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Table 5.1 on page 141 using reading_pp data.
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/reading_pp, clear list if inlist(id, 4, 27, 31, 33, 41, 49, 69, 77, 87)
+--------------------------------------+
| id wave agegrp age piat |
|--------------------------------------|
10. | 4 1 6.5 6 18 |
11. | 4 2 8.5 8.5 31 |
12. | 4 3 10.5 10.66667 50 |
79. | 27 1 6.5 6.25 19 |
80. | 27 2 8.5 9.166667 36 |
|--------------------------------------|
81. | 27 3 10.5 10.91667 57 |
91. | 31 1 6.5 6.333333 18 |
92. | 31 2 8.5 8.833333 31 |
93. | 31 3 10.5 10.91667 51 |
97. | 33 1 6.5 6.333333 18 |
|--------------------------------------|
98. | 33 2 8.5 8.916667 34 |
99. | 33 3 10.5 10.75 29 |
121. | 41 1 6.5 6.333333 18 |
122. | 41 2 8.5 8.75 28 |
123. | 41 3 10.5 10.83333 36 |
|--------------------------------------|
145. | 49 1 6.5 6.5 19 |
146. | 49 2 8.5 8.75 32 |
147. | 49 3 10.5 10.66667 48 |
205. | 69 1 6.5 6.666667 26 |
206. | 69 2 8.5 9.166667 47 |
|--------------------------------------|
207. | 69 3 10.5 11.33333 45 |
229. | 77 1 6.5 6.833333 17 |
230. | 77 2 8.5 8.083333 19 |
231. | 77 3 10.5 10 28 |
259. | 87 1 6.5 6.916667 22 |
|--------------------------------------|
260. | 87 2 8.5 9.416667 49 |
261. | 87 3 10.5 11.5 64 |
+--------------------------------------+
Figure 5.1 on page 143.
preserve keep if inlist(id, 4, 27, 31, 33, 41, 49, 69, 77, 87) graph twoway (scatter piat age) (scatter piat agegrp) (lfit piat age, legend(off)) /// (lfit piat agegrp, legend(off)) , by(id) ylabel(0(20)80) xlabel(6(1) 12)
Table 5.2 on page 145.
Part 1: Unconditional growth model on centered agegrp variable.
gen cagegrp = agegrp - 6.5 xtmixed piat cagegrp || id: cagegrp, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -910.13718 Iteration 1: log likelihood = -909.97622 Iteration 2: log likelihood = -909.97465 Iteration 3: log likelihood = -909.97465
Computing standard errors:
Mixed-effects ML regression Number of obs = 267 Group variable: id Number of groups = 89
Obs per group: min = 3
avg = 3.0
max = 3
Wald chi2(1) = 289.62 Log likelihood = -909.97465 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
piat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cagegrp | 5.030899 .2956204 17.02 0.000 4.451494 5.610304
_cons | 21.16292 .6142662 34.45 0.000 19.95898 22.36686
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(cagegrp) | 4.39745 1.271306 2.495273 7.749681
var(_cons) | 11.04583 6.06258 3.767131 32.38815
cov(cagegrp,_cons) | 1.646659 2.062946 -2.396641 5.689959
-----------------------------+------------------------------------------------
var(Residual) | 27.04309 4.053927 20.15839 36.27911
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 86.92 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Part 2: Unconditional growth model on centered age variable.
gen cage = age - 6.5 xtmixed piat cage || id: cage, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -902.4384 Iteration 1: log likelihood = -901.98942 Iteration 2: log likelihood = -901.95011 Iteration 3: log likelihood = -901.9478 Iteration 4: log likelihood = -901.94777
Computing standard errors:
Mixed-effects ML regression Number of obs = 267 Group variable: id Number of groups = 89
Obs per group: min = 3
avg = 3.0
max = 3
Wald chi2(1) = 303.42 Log likelihood = -901.94777 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
piat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cage | 4.540021 .2606349 17.42 0.000 4.029186 5.050856
_cons | 21.06082 .5593131 37.65 0.000 19.96458 22.15705
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(cage) | 3.301472 1.014522 1.807751 6.029435
var(_cons) | 5.107369 6.028915 .5051372 51.63986
cov(cage,_cons) | 2.366531 1.802022 -1.165368 5.89843
-----------------------------+------------------------------------------------
var(Residual) | 27.44634 4.371408 20.08689 37.50216
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 88.91 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Table 5.3 on page 147 using wages_pp data.
