linear predictions Margins : asbalanced ------------------------------------------------ | df chi2 P>chi2 -------------+---------------------------------- female@prog | 1 | 1 10.06 0.0015 2 | 1 1.72 0.1899 3 | 1 12.33 0.0004 Joint | 3 21.23 0.0001 ------------------------------------------------ -------------------------------------------------------------------------------- | Contrast Std. Err. z P>|z| [95% Conf. Interval] ---------------+---------------------------------------------------------------- female@prog | (1 vs base) 1 | 2.56807 .8096941 3.17 0.002 .9810989 4.155041 (1 vs base) 2 | .7282006 .5554797 1.31 0.190 -.3605197 1.816921 (1 vs base) 3 | 3.42484 .9753415 3.51 0.000 1.513206 5.336474 --------------------------------------------------------------------------------
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