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