-------------
      name:  STATA_Chapter4
       log:  C:\Dropbox\PilesOfVariance\Chapter4\STATA\STATA_Chapter4_Output.smcl
  log type:  smcl
 opened on:  21 Oct 2014, 09:20:47

.
. display as result "Chapter 4 Example: Means by StudyDay for Positive Mood outcome"
Chapter 4 Example: Means by StudyDay for Positive Mood outcome

. tabulate studyday, summarize(posmood)

  studyday: |
     Day of |  Summary of posmood: Positive Mood
Study (1 to |           Rating (1 to 5)
         7) |        Mean   Std. Dev.       Freq.
------------+------------------------------------
          1 |   3.6983522   .75932519         192
          2 |   3.7608782   .74191965         195
          3 |   3.6976149   .75112316         194
          4 |   3.7009648   .76038526         197
          5 |   3.7429638   .72979766         197
          6 |   3.7014449   .71098376         196
          7 |   3.7190701   .74504013         199
------------+------------------------------------
      Total |   3.7173899   .74151661        1370

.
. display as result "Ch 4: Saturated Means, Unstructured R-Only Model"
Ch 4: Saturated Means, Unstructured R-Only Model

. display as result "Test for mean differences across days"
Test for mean differences across days

. mixed posmood i.studyday, ///
>                 || personid: , noconstant variance reml covariance(unstructured) ///
>                 residuals(unstructured,t(studyday)),

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1547.1828  (not concave)
Iteration 1:   log restricted-likelihood = -1066.1668
Iteration 2:   log restricted-likelihood = -1010.9925
Iteration 3:   log restricted-likelihood = -1004.4558
Iteration 4:   log restricted-likelihood = -1004.0025
Iteration 5:   log restricted-likelihood = -1004.0011
Iteration 6:   log restricted-likelihood = -1004.0011

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(6)       =      4.65
Log restricted-likelihood = -1004.0011          Prob > chi2        =    0.5894

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    studyday |
          2  |    .0479807    .0367583      1.31    0.192     -.0240642     .1200256
          3  |    -.012323    .0428554     -0.29    0.774     -.0963181     .0716721
          4  |   -.0182561    .0426912     -0.43    0.669     -.1019294     .0654172
          5  |    .0230229    .0420647      0.55    0.584     -.0594224     .1054683
          6  |   -.0172376    .0448114     -0.38    0.700     -.1050664     .0705911
          7  |    -.011488    .0478975     -0.24    0.810     -.1053653     .0823893
             |
       _cons |    3.734786     .054963     67.95    0.000      3.627061     3.842512
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid:            (empty) |
-----------------------------+------------------------------------------------
Residual: Unstructured       |
                     var(e1) |   .5954834   .0611572      .4869112    .7282652
                     var(e2) |   .5640254   .0574053      .4620247    .6885447
                     var(e3) |   .5772321   .0588677      .4726532      .70495
                     var(e4) |   .5883853   .0595182      .4825679    .7174063
                     var(e5) |   .5417469   .0548186      .4442879    .6605845
                     var(e6) |   .5119749   .0518979      .4197242    .6245011
                     var(e7) |   .5570255   .0560184      .4573748    .6783875
                  cov(e1,e2) |   .4503922   .0528631      .3467826    .5540019
                  cov(e1,e3) |   .4097711   .0516285      .3085812     .510961
                  cov(e1,e4) |   .4152337   .0518406       .313628    .5168393
                  cov(e1,e5) |    .397019   .0496511      .2997046    .4943334
                  cov(e1,e6) |   .3592537   .0471811      .2667803     .451727
                  cov(e1,e7) |   .3517675   .0483655      .2569729    .4465621
                  cov(e2,e3) |   .3988206   .0500033      .3008159    .4968254
                  cov(e2,e4) |   .4284519   .0513819      .3277451    .5291586
                  cov(e2,e5) |   .4088366   .0491871      .3124316    .5052416
                  cov(e2,e6) |   .3549192   .0460214       .264719    .4451195
                  cov(e2,e7) |   .3684874   .0478115      .2747785    .4621963
                  cov(e3,e4) |    .412896   .0510796      .3127817    .5130102
                  cov(e3,e5) |   .4145386   .0498226      .3168882     .512189
                  cov(e3,e6) |   .3528624    .046431      .2618594    .4438655
                  cov(e3,e7) |   .3887702   .0491039      .2925283    .4850121
                  cov(e4,e5) |   .4244063   .0503958      .3256323    .5231802
                  cov(e4,e6) |   .4137844   .0491111      .3175284    .5100404
                  cov(e4,e7) |   .3868429   .0492697      .2902761    .4834098
                  cov(e5,e6) |   .3639662   .0456866      .2744221    .4535104
                  cov(e5,e7) |   .3822045   .0476426      .2888268    .4755823
                  cov(e6,e7) |   .3419375   .0452543      .2532408    .4306342
-----------------------------+------------------------------------------------
LR test vs. linear regression:      chi2(27) =  1086.36   Prob > chi2 = 0.0000


