Version info: Code for this page was tested in Stata 12.1.
For this chapter, you will need to use the syntax provided in Appendix A to access the School and Mice datasets.
Figure 18.2, page 466
* Figure 18.2, page 466 sort SCHOOL by SCHOOL: egen ordervar = median(MATH) egen id = group(ordervar SCHOOL) graph box MATH, over(id)
Table 18.2, page 468 Estimated coefficients from three naive linear regression models ignoring the hierarchical structure of the school data. Note that for Model 3, we believe there is a typo where the coefficient for “Three hours” was copied for “Four or more hours”.
* Table 18.2, page 468
regress MATH i.iSCHTYPE
regress MATH i.iSCHTYPE SES
regress MATH i.iSCHTYPE SES i.iHOMEW
. regress MATH i.iSCHTYPE
Source | SS df MS Number of obs = 519
-------------+------------------------------ F( 1, 517) = 74.89
Model | 7517.11179 1 7517.11179 Prob > F = 0.0000
Residual | 51890.9345 517 100.369312 R-squared = 0.1265
-------------+------------------------------ Adj R-squared = 0.1248
Total | 59408.0462 518 114.687348 Root MSE = 10.018
------------------------------------------------------------------------------
MATH | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -7.805556 .9019425 -8.65 0.000 -9.577479 -6.033634
_cons | 56.4901 .7048956 80.14 0.000 55.10529 57.87491
------------------------------------------------------------------------------
. regress MATH i.iSCHTYPE SES
Source | SS df MS Number of obs = 519
-------------+------------------------------ F( 2, 516) = 86.56
Model | 14923.9649 2 7461.98243 Prob > F = 0.0000
Residual | 44484.0814 516 86.20946 R-squared = 0.2512
-------------+------------------------------ Adj R-squared = 0.2483
Total | 59408.0462 518 114.687348 Root MSE = 9.2849
------------------------------------------------------------------------------
MATH | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -2.690174 1.001647 -2.69 0.007 -4.657982 -.7223663
SES | 5.144264 .5549883 9.27 0.000 4.05395 6.234579
_cons | 53.37222 .7347965 72.64 0.000 51.92866 54.81578
------------------------------------------------------------------------------
. regress MATH i.iSCHTYPE SES i.iHOMEW
Source | SS df MS Number of obs = 519
-------------+------------------------------ F( 7, 511) = 39.29
Model | 20787.198 7 2969.59972 Prob > F = 0.0000
Residual | 38620.8482 511 75.5789593 R-squared = 0.3499
-------------+------------------------------ Adj R-squared = 0.3410
Total | 59408.0462 518 114.687348 Root MSE = 8.6936
------------------------------------------------------------------------------
MATH | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -1.604598 .9512725 -1.69 0.092 -3.473485 .2642879
SES | 4.27564 .5316148 8.04 0.000 3.23122 5.320059
|
iHOMEW |
1 | -1.390219 1.463883 -0.95 0.343 -4.266189 1.485751
2 | .2264091 1.578583 0.14 0.886 -2.874903 3.327721
3 | 5.208512 1.852822 2.81 0.005 1.568426 8.848598
4 | 7.560103 1.889684 4.00 0.000 3.847598 11.27261
5 | 8.073905 1.9118 4.22 0.000 4.317949 11.82986
|
_cons | 51.37485 1.508053 34.07 0.000 48.41211 54.3376
------------------------------------------------------------------------------
Table 18.3, page 472 Estimated coefficients from three random slope regression models accounting for the hierarchical structure of the school data.