clear use http://www.ats.ucla.edu/stat/stata/examples/alda/data/wages_pp list exper lnw black hgc uerate if id == 206 | id == 332 | id ==1028
+--------------------------------------+
| exper lnw black hgc uerate |
|--------------------------------------|
75. | 1.874 2.028 0 10 9.2 |
76. | 2.814 2.297 0 10 11 |
77. | 4.314 2.482 0 10 6.295 |
197. | .125 1.63 0 8 7.1 |
198. | 1.625 1.476 0 8 9.6 |
|--------------------------------------|
199. | 2.413 1.804 0 8 7.2 |
200. | 3.393 1.439 0 8 6.195 |
201. | 4.47 1.748 0 8 5.595 |
202. | 5.178 1.526 0 8 4.595 |
203. | 6.082 2.044 0 8 4.295 |
|--------------------------------------|
204. | 7.043 2.179 0 8 3.395 |
205. | 8.197 2.186 0 8 4.395 |
206. | 9.092 4.035 0 8 6.695 |
466. | .004 .872 1 8 9.3 |
467. | .035 .903 1 8 7.4 |
|--------------------------------------|
468. | .515 1.389 1 8 7.3 |
469. | 1.483 2.324 1 8 7.4 |
470. | 2.141 1.484 1 8 6.295 |
471. | 3.161 1.705 1 8 5.895 |
472. | 4.103 2.343 1 8 6.9 |
+--------------------------------------+
Table 5.4 on page 149.
Model A: Unconditional growth model
xtmixed lnw exper || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2460.7432 Iteration 1: log likelihood = -2460.6972 Iteration 2: log likelihood = -2460.6971
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(1) = 380.59 Log likelihood = -2460.6971 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | .0456807 .0023416 19.51 0.000 .0410913 .0502701
_cons | 1.715604 .0107965 158.90 0.000 1.694443 1.736765
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .001726 .00022 .0013444 .0022158
var(_cons) | .0542681 .0050012 .0453001 .0650114
cov(exper,_cons) | -.0029149 .000869 -.004618 -.0012118
-----------------------------+------------------------------------------------
var(Residual) | .0951047 .0019442 .0913694 .0989927
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1580.05 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model B: Conditional growth model
gen hgc_exper = hgc_9*exper gen bxexp = black*exper xi: xtmixed lnw exper black hgc_9 hgc_exper bxexp || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2436.9369 Iteration 1: log likelihood = -2436.8758 Iteration 2: log likelihood = -2436.8757
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(5) = 441.56 Log likelihood = -2436.8757 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | .0493428 .0026317 18.75 0.000 .0441848 .0545008
black | .0153954 .0239265 0.64 0.520 -.0314996 .0622905
hgc_9 | .0349201 .0078815 4.43 0.000 .0194727 .0503675
hgc_exper | .0012794 .0017232 0.74 0.458 -.0020979 .0046568
bxexp | -.0182129 .0054991 -3.31 0.001 -.0289911 -.0074348
_cons | 1.717139 .0125424 136.91 0.000 1.692556 1.741721
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016358 .0002139 .001266 .0021137
var(_cons) | .0517481 .0048685 .0430341 .0622265
cov(exper,_cons) | -.0028508 .0008441 -.0045052 -.0011965
-----------------------------+------------------------------------------------
var(Residual) | .0951938 .0019462 .0914547 .0990857
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1465.80 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model C: conditional growth model
xi: xtmixed lnw exper hgc_9 bxexp || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2437.4097 Iteration 1: log likelihood = -2437.3518 Iteration 2: log likelihood = -2437.3518
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(3) = 439.40 Log likelihood = -2437.3518 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | .048847 .0025134 19.43 0.000 .0439208 .0537732
hgc_9 | .0383608 .0064334 5.96 0.000 .0257516 .05097
bxexp | -.016115 .0045114 -3.57 0.000 -.0249571 -.0072729
_cons | 1.721475 .0106971 160.93 0.000 1.700509 1.742441
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016467 .0002141 .0012762 .0021247
var(_cons) | .0518309 .0048732 .0431081 .0623188
cov(exper,_cons) | -.0028798 .0008455 -.0045369 -.0012227
-----------------------------+------------------------------------------------
var(Residual) | .0951735 .0019453 .0914361 .0990637
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1474.50 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Figure 5.2 on page 150. We will have to create a data set first for generating predicted values for different groups.