Note: The reported degrees of freedom
assumes the null hypothesis is not on the
boundary of the parameter space.  If this is not
true, then the reported test is
conservative.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1004.001     35     2078.002    2193.443
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.595
2   |  0.450     0.564
3   |  0.410     0.399     0.577
4   |  0.415     0.428     0.413     0.588
5   |  0.397     0.409     0.415     0.424     0.542
6   |  0.359     0.355     0.353     0.414     0.364     0.512
7   |  0.352     0.368     0.389     0.387     0.382     0.342     0.557

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.772     0.751     0.760     0.767     0.736     0.716     0.746


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.777     1.000
3   |  0.699     0.699     1.000
4   |  0.701     0.744     0.708     1.000
5   |  0.699     0.740     0.741     0.752     1.000
6   |  0.651     0.660     0.649     0.754     0.691     1.000
7   |  0.611     0.657     0.686     0.676     0.696     0.640     1.000

.       contrast i.studyday,

Contrasts of marginal linear predictions


Margins  : asbalanced


 -------------+----------------------------------
             |         df         chi2      P>chi2
 -------------+----------------------------------
posmood      |
    studyday  |          6         4.65      0.5894
 -------------+----------------------------------

.       margins  i.studyday,

Adjusted predictions                              Number of obs   =       1370


Expression  : Linear prediction, fixed portion, predict()


-------------+----------------------------------------------------------------
             |            Delta-method
             |     Margin    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
    studyday |
          1  |    3.734786     .054963     67.95    0.000      3.627061     3.842512
          2  |    3.782767    .0533208     70.94    0.000       3.67826     3.887274
          3  |    3.722463    .0540112     68.92    0.000      3.616603     3.828324
          4  |     3.71653    .0543587     68.37    0.000      3.609989     3.823071
          5  |    3.757809    .0521661     72.04    0.000      3.655566     3.860053
          6  |    3.717549    .0507882     73.20    0.000      3.618006     3.817092
          7  |    3.723298     .052829     70.48    0.000      3.619756     3.826841
-------------+----------------------------------------------------------------

.       margins  i.studyday, pwcompare(pveffects)

Pairwise comparisons of adjusted predictions


Expression  : Linear prediction, fixed portion, predict()


-------------+---------------------------------------
             |            Delta-method     Una djusted
             |   Contrast    Std. Err.       z    P>|z|
-------------+---------------------------------------
    studyday |
     2 vs 1  |    .0479807    .0367583      1.31    0.192
     3 vs 1  |    -.012323    .0428554     -0.29    0.774
     4 vs 1  |   -.0182561    .0426912     -0.43    0.669
     5 vs 1  |    .0230229    .0420647      0.55    0.584
     6 vs 1  |   -.0172376    .0448114     -0.38    0.700
     7 vs 1  |    -.011488    .0478975     -0.24    0.810
     3 vs 2  |   -.0603037    .0420789     -1.43    0.152
     4 vs 2  |   -.0662368    .0388804     -1.70    0.088
     5 vs 2  |   -.0249578    .0383903     -0.65    0.516
     6 vs 2  |   -.0652184    .0432831     -1.51    0.132
     7 vs 2  |   -.0594687    .0441493     -1.35    0.178
     4 vs 3  |   -.0059331    .0417194     -0.14    0.887
     5 vs 3  |    .0353459    .0386444      0.91    0.360
     6 vs 3  |   -.0049146    .0443572     -0.11    0.912
     7 vs 3  |     .000835    .0426672      0.02    0.984
     5 vs 4  |     .041279    .0378446      1.09    0.275
     6 vs 4  |    .0010184    .0373721      0.03    0.978
     7 vs 4  |    .0067681    .0433284      0.16    0.876
     6 vs 5  |   -.0402606     .040743     -0.99    0.323
     7 vs 5  |   -.0345109    .0411119     -0.84    0.401
     7 vs 6  |    .0057496    .0441701      0.13    0.896
-------------+---------------------------------------

.
. display as result "Ch 4: Empty Means, Unstructured R-Only Model"
Ch 4: Empty Means, Unstructured R-Only Model

. display as result "Best-fitting and least parsimonious baseline"
Best-fitting and least parsimonious baseline

. mixed posmood , ///
>                 || personid: , noconstant variance reml covariance(unstructured) ///
>                 residuals(unstructured,t(studyday)),

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1536.7281  (not concave)
Iteration 1:   log restricted-likelihood = -1055.8937
Iteration 2:   log restricted-likelihood = -999.93878
Iteration 3:   log restricted-likelihood = -992.21623
Iteration 4:   log restricted-likelihood = -991.55536
Iteration 5:   log restricted-likelihood =  -991.5533
Iteration 6:   log restricted-likelihood =  -991.5533

