Chapter 12 Exercises: Solutions

Chapter 12 Exercises: Solutions

1a.

. oprobit fechld i.sex educ age kidjob sibs
Iteration 0: log likelihood = -1494.7622
Iteration 1: log likelihood = -1430.925
Iteration 2: log likelihood = -1430.8529
Iteration 3: log likelihood = -1430.8529
Ordered probit regression Number of obs = 1251
LR chi2(5) = 127.82
Prob > chi2 = 0.0000
Log likelihood = -1430.8529 Pseudo R2 = 0.0428
------
fechld | Coef. Std. Err. z P>|z| [95% Conf. Interval]
------+------
sex |
female | -.4256082 .0626415 -6.79 0.000 -.5483834 -.3028331
educ | -.0614096 .010567 -5.81 0.000 -.0821205 -.0406987
age | .0035244 .0017628 2.00 0.046 .0000693 .0069795
kidjob | -.164669 .0288048 -5.72 0.000 -.2211253 -.1082127
sibs | .0275506 .0101488 2.71 0.007 .0076592 .0474419
------+------
/cut1 | -1.992699 .2062542 -2.39695 -1.588448
/cut2 | -.6844431 .2014548 -1.079287 -.289599
/cut3 | .4031797 .2035688 .0041921 .8021673
------

LR χ2(5) = 127.82, p < .001. This indicated that the full probit model with five predictors provides a better fit than the null model with no independent variables in predicting the ordinal response variable.

1b.

Deviance = 2861.706.

1c. For the sex predictor, the probit coefficient β = –.426; for the educ predictor, the probit coefficient β = –.061. Both are significant.

1d.

Being a female decreases the probability of disagreeing with the statement “mother working does not hurt children” when holding all the other predictors constant. In other words, being a female increases the probability of agreeing with the statement “mother working does not hurt children.” Please note that the ordinal response variable fechld has four categories with 1 = strongly agree and 4 = strongly disagree.
An increase in educ is associated with the increase in the probability of agreeing with the statement “mother working does not hurt children.”

1e. The estimated probabilities of being category 4 at age of 30, 40, and 50 are .036, .039, and .042, respectively.

. margins, predict (outcome(4)) at(age = (30 40 50)) atmeans vsquish
Adjusted predictions Number of obs = 1251
Model VCE : OIM
Expression : Pr(fechld==4), predict(outcome(4))
1._at : 1.sex = .4516387 (mean)
2.sex = .5483613 (mean)
educ = 13.6195 (mean)
age = 30
kidjob = 3.221423 (mean)
sibs = 3.641886 (mean)
2._at : 1.sex = .4516387 (mean)
2.sex = .5483613 (mean)
educ = 13.6195 (mean)
age = 40
kidjob = 3.221423 (mean)
sibs = 3.641886 (mean)
3._at : 1.sex = .4516387 (mean)
2.sex = .5483613 (mean)
educ = 13.6195 (mean)
age = 50
kidjob = 3.221423 (mean)
sibs = 3.641886 (mean)
| Delta-method
| Margin Std. Err. Z P>|z| [95% Conf. Interval]
------+------
_at |
1 | .0361411 .005518 6.55 0.000 .0253259 .0469562
2 | .0390268 .005357 7.29 0.000 .0285273 .0495262
3 | .0420973 .0055572 7.58 0.000 .0312053 .0529893
------

2a.

The log likelihood ratio test for the fitted model χ2(8) = 197.51, p < .001. This indicates that the five-predictor model provides a better fit than the null model.

2b.