input exper hgc_9 black group exper hgc_9 black group 0 0 0 1 10 0 0 1 0 0 1 2 10 0 1 2 0 3 0 3 10 3 0 3 0 3 1 4 10 3 1 4 end gen bxexp = black*exper save fig5_2
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/wages_pp, clear gen bxexp = black*exper xi: xtmixed lnw exper hgc_9 bxexp || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2437.4097 Iteration 1: log likelihood = -2437.3518 Iteration 2: log likelihood = -2437.3518
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(3) = 439.40 Log likelihood = -2437.3518 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | .048847 .0025134 19.43 0.000 .0439208 .0537732
hgc_9 | .0383608 .0064334 5.96 0.000 .0257516 .05097
bxexp | -.016115 .0045114 -3.57 0.000 -.0249571 -.0072729
_cons | 1.721475 .0106971 160.93 0.000 1.700509 1.742441
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016467 .0002141 .0012762 .0021247
var(_cons) | .0518309 .0048732 .0431081 .0623188
cov(exper,_cons) | -.0028798 .0008455 -.0045369 -.0012227
-----------------------------+------------------------------------------------
var(Residual) | .0951735 .0019453 .0914361 .0990637
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1474.50 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
use fig5_2, clear predict p (option xb assumed)
twoway scatter p exper, c(L) ytitle("predicted lnw")
Table 5.5 on page 154 using wages_small_pp data. Stata does not have problem estimating this model.
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/wages_small_pp
gen bexper = black*exper
xtmixed lnw hgc_9 exper bexper || id: exper, var mle cov(un)
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -144.13188 Iteration 1: log likelihood = -142.21488 Iteration 2: log likelihood = -142.01812 Iteration 3: log likelihood = -141.9574 Iteration 4: log likelihood = -141.9398 Iteration 5: log likelihood = -141.93609 Iteration 6: log likelihood = -141.93515 Iteration 7: log likelihood = -141.93492 Iteration 8: log likelihood = -141.93487 Iteration 9: log likelihood = -141.93486
Computing standard errors:
Mixed-effects ML regression Number of obs = 257 Group variable: id Number of groups = 124
Obs per group: min = 1
avg = 2.1
max = 3
Wald chi2(3) = 11.96 Log likelihood = -141.93486 Prob > chi2 = 0.0075
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hgc_9 | .0461057 .024471 1.88 0.060 -.0018565 .0940679
exper | .0516136 .0210767 2.45 0.014 .010304 .0929232
bexper | -.0596725 .0347673 -1.72 0.086 -.1278152 .0084701
_cons | 1.737337 .0475981 36.50 0.000 1.644046 1.830628
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | 3.57e-06 .0000829 5.94e-26 2.14e+14
var(_cons) | .0821216 .0320226 .0382418 .1763503
cov(exper,_cons) | .0005401 .0061749 -.0115624 .0126427
-----------------------------+------------------------------------------------
var(Residual) | .1149779 .0147141 .0894713 .1477561
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 23.71 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Fixed rates of change approach:
xi: xtmixed lnw exper hgc_9 bxexp || id: , mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -141.94137 Iteration 1: log likelihood = -141.93861 Iteration 2: log likelihood = -141.93861
Computing standard errors:
Mixed-effects ML regression Number of obs = 257 Group variable: id Number of groups = 124
Obs per group: min = 1
avg = 2.1
max = 3
Wald chi2(3) = 12.09 Log likelihood = -141.93861 Prob > chi2 = 0.0071
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper | .0517798 .0209332 2.47 0.013 .0107516 .0928081
hgc_9 | .0457585 .0244959 1.87 0.062 -.0022525 .0937696
bxexp | -.0600723 .0345782 -1.74 0.082 -.1278443 .0076996
_cons | 1.737344 .0477509 36.38 0.000 1.643754 1.830934
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity |
var(_cons) | .0842504 .0211917 .0514597 .1379356
-----------------------------+------------------------------------------------
var(Residual) | .1147999 .0145473 .0895526 .1471652
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 23.71 Prob >= chibar2 = 0.0000
Table 5.6 on page 161 using unemployment_pp data.