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood =  -991.5533          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735287    .0449729     83.06    0.000      3.647142     3.823433
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid:            (empty) |
-----------------------------+------------------------------------------------
Residual: Unstructured       |
                     var(e1) |   .5953499   .0610296      .4869846     .727829
                     var(e2) |   .5631702   .0573903      .4612085    .6876732
                     var(e3) |   .5774636   .0588131      .4729683    .7050456
                     var(e4) |   .5884928   .0594675      .4827551    .7173902
                     var(e5) |   .5406841   .0546713      .4434802    .6591934
                     var(e6) |   .5121272   .0518758      .4199094    .6245974
                     var(e7) |   .5565283   .0559129      .4570559    .6776497
                  cov(e1,e2) |   .4495077   .0527821      .3460568    .5529587
                  cov(e1,e3) |   .4107404    .051598      .3096102    .5118706
                  cov(e1,e4) |    .415833   .0517968      .3143132    .5173528
                  cov(e1,e5) |   .3969976   .0495731       .299836    .4941591
                  cov(e1,e6) |    .360047   .0471634      .2676083    .4524856
                  cov(e1,e7) |   .3525828   .0483205      .2578763    .4472893
                  cov(e2,e3) |   .3974823   .0499162      .2996484    .4953162
                  cov(e2,e4) |   .4265111   .0512419      .3260787    .5269434
                  cov(e2,e5) |   .4082761   .0491782      .3118885    .5046637
                  cov(e2,e6) |   .3534403   .0459387      .2634022    .4434785
                  cov(e2,e7) |   .3671575   .0477108       .273646    .4606691
                  cov(e3,e4) |   .4139152    .051089      .3137827    .5140477
                  cov(e3,e5) |   .4140917   .0497372      .3166085    .5115749
                  cov(e3,e6) |   .3540279   .0464611      .2629659      .44509
                  cov(e3,e7) |   .3895517    .049086      .2933449    .4857585
                  cov(e4,e5) |   .4236609   .0502866      .3251011    .5222208
                  cov(e4,e6) |   .4146427   .0491303      .3183491    .5109363
                  cov(e4,e7) |   .3876445   .0492596      .2910975    .4841916
                  cov(e5,e6) |   .3636233   .0456202      .2742094    .4530371
                  cov(e5,e7) |   .3817583   .0475456      .2885706     .474946
                  cov(e6,e7) |   .3427667    .045267       .254045    .4314884
-----------------------------+------------------------------------------------
LR test vs. linear regression:      chi2(27) =  1090.35   Prob > chi2 = 0.0000


Note: The reported degrees of freedom
assumes the null hypothesis is not on the
boundary of the parameter space.  If this is not
true, then the reported test is
conservative.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -991.5533     29     2041.107    2136.758
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.595
2   |  0.450     0.563
3   |  0.411     0.397     0.577
4   |  0.416     0.427     0.414     0.588
5   |  0.397     0.408     0.414     0.424     0.541
6   |  0.360     0.353     0.354     0.415     0.364     0.512
7   |  0.353     0.367     0.390     0.388     0.382     0.343     0.557

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.772     0.750     0.760     0.767     0.735     0.716     0.746


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.776     1.000
3   |  0.701     0.697     1.000
4   |  0.703     0.741     0.710     1.000
5   |  0.700     0.740     0.741     0.751     1.000
6   |  0.652     0.658     0.651     0.755     0.691     1.000
7   |  0.613     0.656     0.687     0.677     0.696     0.642     1.000

.       estimates store UN,

.
. display as result "Ch 4: Empty Means, Compound Symmetry R-Only Model"
Ch 4: Empty Means, Compound Symmetry R-Only Model

. display as result "Worst-fitting and most parsimonious baseline"
Worst-fitting and most parsimonious baseline

. mixed posmood , ///
>                 || personid: , noconstant variance reml covariance(unstructured) ///
>                 residuals(exchangeable,t(studyday)),


Note: t() not required for this residual
structure; ignored


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1536.7281
Iteration 1:   log restricted-likelihood = -1015.6142
Iteration 2:   log restricted-likelihood = -1014.6019
Iteration 3:   log restricted-likelihood = -1014.6006
Iteration 4:   log restricted-likelihood = -1014.6006

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1014.6006          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735623    .0455563     82.00    0.000      3.646335     3.824912
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid:            (empty) |
-----------------------------+------------------------------------------------
Residual: Exchangeable       |
                      var(e) |   .5604235   .0421149      .4836709    .6493558
                      cov(e) |   .3899991   .0417079      .3082531    .4717452
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(1) =  1044.25   Prob > chi2 = 0.0000


Note: The reported degrees of freedom
assumes the null hypothesis is not on the
boundary of the parameter space.  If this is not
true, then the reported test is
conservative.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1014.601      3     2035.201    2045.096
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat wcorrelation, covariance,


