Jason T. Newsom,
Richard N. Jones, & Scott M. Hofer.
Longitudinal
data analysis: A practical guide for researchers in aging, health, and social
sciences
CHAPTER 7
Shaw BA & Liang J
Table 7.1
Multilevel Regression of BMI over Time &
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 1
Bmi =
body mass index
Ctime =
time centered
xtmixed bmi ctime, || id:, covariance(unstructured) variance
Note: single-variable random-effects specification;
covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood = -98872.948
Iteration 1: log
restricted-likelihood = -98872.948
Computing standard errors:
Mixed-effects REML regression
Number of obs = 42721
Group variable: id Number
of groups = 7377
Obs per group: min = 1
avg = 5.8
max
=
6
Wald chi2(1) = 468.78
Log restricted-likelihood = -98872.948 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
bmi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ctime | .0534405 .0024682 21.65 0.000 .0486028 .0582781
_cons | 28.09735 .059834 469.59 0.000 27.98008 28.21463
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate
Std. Err.
[95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons) |
25.86636
.4350063
25.02766
26.73317
-----------------------------+------------------------------------------------
var(Residual) |
3.054958
.022982
3.010244
3.100335
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 66946.57 Prob >= chibar2 =
0.0000
Table 7.2 Multilevel Regression of
BMI over Time, baseline age, and gender
Model 2
gen agetime=ctime*Zage
(1046 missing values generated)
xtmixed bmi Zage ctime agetime, || id:, covariance(unstructured) variance
Note: single-variable random-effects specification;
covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood = -98715.888
Iteration 1: log
restricted-likelihood = -98715.888
Computing standard errors:
Mixed-effects REML regression
Number of obs = 42721
Group variable: id
Number of groups
=
7377
Obs
per group: min = 1
avg = 5.8
max = 6
Wald chi2(3) = 802.21
Log restricted-likelihood = -98715.888 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
bmi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Zage | -.2979477 .0597485 -4.99 0.000 -.4150526 -.1808429
ctime | .0536783 .0024578 21.84 0.000 .0488612 .0584954
agetime | -.0430268
.0024645 -17.46 0.000 -.0478571 -.0381966
_cons | 28.09761 .0597372 470.35 0.000 27.98053 28.21469
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate
Std. Err.
[95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons) | 25.78559 .4336245 24.94956 26.64964
-----------------------------+------------------------------------------------
var(Residual) |
3.028948 .0227866 2.984614 3.073939
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 67123.00 Prob >= chibar2 =
0.0000
.
Table 7.2
Multilevel Regression of BMI over Time, baseline age, and gender
Model 3
. gen sextime= Zgender*ctime
(1046 missing values generated)
. xtmixed bmi Zage Zgender ctime agetime sextime, || id:,
covariance(unstructured) variance
Note: single-variable random-effects specification; covariance structure set to
identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood = -98718.305
Iteration 1: log
restricted-likelihood = -98718.305
Computing standard errors:
Mixed-effects REML regression
Number of obs = 42721
Group variable: id
Number of groups
=
7377
Obs per group: min = 1
avg = 5.8
max
= 6
Wald chi2(5) = 811.40
Log restricted-likelihood = -98718.305 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
bmi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Zage | -.2842451 .0613763 -4.63 0.000 -.4045403
-.1639498
Zgender | -.0600277 .0613671 -0.98 0.328 -.1803049 .0602496
ctime | .0537244 .0024576 21.86 0.000 .0489076 .0585411
agetime | -.041395 .0025302 -16.36 0.000 -.0463541 -.0364358
sextime | -.0071688 .0025213 -2.84 0.004 -.0121104 -.0022272
_cons | 28.09756 .0597368 470.36 0.000 27.98047 28.21464
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate
Std. Err.
[95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons)
| 25.78532 .4336443 24.94925 26.64941
-----------------------------+------------------------------------------------
var(Residual) |
3.028354 .0227824 2.984028 3.073337
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 67129.34 Prob >= chibar2 =
0.0000
Table 7.2 Multilevel Regression of
BMI over Time, baseline age, and gender
Model 4
. xtmixed bmi Zage Zgender ctime agetime sextime genderage, || id:, covariance(unstructured) variance
Note: single-variable random-effects specification;
covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood =
-98719.74
Iteration 1: log
restricted-likelihood =
-98719.74
Computing standard errors:
Mixed-effects REML regression
Number of obs = 42721
Group variable: id
Number of groups
=
7377
Obs per group: min = 1
avg = 5.8
max = 6
Wald chi2(6) = 812.29
Log restricted-likelihood =
-98719.74 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
bmi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Zage | -.2785243 .0616768 -4.52 0.000 -.3994087 -.1576399
Zgender | -.0583219 .0613943 -0.95 0.342 -.1786526 .0620088
ctime | .0537234 .0024576 21.86 0.000 .0489066 .0585401
agetime | -.0413954 .0025302
-16.36 0.000 -.0463545 -.0364362
sextime | -.0071682 .0025213 -2.84 0.004
-.0121098 -.0022266
genderage | -.05742 .0609893 -0.94 0.346 -.1769567 .0621167
_cons | 28.11069 .0613445 458.24 0.000 27.99046 28.23092
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate
Std. Err.