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/unemployment_pp, clear
list id months cesd unemp if id == 7589 | id == 55697 | id == 67641 | id ==65441 | id == 53782
+---------------------------------+
| id months cesd unemp |
|---------------------------------|
212. | 7589 1.314168 36 1 |
213. | 7589 5.092402 40 1 |
214. | 7589 11.79466 39 1 |
454. | 53782 .4271047 22 1 |
455. | 53782 4.238193 15 0 |
|---------------------------------|
456. | 53782 11.07187 21 1 |
504. | 55697 1.347023 7 1 |
505. | 55697 5.782341 4 1 |
623. | 65441 1.084189 27 1 |
624. | 65441 4.698152 15 1 |
|---------------------------------|
625. | 65441 11.26899 7 0 |
647. | 67641 .3285421 32 1 |
648. | 67641 4.106776 9 0 |
649. | 67641 10.94045 10 0 |
+---------------------------------+
Table 5.7 on page 163.
Model A: Initial growth model:
xi: xtmixed cesd months || id: months, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2567.3171 Iteration 1: log likelihood = -2566.5828 Iteration 2: log likelihood = -2566.5688 Iteration 3: log likelihood = -2566.5687
Computing standard errors:
Mixed-effects ML regression Number of obs = 674 Group variable: id Number of groups = 254
Obs per group: min = 1
avg = 2.7
max = 3
Wald chi2(1) = 25.86 Log likelihood = -2566.5687 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | -.4219943 .0829791 -5.09 0.000 -.5846302 -.2593583
_cons | 17.66936 .7755634 22.78 0.000 16.14929 19.18944
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .3550396 .1844914 .1282217 .9830869
var(_cons) | 86.8483 14.96308 61.95951 121.7348
cov(months,_cons) | -3.057268 1.384603 -5.771041 -.3434951
-----------------------------+------------------------------------------------
var(Residual) | 68.85002 6.60262 57.05254 83.087
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 106.52 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model B: Main effect of unemployment
xi: xtmixed cesd months unemp || id: months, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2554.2517 Iteration 1: log likelihood = -2553.8054 Iteration 2: log likelihood = -2553.8016 Iteration 3: log likelihood = -2553.8016
Computing standard errors:
Mixed-effects ML regression Number of obs = 674 Group variable: id Number of groups = 254
Obs per group: min = 1
avg = 2.7
max = 3
Wald chi2(2) = 52.78 Log likelihood = -2553.8016 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | -.2019835 .0933162 -2.16 0.030 -.38488 -.019087
unemp | 5.111305 .9888446 5.17 0.000 3.173205 7.049405
_cons | 12.6656 1.242071 10.20 0.000 10.23118 15.10001
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .4647019 .1797873 .2176985 .9919587
var(_cons) | 93.51871 14.82016 68.54982 127.5824
cov(months,_cons) | -3.894087 1.370257 -6.579741 -1.208433
-----------------------------+------------------------------------------------
var(Residual) | 62.38761 6.013247 51.64818 75.36013
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 114.84 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model C: Effect of unemployment on initial status and growth rate
gen unempxmth = unemp*months
xi: xtmixed cesd months unemp unempxmth|| id: months, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2551.9898 Iteration 1: log likelihood = -2551.5272 Iteration 2: log likelihood = -2551.5235 Iteration 3: log likelihood = -2551.5235
Computing standard errors:
Mixed-effects ML regression Number of obs = 674 Group variable: id Number of groups = 254
Obs per group: min = 1
avg = 2.7
max = 3
Wald chi2(3) = 57.88 Log likelihood = -2551.5235 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | .162036 .1936623 0.84 0.403 -.2175351 .5416072
unemp | 8.529059 1.877875 4.54 0.000 4.848492 12.20963
unempxmth | -.4652222 .2172146 -2.14 0.032 -.890955 -.0394895
_cons | 9.616744 1.889309 5.09 0.000 5.913766 13.31972
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .4512058 .1773447 .2088397 .9748464
var(_cons) | 93.71305 14.77709 68.79849 127.6501
cov(months,_cons) | -3.873144 1.358796 -6.536335 -1.209953
-----------------------------+------------------------------------------------
var(Residual) | 62.03126 5.965555 51.37484 74.8981
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 116.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model D: Allowing unemp to have both fix and random effects. It seems that we have trouble to make it converge using the default algorithm (NR) for mle. The variance-covariance matrix from the output by SAS is in fact not positive-definite. Stata's xtmixed has difficult time to calculate the variance-covariance matrix.We have experimented with other algorithms, such as DFP. But the results are not very stable. So we decided to use the default algorithm even we don't have a variance-covariance matrix.