Covariances
for personid = 1:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.390     0.560
3   |  0.390     0.390     0.560
4   |  0.390     0.390     0.390     0.560
5   |  0.390     0.390     0.390     0.390     0.560
6   |  0.390     0.390     0.390     0.390     0.390     0.560
7   |  0.390     0.390     0.390     0.390     0.390     0.390     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.696     1.000
3   |  0.696     0.696     1.000
4   |  0.696     0.696     0.696     1.000
5   |  0.696     0.696     0.696     0.696     1.000
6   |  0.696     0.696     0.696     0.696     0.696     1.000
7   |  0.696     0.696     0.696     0.696     0.696     0.696     1.000

.       estimates store CS,

.       lrtest UN CS,

Likelihood-ratio test                                 LR chi2(26) =     46.09
(Assumption: CS nested in UN)                         Prob > chi2 =    0.0089


Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space.  If this is not true, then the reported test is conservative.


Note: LR tests based on REML are valid
only when the fixed-effects specification is identical for
both models.


.
. display as result "Ch 4: Empty Means, First-Order Auto-Regressive R-Only Model"
Ch 4: Empty Means, First-Order Auto-Regressive R-Only Model

. mixed posmood , ///
>                 || personid: , noconstant variance reml covariance(unstructured) ///
>                 residuals(ar1,t(studyday)),


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1536.7281
Iteration 1:   log restricted-likelihood = -1363.0029
Iteration 2:   log restricted-likelihood = -1143.4914
Iteration 3:   log restricted-likelihood = -1139.9882
Iteration 4:   log restricted-likelihood = -1139.8961
Iteration 5:   log restricted-likelihood = -1139.8961

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1139.8961          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.731198    .0375553     99.35    0.000      3.657591     3.804805
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid:            (empty) |
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |   .7129477   .0181635      .6754792     .746744
                      var(e) |   .5627133   .0331484       .501354    .6315822
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(1) =   793.66   Prob > chi2 = 0.0000


Note: The reported degrees of freedom
assumes the null hypothesis is not on the
boundary of the parameter space.  If this is not
true, then the reported test is
conservative.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1139.896      3     2285.792    2295.687
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.563
2   |  0.401     0.563
3   |  0.286     0.401     0.563
4   |  0.204     0.286     0.401     0.563
5   |  0.145     0.204     0.286     0.401     0.563
6   |  0.104     0.145     0.204     0.286     0.401     0.563
7   |  0.074     0.104     0.145     0.204     0.286     0.401     0.563

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.750     0.750     0.750     0.750     0.750     0.750     0.750


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.713     1.000
3   |  0.508     0.713     1.000
4   |  0.362     0.508     0.713     1.000
5   |  0.258     0.362     0.508     0.713     1.000
6   |  0.184     0.258     0.362     0.508     0.713     1.000
7   |  0.131     0.184     0.258     0.362     0.508     0.713     1.000

.       estimates store AR1,

.       lrtest UN AR1,

Likelihood-ratio test                                 LR chi2(26) =    296.69
(Assumption: AR1 nested in UN)                        Prob > chi2 =    0.0000


Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space.  If this is not true, then the reported test is conservative.


Note: LR tests based on REML are valid
only when the fixed-effects specification is identical for
both models.


.
. display as result "Ch 4: Empty Means, n-1 Lag Toeplitz R-Only Model"
Ch 4: Empty Means, n-1 Lag Toeplitz R-Only Model

. mixed posmood , ///
>                 || personid: , noconstant variance reml covariance(unstructured) ///
>                 residuals(toeplitz6,t(studyday)),


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1536.7281  (not concave)
Iteration 1:   log restricted-likelihood = -1290.0003  (not concave)
Iteration 2:   log restricted-likelihood = -1127.4645
Iteration 3:   log restricted-likelihood = -1103.9003
Iteration 4:   log restricted-likelihood = -1045.7564
Iteration 5:   log restricted-likelihood = -1010.5271
Iteration 6:   log restricted-likelihood = -1004.9793
Iteration 7:   log restricted-likelihood = -1004.9531
Iteration 8:   log restricted-likelihood = -1004.9531

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1004.9531          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735746    .0455171     82.07    0.000      3.646534     3.824958
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid:            (empty) |
-----------------------------+------------------------------------------------
Residual: Toeplitz(6)        |
                        cov1 |   .3985692   .0420015      .3162478    .4808906
                        cov2 |   .4062513   .0419684      .3239948    .4885078
                        cov3 |   .3850755   .0419538      .3028475    .4673035
                        cov4 |   .3823008    .042189      .2996118    .4649897
                        cov5 |   .3709108    .042686      .2872478    .4545738
                        cov6 |   .3477053   .0439774      .2615112    .4338995
                      var(e) |   .5609115   .0421003      .4841788    .6498049
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(6) =  1063.55   Prob > chi2 = 0.0000