* Table 18.3, page 472
xtmixed MATH i.iSCHTYPE || SCHOOL:
xtmixed MATH i.iSCHTYPE SES || SCHOOL:
xtmixed MATH i.iSCHTYPE SES i.iHOMEW || SCHOOL:
. xtmixed MATH i.iSCHTYPE || SCHOOL:
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1896.834
Iteration 1: log likelihood = -1896.834
Computing standard errors:
Mixed-effects ML regression Number of obs = 519
Group variable: SCHOOL Number of groups = 23
Obs per group: min = 5
avg = 22.6
max = 67
Wald chi2(1) = 8.37
Log likelihood = -1896.834 Prob > chi2 = 0.0038
------------------------------------------------------------------------------
MATH | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -5.917381 2.045617 -2.89 0.004 -9.926718 -1.908045
_cons | 54.67714 1.666538 32.81 0.000 51.41078 57.94349
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
SCHOOL: Identity |
sd(_cons) | 4.14692 .7461234 2.914577 5.900324
-----------------------------+------------------------------------------------
sd(Residual) | 9.012207 .2858282 8.469051 9.590198
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 69.18 Prob >= chibar2 = 0.0000
. xtmixed MATH i.iSCHTYPE SES || SCHOOL:
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1873.2488
Iteration 1: log likelihood = -1873.2488
Computing standard errors:
Mixed-effects ML regression Number of obs = 519
Group variable: SCHOOL Number of groups = 23
Obs per group: min = 5
avg = 22.6
max = 67
Wald chi2(2) = 63.07
Log likelihood = -1873.2488 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
MATH | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -2.439539 1.765271 -1.38 0.167 -5.899407 1.02033
SES | 4.157041 .5842519 7.12 0.000 3.011928 5.302153
_cons | 52.80351 1.407527 37.52 0.000 50.04481 55.56221
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
SCHOOL: Identity |
sd(_cons) | 3.286817 .6568919 2.221556 4.862882
-----------------------------+------------------------------------------------
sd(Residual) | 8.668816 .2751664 8.145934 9.225262
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 36.42 Prob >= chibar2 = 0.0000
. xtmixed MATH i.iSCHTYPE SES i.iHOMEW || SCHOOL:
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -1836.8366
Iteration 1: log likelihood = -1836.8366
Computing standard errors:
Mixed-effects ML regression Number of obs = 519
Group variable: SCHOOL Number of groups = 23
Obs per group: min = 5
avg = 22.6
max = 67
Wald chi2(7) = 148.88
Log likelihood = -1836.8366 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
MATH | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
1.iSCHTYPE | -1.634042 1.71019 -0.96 0.339 -4.985953 1.717868
SES | 3.48564 .5527899 6.31 0.000 2.402191 4.569088
|
iHOMEW |
1 | -1.296386 1.414758 -0.92 0.359 -4.06926 1.476489
2 | .7045507 1.530507 0.46 0.645 -2.295187 3.704289
3 | 5.297748 1.787483 2.96 0.003 1.794345 8.801151
4 | 7.632283 1.820814 4.19 0.000 4.063553 11.20101
5 | 7.713808 1.855085 4.16 0.000 4.077909 11.34971
|
_cons | 50.98939 1.85495 27.49 0.000 47.35376 54.62503
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
SCHOOL: Identity |
sd(_cons) | 3.230354 .6381913 2.19324 4.757887
-----------------------------+------------------------------------------------
sd(Residual) | 8.066908 .2562394 7.580002 8.585091
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 35.89 Prob >= chibar2 = 0.0000
Figure 18.3 is not reproduced.
Table 18.4, page 480 is not reproduced — it is just the AICs from running all possible sets of 2 and 3 predictors in xtmixed.
Figure 18.4, page 483 Weight over time for 14 Mice.
* Figure 18.4, page 483 twoway line WEIGHT DAY, lstyle(ID)
Table 18.5, page 485 Estimates for random intercept and random slope models with different correlation structures. Note that these are complex random effects models to be fitting on only 14 mice. The parameter estimates vary between packages, with some reporting Errors or warnings in the optimization.