xi: xtmixed cesd unemp unempxmth || id: unemp unempxmth , mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2552.1214 Iteration 1: log likelihood = -2548.5862 Iteration 2: log likelihood = -2548.1007 Iteration 3: log likelihood = -2547.7787 Iteration 4: log likelihood = -2547.6959 Iteration 5: log likelihood = -2547.6587 Iteration 6: log likelihood = -2547.6504 Iteration 7: log likelihood = -2547.6481 (not concave) Iteration 8: log likelihood = -2547.648 Iteration 9: log likelihood = -2547.6475 Iteration 10: log likelihood = -2547.6474 Iteration 11: log likelihood = -2547.6474 Iteration 12: log likelihood = -2547.6474 (not concave) Iteration 13: log likelihood = -2547.6474 Iteration 14: log likelihood = -2547.6474 (not concave) Iteration 15: log likelihood = -2547.6474
Computing standard errors: standard error calculation failed
Mixed-effects ML regression Number of obs = 674 Group variable: id Number of groups = 254
Obs per group: min = 1
avg = 2.7
max = 3
Wald chi2(2) = 55.93 Log likelihood = -2547.6474 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
unemp | 6.927277 .930033 7.45 0.000 5.104445 8.750108
unempxmth | -.3029831 .1120893 -2.70 0.007 -.5226741 -.0832921
_cons | 11.19491 .7898805 14.17 0.000 9.646771 12.74305
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(unemp) | 44.96733 . . .
var(unempx~h) | .753401 . . .
var(_cons) | 45.25229 . . .
cov(unemp,unempx~h) | -5.628865 . . .
cov(unemp,_cons) | 6.544479 . . .
cov(unempx~h,_cons) | .6510678 . . .
-----------------------------+------------------------------------------------
var(Residual) | 59.01838 . . .
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 124.60 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Figure 5.3 on page 165 based on model B from the previous example. We will have to create a small data set for generating predicted values.
input months unemp group 0 1 1 5 1 1 14 1 1 0 1 2 5 1 2 5 0 2 14 0 2 0 1 3 10 1 3 10 0 3 14 0 3 0 1 4 5 1 4 5 0 4 10 0 4 10 1 4 14 1 4 end
save fig5_3 file fig5_3.dta saved
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/unemployment_pp, clear
xtmixed cesd months unemp || id: months, cov(un) var mle nolog
Mixed-effects ML regression Number of obs = 674 Group variable: id Number of groups = 254
Obs per group: min = 1
avg = 2.7
max = 3
Wald chi2(2) = 52.78 Log likelihood = -2553.8016 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | -.2019835 .0933162 -2.16 0.030 -.38488 -.019087
unemp | 5.111305 .9888446 5.17 0.000 3.173205 7.049405
_cons | 12.6656 1.242071 10.20 0.000 10.23118 15.10001
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .4647019 .1797873 .2176985 .9919587
var(_cons) | 93.51871 14.82016 68.54982 127.5824
cov(months,_cons) | -3.894087 1.370257 -6.579741 -1.208433
-----------------------------+------------------------------------------------
var(Residual) | 62.38761 6.013247 51.64818 75.36013
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 114.84 Prob > chi2 = 0.0000
use fig5_3, clear
predict p (option xb assumed)
twoway scatter p month, by(group) c(L)
Figure 5.4 on page 167 based on Model B, C and D from previous example.Leftmost panel using Model B:
xi: xtmixed cesd months unemp || id: months, mle cov(un) var
(output omitted)
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | -.2019835 .0933162 -2.16 0.030 -.38488 -.019087
unemp | 5.111305 .9888446 5.17 0.000 3.173205 7.049405
_cons | 12.6656 1.242071 10.20 0.000 10.23118 15.10001
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .4647019 .1797873 .2176985 .9919587
var(_cons) | 93.51871 14.82016 68.54982 127.5824
cov(months,_cons) | -3.894087 1.370257 -6.579741 -1.208433
-----------------------------+------------------------------------------------
var(Residual) | 62.38761 6.013247 51.64818 75.36013
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 114.84 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
predict p (option xb assumed)
sort unemp months
scatter p months, c(L)
Panel in the middle using Model C:
xi: xtmixed cesd months unemp unempxmth || id: months, mle cov(un) var