Note: The reported degrees of freedom
assumes the null hypothesis is not on the
boundary of the parameter space.  If this is not
true, then the reported test is
conservative.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1004.953      8     2025.906    2052.293
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.561
2   |  0.399     0.561
3   |  0.406     0.399     0.561
4   |  0.385     0.406     0.399     0.561
5   |  0.382     0.385     0.406     0.399     0.561
6   |  0.371     0.382     0.385     0.406     0.399     0.561
7   |  0.348     0.371     0.382     0.385     0.406     0.399     0.561

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.711     1.000
3   |  0.724     0.711     1.000
4   |  0.687     0.724     0.711     1.000
5   |  0.682     0.687     0.724     0.711     1.000
6   |  0.661     0.682     0.687     0.724     0.711     1.000
7   |  0.620     0.661     0.682     0.687     0.724     0.711     1.000

.       estimates store TOEP7,

.       lrtest UN TOEP7,

Likelihood-ratio test                                 LR chi2(21) =     26.80
(Assumption: TOEP7 nested in UN)                      Prob > chi2 =    0.1776


Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space.  If this is not true, then the reported test is conservative.


Note: LR tests based on REML are valid
only when the fixed-effects specification is identical for
both models.


.       lrtest TOEP7 CS,

Likelihood-ratio test                                 LR chi2(5)  =     19.30
(Assumption: CS nested in TOEP7)                      Prob > chi2 =    0.0017


Note: LR tests based on REML are valid
only when the fixed-effects specification is identical for
both models.


.       lrtest TOEP7 AR1,

Likelihood-ratio test                                 LR chi2(5)  =    269.89
(Assumption: AR1 nested in TOEP7)                     Prob > chi2 =    0.0000


Note: LR tests based on REML are valid
only when the fixed-effects specification is identical for
both models.


.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "Diagonal R"
Diagonal R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(independent,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: t() not required for this residual
structure; ignored


Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1014.6006

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1014.6006          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735623    .0455563     82.00    0.000      3.646335     3.824912
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3899992   .0417079      .3162518    .4809438
-----------------------------+------------------------------------------------
               var(Residual) |   .1704244   .0070485      .1571546    .1848146
-----------------------------+------------------------------------------------
LR test vs. linear regression: chibar2(01) =  1044.25 Prob >= chibar2 =  0.0000

.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1014.601      3     2035.201    2045.096
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat icc,

Intraclass correlation

 -----------------------------+------------------------------------------------
                        Level |        ICC   Std. Err.     [95% Conf. Interval]
 -----------------------------+------------------------------------------------
                     personid |   .6959008   .0244804     .6459137     .7416536
 -----------------------------+------------------------------------------------

.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3899992

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.390     0.560
3   |  0.390     0.390     0.560
4   |  0.390     0.390     0.390     0.560
5   |  0.390     0.390     0.390     0.390     0.560
6   |  0.390     0.390     0.390     0.390     0.390     0.560
7   |  0.390     0.390     0.390     0.390     0.390     0.390     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


obs   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.696     1.000
3   |  0.696     0.696     1.000
4   |  0.696     0.696     0.696     1.000
5   |  0.696     0.696     0.696     0.696     1.000
6   |  0.696     0.696     0.696     0.696     0.696     1.000
7   |  0.696     0.696     0.696     0.696     0.696     0.696     1.000

.       estimates store RIDIAG,

.       lrtest UN RIDIAG, force

Likelihood-ratio test                                 LR chi2(26) =     46.09
(Assumption: RIDIAG nested in UN)                     Prob > chi2 =    0.0089

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "Diagonal Heterogeneous R"
Diagonal Heterogeneous R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(banded0,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1010.2695
Iteration 2:   log restricted-likelihood = -1009.3552
Iteration 3:   log restricted-likelihood = -1009.3536
Iteration 4:   log restricted-likelihood = -1009.3536

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1009.3536          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.737317    .0457261     81.73    0.000      3.647695     3.826938
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3936441   .0420571      .3192722    .4853404
-----------------------------+------------------------------------------------
Residual: Banded(0)          |
                     var(e1) |   .1886439   .0220104      .1500814    .2371147
                     var(e2) |   .1529311   .0183265      .1209184    .1934191
                     var(e3) |   .1761755   .0206031      .1400879    .2215595
                     var(e4) |   .1477523   .0176886      .1168505    .1868263
                     var(e5) |   .1353809   .0164482      .1066939    .1717809
                     var(e6) |   .1785993   .0208261      .1421094    .2244589
                     var(e7) |   .2115856   .0238248      .1696835     .263835
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(7) =  1054.75   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1009.354      9     2036.707    2066.392
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3936441

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.582
2   |  0.394     0.547
3   |  0.394     0.394     0.570
4   |  0.394     0.394     0.394     0.541
5   |  0.394     0.394     0.394     0.394     0.529
6   |  0.394     0.394     0.394     0.394     0.394     0.572
7   |  0.394     0.394     0.394     0.394     0.394     0.394     0.605

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.763     0.739     0.755     0.736     0.727     0.756     0.778