. mlogit, rrr
Multinomial logistic regression Number of obs = 1953
LR chi2(8) = 197.51
Prob > chi2 = 0.0000
Log likelihood = -1779.706 Pseudo R2 = 0.0526
------
happy | RRR Std. Err. z P>|z| [95% Conf. Interval]
------+------
1 |
sex |
female | 1.145408 .177523 0.88 0.381 .8453479 1.551977
educ | 1.074884 .0263572 2.94 0.003 1.024446 1.127804
age | .9874738 .0043841 -2.84 0.005 .9789185 .9961039
satfin | .2638017 .0302837 -11.61 0.000 .2106503 .3303644
_cons | 24.11205 12.57427 6.10 0.000 8.676375 67.00853
------+------
pretty_happy |
sex |
female | 1.005775 .1409373 0.04 0.967 .7642296 1.323665
educ | 1.104624 .0246543 4.46 0.000 1.057344 1.154018
age | .9902186 .0040156 -2.42 0.015 .9823794 .9981205
satfin | .463942 .0485022 -7.35 0.000 .3779862 .5694446
_cons | 9.862793 4.738469 4.76 0.000 3.846358 25.29008
------+------
not_too_happy | (base outcome)
------

The logit coefficients of educ across two binary models are .072 and .100, respectively. They are both significant. The first binary model compares category 1 with category 3, and the second model compares category 2 with category 3.

2c. The odds ratios for educ across two binary comparisons are 1.075 and 1.105, respectively. They indicate that the increase in years of education is associated with the increase in the odds of being very happy and the odds of being pretty happy versus being not too happy.

2d. The odds ratios for satfin across two binary comparisons are .264 and .464, respectively. They indicate that the less satisfaction with financial situation is associated with the decrease in the odds of being very happy and the odds of being pretty happy. In other words, more satisfaction with financial situation increases the odds of being pretty happy and very happy. Please note that the satfin is coded as follows: “pretty well satisfied” = 1, “more or less satisfied” = 2, and “not satisfied at all” = 3.

2e.The two equations can be expressed as:

ln = +sex +educ –age –satfin

ln = +sex +educ –age –satfin

2f.

. listcoef
mlogit (N=1953): Factor change in the odds of happy
Variable: 2.sex (sd=0.498)
------
| b z P>|z| e^b e^bStdX
------+------
1 vs pretty happy | 0.1300 1.240 0.215 1.139 1.067
1 vs not too happ | 0.1358 0.876 0.381 1.145 1.070
pretty happy vs 1 | -0.1300 -1.240 0.215 0.878 0.937
pretty happy vs not too happ | 0.0058 0.041 0.967 1.006 1.003
not too happ vs 1 | -0.1358 -0.876 0.381 0.873 0.935
not too happ vs pretty happy | -0.0058 -0.041 0.967 0.994 0.997
------
Variable: educ (sd=3.123)
------
| b z P>|z| e^b e^bStdX
------+------
1 vs pretty happy | -0.0273 -1.596 0.111 0.973 0.918
1 vs not too happ | 0.0722 2.945 0.003 1.075 1.253
pretty happy vs 1 | 0.0273 1.596 0.111 1.028 1.089
pretty happy vs not too happ | 0.0995 4.458 0.000 1.105 1.365
not too happ vs 1 | -0.0722 -2.945 0.003 0.930 0.798
not too happ vs pretty happy | -0.0995 -4.458 0.000 0.905 0.733
------
Variable: age (sd=17.677)
------
| b z P>|z| e^b e^bStdX
------+------
1 vs pretty happy | -0.0028 -0.939 0.348 0.997 0.952
1 vs not too happ | -0.0126 -2.839 0.005 0.987 0.800
pretty happy vs 1 | 0.0028 0.939 0.348 1.003 1.050
pretty happy vs not too happ | -0.0098 -2.424 0.015 0.990 0.841
not too happ vs 1 | 0.0126 2.839 0.005 1.013 1.250
not too happ vs pretty happy | 0.0098 2.424 0.015 1.010 1.190
------
Variable: satfin (sd=0.751)
------
| b z P>|z| e^b e^bStdX
------+------
1 vs pretty happy | -0.5646 -7.641 0.000 0.569 0.654
1 vs not too happ | -1.3326 -11.608 0.000 0.264 0.368
pretty happy vs 1 | 0.5646 7.641 0.000 1.759 1.528
pretty happy vs not too happ | -0.7680 -7.346 0.000 0.464 0.562
not too happ vs 1 | 1.3326 11.608 0.000 3.791 2.721
not too happ vs pretty happy | 0.7680 7.346 0.000 2.155 1.780
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