(output omitted)
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
months | .162036 .1936623 0.84 0.403 -.2175351 .5416072
unemp | 8.529059 1.877875 4.54 0.000 4.848492 12.20963
unempxmth | -.4652222 .2172146 -2.14 0.032 -.890955 -.0394895
_cons | 9.616744 1.889309 5.09 0.000 5.913766 13.31972
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(months) | .4512058 .1773447 .2088397 .9748464
var(_cons) | 93.71305 14.77709 68.79849 127.6501
cov(months,_cons) | -3.873144 1.358796 -6.536335 -1.209953
-----------------------------+------------------------------------------------
var(Residual) | 62.03126 5.965555 51.37484 74.8981
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 116.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
predict pc (option xb assumed)
sort unemp months
scatter pc months, c(L)
Rightmost panel using Model D:
xi: xtmixed cesd unemp unempxmth || id: unemp unempxmth , mle cov(un) var
(output omitted)
------------------------------------------------------------------------------
cesd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
unemp | 6.927277 .930033 7.45 0.000 5.104445 8.750108
unempxmth | -.3029831 .1120893 -2.70 0.007 -.5226741 -.0832921
_cons | 11.19491 .7898805 14.17 0.000 9.646771 12.74305
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(unemp) | 44.96733 . . .
var(unempx~h) | .753401 . . .
var(_cons) | 45.25229 . . .
cov(unemp,unempx~h) | -5.628865 . . .
cov(unemp,_cons) | 6.544479 . . .
cov(unempx~h,_cons) | .6510678 . . .
-----------------------------+------------------------------------------------
var(Residual) | 59.01838 . . .
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(6) = 124.60 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
predict pd (option xb assumed)
sort unemp months
scatter pd months, c(L)
Table 5.8 on page 175 using data set wages_pp.
Model A: Unemployment rate centered around 7
xtmixed lnw hgc_9 ue_7 exper bexper || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2415.3186 Iteration 1: log likelihood = -2415.2596 Iteration 2: log likelihood = -2415.2595
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(4) = 488.69 Log likelihood = -2415.2595 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hgc_9 | .040011 .0063627 6.29 0.000 .0275403 .0524816
ue_7 | -.0119504 .0017916 -6.67 0.000 -.015462 -.0084389
exper | .0440539 .0026034 16.92 0.000 .0389513 .0491564
bexper | -.0181832 .0044837 -4.06 0.000 -.0269711 -.0093953
_cons | 1.748989 .0113993 153.43 0.000 1.726646 1.771331
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016317 .0002126 .001264 .0021064
var(_cons) | .0506369 .0048085 .0420374 .0609955
cov(exper,_cons) | -.0029129 .0008386 -.0045565 -.0012693
-----------------------------+------------------------------------------------
var(Residual) | .0947952 .0019382 .0910714 .0986711
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1423.34 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model B: Within context centering
xtmixed lnw hgc_9 ue_mean ue_person_centered exper bexper || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2413.5457 Iteration 1: log likelihood = -2413.4893 Iteration 2: log likelihood = -2413.4892
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(5) = 494.17 Log likelihood = -2413.4892 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hgc_9 | .0401695 .0063507 6.33 0.000 .0277224 .0526166
ue_mean | -.0177091 .0035202 -5.03 0.000 -.0246085 -.0108097
ue_person_~d | -.0099015 .0020973 -4.72 0.000 -.0140121 -.0057909
exper | .0450568 .0026498 17.00 0.000 .0398632 .0502503
bexper | -.0188696 .0044769 -4.21 0.000 -.0276441 -.010095
_cons | 1.87426 .0295235 63.48 0.000 1.816395 1.932125
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016286 .0002123 .0012615 .0021026
var(_cons) | .0510114 .0048412 .042353 .0614399
cov(exper,_cons) | -.0030248 .0008431 -.0046772 -.0013724
-----------------------------+------------------------------------------------
var(Residual) | .0948018 .0019384 .0910777 .0986782