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.698     1.000
3   |  0.683     0.705     1.000
4   |  0.701     0.724     0.709     1.000
5   |  0.709     0.732     0.717     0.736     1.000
6   |  0.682     0.704     0.689     0.707     0.715     1.000
7   |  0.663     0.684     0.670     0.688     0.696     0.669     1.000

.       estimates store RIDIAGH,

.       lrtest UN RIDIAGH, force

Likelihood-ratio test                                 LR chi2(20) =     35.60
(Assumption: RIDIAGH nested in UN)                    Prob > chi2 =    0.0171

.       lrtest RIDIAGH RIDIAG, force

Likelihood-ratio test                                 LR chi2(6)  =     10.49
(Assumption: RIDIAG nested in RIDIAGH)                Prob > chi2 =    0.1053

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "First-Order Autoregressive R"
First-Order Autoregressive R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(ar1,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1013.7119
Iteration 2:   log restricted-likelihood = -1013.7108
Iteration 3:   log restricted-likelihood = -1013.7108

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1013.7108          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735589    .0455582     82.00    0.000      3.646297     3.824882
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3875076   .0417653      .3137171    .4786546
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |    .049051   .0370822     -.0237603    .1213446
                      var(e) |   .1729692   .0075578      .1587726    .1884351
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(2) =  1046.03   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1013.711      4     2035.422    2048.615
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3875076

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.396     0.560
3   |  0.388     0.396     0.560
4   |  0.388     0.388     0.396     0.560
5   |  0.388     0.388     0.388     0.396     0.560
6   |  0.388     0.388     0.388     0.388     0.396     0.560
7   |  0.388     0.388     0.388     0.388     0.388     0.396     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.707     1.000
3   |  0.692     0.707     1.000
4   |  0.691     0.692     0.707     1.000
5   |  0.691     0.691     0.692     0.707     1.000
6   |  0.691     0.691     0.691     0.692     0.707     1.000
7   |  0.691     0.691     0.691     0.691     0.692     0.707     1.000

.       estimates store RIAR1,

.       lrtest UN RIAR1, force

Likelihood-ratio test                                 LR chi2(25) =     44.31
(Assumption: RIAR1 nested in UN)                      Prob > chi2 =    0.0100

.       lrtest RIAR1 AR1, force

Likelihood-ratio test                                 LR chi2(1)  =    252.37
(Assumption: AR1 nested in RIAR1)                     Prob > chi2 =    0.0000

.       lrtest RIAR1 RIDIAG, force

Likelihood-ratio test                                 LR chi2(1)  =      1.78
(Assumption: RIDIAG nested in RIAR1)                  Prob > chi2 =    0.1822

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "1-Lag Toeplitz R"
1-Lag Toeplitz R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(toeplitz1,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1013.8696
Iteration 2:   log restricted-likelihood = -1013.8687
Iteration 3:   log restricted-likelihood = -1013.8687

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1013.8687          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |     3.73559    .0455582     82.00    0.000      3.646298     3.824883
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3880861   .0417458      .3143155    .4791709
-----------------------------+------------------------------------------------
Residual: Toeplitz(1)        |
                        cov1 |   .0068289   .0056637     -.0042717    .0179294
                      var(e) |   .1723496   .0073825      .1584709    .1874438
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(2) =  1045.72   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1013.869      4     2035.737    2048.931
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3880861

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.395     0.560
3   |  0.388     0.395     0.560
4   |  0.388     0.388     0.395     0.560
5   |  0.388     0.388     0.388     0.395     0.560
6   |  0.388     0.388     0.388     0.388     0.395     0.560
7   |  0.388     0.388     0.388     0.388     0.388     0.395     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.705     1.000
3   |  0.692     0.705     1.000
4   |  0.692     0.692     0.705     1.000
5   |  0.692     0.692     0.692     0.705     1.000
6   |  0.692     0.692     0.692     0.692     0.705     1.000
7   |  0.692     0.692     0.692     0.692     0.692     0.705     1.000

.       estimates store RITOEP2,

.       lrtest UN RITOEP2, force

Likelihood-ratio test                                 LR chi2(25) =     44.63
(Assumption: RITOEP2 nested in UN)                    Prob > chi2 =    0.0092

.       lrtest RITOEP2 RIDIAG, force

Likelihood-ratio test                                 LR chi2(1)  =      1.46
(Assumption: RIDIAG nested in RITOEP2)                Prob > chi2 =    0.2263

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "2-Lag Toeplitz R"
2-Lag Toeplitz R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(toeplitz2,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1008.6157
Iteration 2:   log restricted-likelihood = -1008.3885
Iteration 3:   log restricted-likelihood = -1008.3883
Iteration 4:   log restricted-likelihood = -1008.3883

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1008.3883          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.736045    .0455345     82.05    0.000      3.646799     3.825291
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3796504   .0418025      .3059567    .4710942
-----------------------------+------------------------------------------------
Residual: Toeplitz(2)        |
                        cov1 |   .0165299   .0074017      .0020227     .031037
                        cov2 |   .0228999   .0069343      .0093089    .0364909
                      var(e) |   .1805455   .0085265       .164584    .1980551
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(3) =  1056.68   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1008.388      5     2026.777    2043.268
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3796504