[95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons) |
25.78576
.4336805
24.94962
26.64993
-----------------------------+------------------------------------------------
var(Residual) |
3.028353 .0227824 2.984028 3.073336
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 67126.42 Prob >= chibar2 =
0.0000
.
Table 7.3
Multilevel Regression of BMI over Time and time-varying marital status
Model 5
xtmixed bmi Zage
Zgender ctime agetime
sextime genderage married, || id:, covariance(unstructured) variance
Note: single-variable random-effects specification; covariance structure set to
identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood = -98674.643
Iteration 1: log
restricted-likelihood = -98674.643
Computing standard errors:
Mixed-effects REML regression
Number of obs = 42713
Group variable: id
Number of groups
=
7377
Obs per group: min = 1
avg = 5.8
max
= 6
Wald chi2(7) = 880.58
Log restricted-likelihood = -98674.643 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
bmi | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Zage | -.2616285 .0617824 -4.23 0.000 -.3827198 -.1405372
Zgender | -.0975324 .0616528 -1.58 0.114 -.2183697 .0233048
ctime | .0576435 .0025014 23.04 0.000 .0527407 .0625462
agetime | -.0405541 .0025296
-16.03 0.000 -.045512 -.0355963
sextime | -.0091027 .0025297 -3.60 0.000 -.0140608 -.0041445
genderage | -.0763519 .0611033 -1.25 0.211 -.1961122 .0434084
married | .3824194 .0467899 8.17 0.000 .290713 .4741258
_cons | 27.82797 .0704854 394.80 0.000 27.68982 27.96612
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons) |
25.84753
.4347959
25.00924
26.71392
-----------------------------+------------------------------------------------
var(Residual) |
3.021741 .0227368 2.977505 3.066634
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 67146.59 Prob >= chibar2 =
0.0000
Table 7.3
Multilevel Regression of BMI over Time and time-varying marital status
Model 5
. gen agemar= Zage* married
. gen sexagemar=genderage*married
. gen sexmar=Zgender*married
. xtmixed ctime Zage Zgender agetime sextime genderage married agemar sexmar
sexagemar, || id:, covariance(unstructured) variance
Note: single-variable random-effects specification;
covariance structure set to identity
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log
restricted-likelihood = -114697.89
Iteration 1: log
restricted-likelihood = -114516.32
Iteration 2: log
restricted-likelihood = -114513.72
Iteration 3: log
restricted-likelihood = -114513.72
Computing standard errors:
Mixed-effects REML regression
Number of obs = 43207
Group variable: id
Number of groups
=
7377
Obs per group: min = 1
avg
=
5.9
max = 6
Wald chi2(9) = 349.18
Log restricted-likelihood = -114513.72 Prob >
chi2
= 0.0000
------------------------------------------------------------------------------
ctime |
Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Zage | .0820337 .0413418 1.98 0.047 .0010052 .1630622
Zgender | -.066591 .0385191 -1.73 0.084 -.1420871 .008905
agetime | -.0022576 .0049635 -0.45 0.649 -.0119859 .0074706
sextime | .0023807 .0049409 0.48 0.630 -.0073033 .0120648
genderage | .1802922 .0426636 4.23 0.000 .0966731 .2639113
married | -.6437547 .0417717
-15.41 0.000 -.7256257 -.5618837
agemar
| -.1334203 .0457766 -2.91 0.004 -.2231408 -.0436998
sexmar
| .1706389 .0433057 3.94 0.000 .0857613 .2555165
sexagemar | -.1650699 .0466856 -3.54 0.000 -.2565721 -.0735678
_cons | .4612832 .036657 12.58 0.000 .3894368 .5331297
------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate
Std. Err.
[95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Identity
|
var(_cons) |
2.24e-21
1.31e-21
7.12e-22
7.05e-21
-----------------------------+------------------------------------------------
var(Residual) |
11.72414 .0797779 11.56881 11.88154
------------------------------------------------------------------------------
LR test vs. linear regression: chibar2(01) = 0.00 Prob >= chibar2 = 1.0000