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1407.18 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model C: Centering on time-1
xtmixed lnw hgc_9 ue1 ue_centert1 exper bexper || id: exper, mle cov(un) var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -2412.9798 Iteration 1: log likelihood = -2412.9209 Iteration 2: log likelihood = -2412.9208
Computing standard errors:
Mixed-effects ML regression Number of obs = 6402 Group variable: id Number of groups = 888
Obs per group: min = 1
avg = 7.2
max = 13
Wald chi2(5) = 493.23 Log likelihood = -2412.9208 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
lnw | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hgc_9 | .0399276 .0063491 6.29 0.000 .0274835 .0523717
ue1 | -.0161774 .0026484 -6.11 0.000 -.0213682 -.0109866
ue_centert1 | -.010309 .0019445 -5.30 0.000 -.0141201 -.006498
exper | .0447649 .0026249 17.05 0.000 .0396202 .0499096
bexper | -.0183238 .0044848 -4.09 0.000 -.0271138 -.0095338
_cons | 1.869345 .0260316 71.81 0.000 1.818324 1.920366
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(exper) | .0016354 .0002129 .0012672 .0021107
var(_cons) | .0502771 .0047894 .0417143 .0605976
cov(exper,_cons) | -.0029024 .0008381 -.004545 -.0012598
-----------------------------+------------------------------------------------
var(Residual) | .0947669 .0019371 .0910452 .0986406
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 1423.82 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Table 5.10 on page 184 using medication_pp data.
Model A: TIME
use http://www.ats.ucla.edu/stat/stata/examples/alda/data/medication_pp, clear
gen ttime = treat*time
xtmixed pos treat time ttime || id: time, cov(un) mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -6340.2258 Iteration 1: log likelihood = -6340.2258
Computing standard errors:
Mixed-effects ML regression Number of obs = 1242 Group variable: id Number of groups = 64
Obs per group: min = 2
avg = 19.4
max = 21
Wald chi2(3) = 7.05 Log likelihood = -6340.2258 Prob > chi2 = 0.0702
------------------------------------------------------------------------------
pos | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treat | -3.109294 12.33256 -0.25 0.801 -27.28067 21.06208
time | -2.418128 1.730852 -1.40 0.162 -5.810535 .9742796
ttime | 5.53681 2.277846 2.43 0.015 1.072314 10.00131
_cons | 167.4635 9.32626 17.96 0.000 149.1843 185.7426
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(time) | 63.73588 14.27148 41.09476 98.8511
var(_cons) | 2111.401 420.2165 1429.428 3118.739
cov(time,_cons) | -121.6214 59.03397 -237.3259 -5.916964
-----------------------------+------------------------------------------------
var(Residual) | 1229.93 52.09137 1131.955 1336.384
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 971.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model B: TIME-3.33
gen ttime333 = treat*time333
xtmixed pos treat time333 ttime333 || id: time333, cov(un) mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -6340.2258 Iteration 1: log likelihood = -6340.2258
Computing standard errors:
Mixed-effects ML regression Number of obs = 1242 Group variable: id Number of groups = 64
Obs per group: min = 2
avg = 19.4
max = 21
Wald chi2(3) = 7.05 Log likelihood = -6340.2258 Prob > chi2 = 0.0702
------------------------------------------------------------------------------
pos | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treat | 15.34674 11.54466 1.33 0.184 -7.280383 37.97386
time333 | -2.418128 1.730852 -1.40 0.162 -5.810535 .9742798
ttime333 | 5.536811 2.277846 2.43 0.015 1.072314 10.00131
_cons | 159.403 8.764519 18.19 0.000 142.2249 176.5812
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(time333) | 63.73589 14.27147 41.09478 98.85109
var(_cons) | 2008.768 367.2589 1403.804 2874.44
cov(time333,_cons) | 90.8317 52.45916 -11.98636 193.6498
-----------------------------+------------------------------------------------
var(Residual) | 1229.929 52.09137 1131.955 1336.384
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 971.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Model C: TIME-6.67