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.396     0.560
3   |  0.403     0.396     0.560
4   |  0.380     0.403     0.396     0.560
5   |  0.380     0.380     0.403     0.396     0.560
6   |  0.380     0.380     0.380     0.403     0.396     0.560
7   |  0.380     0.380     0.380     0.380     0.403     0.396     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.748     0.748     0.748     0.748     0.748     0.748     0.748


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.707     1.000
3   |  0.719     0.707     1.000
4   |  0.678     0.719     0.707     1.000
5   |  0.678     0.678     0.719     0.707     1.000
6   |  0.678     0.678     0.678     0.719     0.707     1.000
7   |  0.678     0.678     0.678     0.678     0.719     0.707     1.000

.       estimates store RITOEP3,

.       lrtest UN RITOEP3, force

Likelihood-ratio test                                 LR chi2(24) =     33.67
(Assumption: RITOEP3 nested in UN)                    Prob > chi2 =    0.0907

.       lrtest RITOEP3 RITOEP2, force

Likelihood-ratio test                                 LR chi2(1)  =     10.96
(Assumption: RITOEP2 nested in RITOEP3)               Prob > chi2 =    0.0009

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "3-Lag Toeplitz R"
3-Lag Toeplitz R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(toeplitz3,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1008.3161
Iteration 2:   log restricted-likelihood = -1007.9107
Iteration 3:   log restricted-likelihood = -1007.9089
Iteration 4:   log restricted-likelihood = -1007.9089

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1007.9089          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.736328    .0455149     82.09    0.000      3.647121     3.825536
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3756339   .0419819      .3017395    .4676247
-----------------------------+------------------------------------------------
Residual: Toeplitz(3)        |
                        cov1 |   .0208167   .0088329      .0035045    .0381289
                        cov2 |   .0270731   .0081924      .0110164    .0431299
                        cov3 |   .0083732   .0085676     -.0084189    .0251653
                      var(e) |   .1843458   .0096796      .1663178    .2043281
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(4) =  1057.64   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1007.909      6     2027.818    2047.608
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3756339

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.396     0.560
3   |  0.403     0.396     0.560
4   |  0.384     0.403     0.396     0.560
5   |  0.376     0.384     0.403     0.396     0.560
6   |  0.376     0.376     0.384     0.403     0.396     0.560
7   |  0.376     0.376     0.376     0.384     0.403     0.396     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.748     0.748     0.748     0.748     0.748     0.748     0.748


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.708     1.000
3   |  0.719     0.708     1.000
4   |  0.686     0.719     0.708     1.000
5   |  0.671     0.686     0.719     0.708     1.000
6   |  0.671     0.671     0.686     0.719     0.708     1.000
7   |  0.671     0.671     0.671     0.686     0.719     0.708     1.000

.       estimates store RITOEP4,

.       lrtest UN RITOEP4, force

Likelihood-ratio test                                 LR chi2(23) =     32.71
(Assumption: RITOEP4 nested in UN)                    Prob > chi2 =    0.0862

.       lrtest RITOEP4 RITOEP3, force

Likelihood-ratio test                                 LR chi2(1)  =      0.96
(Assumption: RITOEP3 nested in RITOEP4)               Prob > chi2 =    0.3275

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "4-Lag Toeplitz R"
4-Lag Toeplitz R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(toeplitz4,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1006.5191
Iteration 2:   log restricted-likelihood = -1006.0853
Iteration 3:   log restricted-likelihood =  -1006.083
Iteration 4:   log restricted-likelihood =  -1006.083

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood =  -1006.083          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |     3.73621    .0455064     82.10    0.000      3.647019     3.825401
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3645197   .0424291      .2901639    .4579295
-----------------------------+------------------------------------------------
Residual: Toeplitz(4)        |
                        cov1 |   .0324198   .0114522      .0099738    .0548658
                        cov2 |   .0408367   .0115906      .0181196    .0635539
                        cov3 |   .0193606   .0105275     -.0012728    .0399941
                        cov4 |   .0189988   .0100417     -.0006825    .0386801
                      var(e) |   .1958136   .0123129      .1731085    .2214966
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(5) =  1061.29   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1006.083      7     2026.166    2049.254
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3645197

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.560
2   |  0.397     0.560
3   |  0.405     0.397     0.560
4   |  0.384     0.405     0.397     0.560
5   |  0.384     0.384     0.405     0.397     0.560
6   |  0.365     0.384     0.384     0.405     0.397     0.560
7   |  0.365     0.365     0.384     0.384     0.405     0.397     0.560

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.708     1.000
3   |  0.723     0.708     1.000
4   |  0.685     0.723     0.708     1.000
5   |  0.684     0.685     0.723     0.708     1.000
6   |  0.651     0.684     0.685     0.723     0.708     1.000
7   |  0.651     0.651     0.684     0.685     0.723     0.708     1.000