* Table 18.5, page 485
xtmixed WEIGHT DAY || ID: DAY, mle residuals(ar 1, t(DAY)) nolrtest nolog nogroup
* log likelihood, AIC, BIC (note nondefault N)
estat ic, n(14)
xtmixed WEIGHT DAY || ID: DAY, mle residuals(exchangeable, t(DAY)) nolrtest nogroup
estat ic, n(14)
. xtmixed WEIGHT DAY || ID: DAY, mle residuals(ar 1, t(DAY)) nolrtest nolog nogroup
Note: time gaps exist in the estimation data
Mixed-effects ML regression Number of obs = 98
Wald chi2(1) = 412.99
Log likelihood = -541.87375 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
WEIGHT | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
DAY | 41.05531 2.02023 20.32 0.000 37.09573 45.01488
_cons | 156.8233 22.00866 7.13 0.000 113.6871 199.9595
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
ID: Independent |
sd(DAY) | 5.071184 1.621431 2.709887 9.49003
sd(_cons) | 5.02e-07 . . .
-----------------------------+------------------------------------------------
Residual: AR(1) |
rho | .8948443 .0371771 .7932106 .9479758
sd(e) | 77.01422 12.31915 56.28766 105.3728
------------------------------------------------------------------------------
. * log likelihood, AIC, BIC (note nondefault N)
. estat ic, n(14)
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 14 . -541.8737 5 1093.747 1096.943
-----------------------------------------------------------------------------
Note: N=14 used in calculating BIC
.
. xtmixed WEIGHT DAY || ID: DAY, mle residuals(exchangeable, t(DAY)) nolrtest nogroup
Note: t() not required for this residual structure; ignored
Obtaining starting values by EM:
Performing gradient-based optimization:
Iteration 0: log likelihood = -559.76833
Iteration 1: log likelihood = -559.262
Iteration 2: log likelihood = -559.21086
Iteration 3: log likelihood = -559.20315
Iteration 4: log likelihood = -559.20143 (backed up)
Iteration 5: log likelihood = -559.20059 (backed up)
Iteration 6: log likelihood = -559.20038 (backed up)
Iteration 7: log likelihood = -559.20028 (backed up)
Iteration 8: log likelihood = -559.20025 (backed up)
numerical derivatives are approximate
nearby values are missing
Iteration 9: log likelihood = -559.20024 (not concave)
numerical derivatives are approximate
nearby values are missing
Iteration 10: log likelihood = -559.20023 (not concave)
numerical derivatives are approximate
nearby values are missing
Iteration 11: log likelihood = -559.20022 (not concave)
numerical derivatives are approximate
nearby values are missing
Iteration 12: log likelihood = -559.19951
numerical derivatives are approximate
nearby values are missing
Iteration 13: log likelihood = -559.15415 (not concave)
numerical derivatives are approximate
nearby values are missing
Iteration 14: log likelihood = -559.15414 (backed up)
numerical derivatives are approximate
nearby values are missing
Iteration 15: log likelihood = -559.15315
numerical derivatives are approximate
nearby values are missing
Iteration 16: log likelihood = -559.15315 (not concave)
numerical derivatives are approximate
nearby values are missing
Iteration 17: log likelihood = -559.15315 (backed up)
Computing standard errors:
Mixed-effects ML regression Number of obs = 98
Wald chi2(1) = 361.72
Log likelihood = -559.15315 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
WEIGHT | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
DAY | 41.05442 2.158596 19.02 0.000 36.82365 45.28519
_cons | 180.4116 11.31704 15.94 0.000 158.2306 202.5926
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
ID: Independent |
sd(DAY) | 7.100342 1.341837 4.902499 10.2835
sd(_cons) | .0004224 . . .
-----------------------------+------------------------------------------------
Residual: Exchangeable |
sd(e) | 56.57587 4.364924 48.6362 65.81166
corr(e) | -.1666667 .000035 -.1667352 -.1665981
------------------------------------------------------------------------------
. estat ic, n(14)
-----------------------------------------------------------------------------
Model | Obs ll(null) ll(model) df AIC BIC
-------------+---------------------------------------------------------------
. | 14 . -559.1531 5 1128.306 1131.502
-----------------------------------------------------------------------------
Note: N=14 used in calculating BIC