gen ttime667 = treat*time667
xtmixed pos treat time667 ttime667 || id: time667, cov(un) mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -6340.2258 Iteration 1: log likelihood = -6340.2258
Computing standard errors:
Mixed-effects ML regression Number of obs = 1242 Group variable: id Number of groups = 64
Obs per group: min = 2
avg = 19.4
max = 21
Wald chi2(3) = 7.05 Log likelihood = -6340.2258 Prob > chi2 = 0.0702
------------------------------------------------------------------------------
pos | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treat | 33.80278 15.1581 2.23 0.026 4.093444 63.51211
time667 | -2.418128 1.730852 -1.40 0.162 -5.810535 .9742797
ttime667 | 5.536811 2.277846 2.43 0.015 1.072314 10.00131
_cons | 151.3426 11.54247 13.11 0.000 128.7198 173.9654
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(time667) | 63.73588 14.27144 41.09481 98.85099
var(_cons) | 3322.485 632.1168 2288.328 4824.004
cov(time667,_cons) | 303.2845 80.90138 144.7207 461.8483
-----------------------------+------------------------------------------------
var(Residual) | 1229.93 52.09138 1131.955 1336.384
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 971.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
Figure 5.5 on page 185
xtmixed pos treat time ttime || id: time, cov(un) mle var
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -6340.2258 Iteration 1: log likelihood = -6340.2258
Computing standard errors:
Mixed-effects ML regression Number of obs = 1242 Group variable: id Number of groups = 64
Obs per group: min = 2
avg = 19.4
max = 21
Wald chi2(3) = 7.05 Log likelihood = -6340.2258 Prob > chi2 = 0.0702
------------------------------------------------------------------------------
pos | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
treat | -3.109294 12.33256 -0.25 0.801 -27.28067 21.06208
time | -2.418128 1.730852 -1.40 0.162 -5.810535 .9742796
ttime | 5.53681 2.277846 2.43 0.015 1.072314 10.00131
_cons | 167.4635 9.32626 17.96 0.000 149.1843 185.7426
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(time) | 63.73588 14.27148 41.09476 98.8511
var(_cons) | 2111.401 420.2165 1429.428 3118.739
cov(time,_cons) | -121.6214 59.03397 -237.3259 -5.916964
-----------------------------+------------------------------------------------
var(Residual) | 1229.93 52.09137 1131.955 1336.384
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 971.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
predict pf (option xb assumed)
scatter pf time, c(L)
Page 188 on modeling initial and final status.
xtmixed pos initial tinit final tfinal, nocons || id: initial final, cov(un) mle var nocons
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -6340.2258 Iteration 1: log likelihood = -6340.2258
Computing standard errors:
Mixed-effects ML regression Number of obs = 1242 Group variable: id Number of groups = 64
Obs per group: min = 2
avg = 19.4
max = 21
Wald chi2(4) = 912.52 Log likelihood = -6340.2258 Prob > chi2 = 0.0000
------------------------------------------------------------------------------
pos | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
initial | 167.4635 9.326258 17.96 0.000 149.1843 185.7426
tinit | -3.109296 12.33256 -0.25 0.801 -27.28066 21.06207
final | 151.3426 11.54248 13.11 0.000 128.7198 173.9654
tfinal | 33.80278 15.1581 2.23 0.026 4.093439 63.51211
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Unstructured |
var(initial) | 2111.399 420.2156 1429.428 3118.735
var(final) | 3322.486 632.1178 2288.328 4824.009
cov(initial,final) | 1300.589 392.7855 530.7431 2070.434
-----------------------------+------------------------------------------------
var(Residual) | 1229.93 52.09137 1131.955 1336.384
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(3) = 971.31 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference
estat recov, corr
Random-effects correlation matrix for level id
| initial final
-------------+----------------------
initial | 1
final | .4910471 1
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