.       estimates store RITOEP5,

.       lrtest UN RITOEP5, force

Likelihood-ratio test                                 LR chi2(22) =     29.06
(Assumption: RITOEP5 nested in UN)                    Prob > chi2 =    0.1432

.       lrtest RITOEP5 RITOEP4, force

Likelihood-ratio test                                 LR chi2(1)  =      3.65
(Assumption: RITOEP4 nested in RITOEP5)               Prob > chi2 =    0.0560

.
. display as result "Ch 4: Empty Means, Random Intercept in G"
Ch 4: Empty Means, Random Intercept in G

. display as result "5-Lag Toeplitz R"
5-Lag Toeplitz R

. mixed posmood , ///
>                 || personid: , variance reml covariance(unstructured) ///
>                 residuals(toeplitz5,t(studyday)),


 Note: single-variable random-effects specification in personid equation; covariance structure set to identity


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -1014.6006
Iteration 1:   log restricted-likelihood = -1014.4112
Iteration 2:   log restricted-likelihood = -1005.6461
Iteration 3:   log restricted-likelihood = -1004.9563
Iteration 4:   log restricted-likelihood = -1004.9531
Iteration 5:   log restricted-likelihood = -1004.9531

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =      1370
Group variable: personid                        Number of groups   =       200

                                                Obs per group: min =         4
                                                               avg =       6.8
                                                               max =         7


                                                Wald chi2(0)       =         .
Log restricted-likelihood = -1004.9531          Prob > chi2        =         .

-------------+----------------------------------------------------------------
      posmood |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       _cons |    3.735746     .045517     82.07    0.000      3.646534     3.824958
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
personid: Identity           |
                  var(_cons) |   .3477049   .0439777      .2713631    .4455236
-----------------------------+------------------------------------------------
Residual: Toeplitz(5)        |
                        cov1 |   .0508638   .0173193      .0169187     .084809
                        cov2 |   .0585459   .0170787      .0250722    .0920196
                        cov3 |   .0373702   .0162133      .0055926    .0691477
                        cov4 |   .0345954    .014628       .005925    .0632659
                        cov5 |   .0232054   .0154535      -.007083    .0534938
                      var(e) |   .2132062   .0178604      .1809232    .2512496
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(6) =  1063.55   Prob > chi2 = 0.0000


Note: LR test is conservative and provided only for reference.


.       estat ic, n(200),

Akaike's information criterion and Bayesian information criterion

-------------+---------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+---------------------------------------------------------------
.            |    200           .   -1004.953      8     2025.906    2052.293
-------------+---------------------------------------------------------------


Note:  N=200 used in calculating BIC


.       estat recovariance, relevel(personid),


Random-effects covariance matrix for level personid


   | _cons
-------------+-----------
_cons   |  .3477049

.       estat recovariance, relevel(personid) correlation,


Random-effects correlation matrix for level personid


   | _cons
-------------+-----------
_cons   |         1

.       estat wcorrelation, covariance,


Covariances
for personid = 1:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  0.561
2   |  0.399     0.561
3   |  0.406     0.399     0.561
4   |  0.385     0.406     0.399     0.561
5   |  0.382     0.385     0.406     0.399     0.561
6   |  0.371     0.382     0.385     0.406     0.399     0.561
7   |  0.348     0.371     0.382     0.385     0.406     0.399     0.561

.       estat wcorrelation,


Standard deviations and correlations
for personid = 1:


Standard deviations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
sd   |  0.749     0.749     0.749     0.749     0.749     0.749     0.749


Correlations:


studyday   | 1    2    3    4    5    6    7
-------------+--------------------------------------------------------
1   |  1.000
2   |  0.711     1.000
3   |  0.724     0.711     1.000
4   |  0.687     0.724     0.711     1.000
5   |  0.682     0.687     0.724     0.711     1.000
6   |  0.661     0.682     0.687     0.724     0.711     1.000
7   |  0.620     0.661     0.682     0.687     0.724     0.711     1.000

.       estimates store RITOEP6,

.       lrtest UN RITOEP6, force

Likelihood-ratio test                                 LR chi2(21) =     26.80
(Assumption: RITOEP6 nested in UN)                    Prob > chi2 =    0.1776

.       lrtest RITOEP6 RITOEP5, force

Likelihood-ratio test                                 LR chi2(1)  =      2.26
(Assumption: RITOEP5 nested in RITOEP6)               Prob > chi2 =    0.1328

.
. ****** END CHAPTER 4 MODELS ******
.
. * Close log
. log close STATA_Chapter4
      name:  STATA_Chapter4
       log:  C:\Dropbox\PilesOfVariance\Chapter4\STATA\STATA_Chapter4_Output.smcl
  log type:  smcl
 closed on:  21 Oct 2014, 09:25:39
-------------