. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * do-file for lecture 12 of VHM 802, Winter 2014
. version 13

. set more off

. cd "h:\vhm\vhm802\data_csv"
h:\vhm\vhm802\data_csv

.
. insheet using guinea_long.csv, clear
(4 vars, 90 obs)

. * profile plots
. twoway (connected weight week), by(group  animal)

. overlay weight week, by(animal) c(l)

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      weight |        90       559.1    58.90881        436        702

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        week |        90    4.333333    1.983074          1          7

. overlay weight week if group==1, by(animal) c(l) /* similar for groups 2,3 */
(60 observations deleted)

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      weight |        30    539.1333    57.39022        436        619

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        week |        30    4.333333    2.005739          1          7

. * mean plot
. preserve /* run together with next 2 lines */

. collapse (mean) weight, by(group week)

. overlay weight week, by(group) c(l)

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      weight |        18       559.1    44.83503      466.4        644

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        week |        18    4.333333    2.029199          1          7

.
end of do-file

. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * disregarding repeated measures (wrong!)
. anova weight group##week

                           Number of obs =      90     R-squared     =  0.5532
                           Root MSE      = 43.7777     Adj R-squared =  0.4477

                  Source |  Partial SS    df       MS           F     Prob > F
              -----------+----------------------------------------------------
                   Model |    170865.3    17     10050.9       5.24     0.0000
                         |
                   group |  18548.0667     2  9274.03333       4.84     0.0107
                    week |    142554.5     5     28510.9      14.88     0.0000
              group#week |  9762.73333    10  976.273333       0.51     0.8781
                         |
                Residual |    137986.8    72  1916.48333
              -----------+----------------------------------------------------
                   Total |    308852.1    89  3470.24831

. * separate analyses for each week
. bysort week: oneway weight group

-------------
-> week = 1

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups          2969.2      2       1484.6      2.10     0.1651
 Within groups          8481.2     12   706.766667
------------------------------------------------------------------------
    Total              11450.4     14   817.885714

Bartlett's test for equal variances:  chi2(2) =   1.4766  Prob>chi2 = 0.478

-------------
-> week = 3

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups          2497.6      2       1248.8      0.87     0.4427
 Within groups         17170.4     12   1430.86667
------------------------------------------------------------------------
    Total                19668     14   1404.85714

Bartlett's test for equal variances:  chi2(2) =   0.4744  Prob>chi2 = 0.789

-------------
-> week = 4

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      302.533333      2   151.266667      0.14     0.8710
 Within groups         12992.4     12       1082.7
------------------------------------------------------------------------
    Total           13294.9333     14   949.638095

Bartlett's test for equal variances:  chi2(2) =   0.5086  Prob>chi2 = 0.775

-------------
-> week = 5

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups           260.4      2        130.2      0.05     0.9476
 Within groups           28906     12   2408.83333
------------------------------------------------------------------------
    Total              29166.4     14   2083.31429

Bartlett's test for equal variances:  chi2(2) =   0.9006  Prob>chi2 = 0.637

-------------
-> week = 6

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      8550.93333      2   4275.46667      1.39     0.2863
 Within groups           36898     12   3074.83333
------------------------------------------------------------------------
    Total           45448.9333     14   3246.35238

Bartlett's test for equal variances:  chi2(2) =   0.6487  Prob>chi2 = 0.723

-------------
-> week = 7

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      13730.1333      2   6865.06667      2.46     0.1276
 Within groups         33538.8     12       2794.9
------------------------------------------------------------------------
    Total           47268.9333     14   3376.35238

Bartlett's test for equal variances:  chi2(2) =   1.1559  Prob>chi2 = 0.561


.
. * response features
. * mean
. preserve /* run together with next 2 lines */

. collapse (mean) weight, by(group animal)

. oneway weight group

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      3091.34348      2   1545.67174      1.06     0.3782
 Within groups      17572.3646     12   1464.36372
------------------------------------------------------------------------
    Total           20663.7081     14   1475.97915

Bartlett's test for equal variances:  chi2(2) =   0.2914  Prob>chi2 = 0.864

.
end of do-file

. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * gain
. preserve /* run together with next 3 lines */

. insheet using guinea_wide.csv, clear
(7 vars, 15 obs)

. gen gain=w7-w5

. oneway gain group

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      11286.5333      2   5643.26667     13.04     0.0010
 Within groups          5194.4     12   432.866667
------------------------------------------------------------------------
    Total           16480.9333     14   1177.20952

Bartlett's test for equal variances:  chi2(2) =  11.8859  Prob>chi2 = 0.003

.
end of do-file

. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * slope
. anova weight animal c.week#animal

                           Number of obs =      90     R-squared     =  0.8947
                           Root MSE      = 23.2769     Adj R-squared =  0.8439

                  Source |  Partial SS    df       MS           F     Prob > F
             ------------+----------------------------------------------------
                   Model |  276343.157    29  9529.07438      17.59     0.0000
                         |
                  animal |  9525.46213    14  680.390152       1.26     0.2618
             animal#week |   152360.89    15  10157.3927      18.75     0.0000
                         |
                Residual |  32508.9429    60  541.815714
             ------------+----------------------------------------------------
                   Total |    308852.1    89  3470.24831

. regress

      Source |       SS       df       MS              Number of obs =      90
-------------+------------------------------           F( 29,    60) =   17.59
       Model |  276343.157    29  9529.07438           Prob > F      =  0.0000
    Residual |  32508.9429    60  541.815714           R-squared     =  0.8947
-------------+------------------------------           Adj R-squared =  0.8439
       Total |    308852.1    89  3470.24831           Root MSE      =  23.277

--------------+----------------------------------------------------------------
        weight |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
--------------+----------------------------------------------------------------
       animal |
           2  |    24.82857    32.44488      0.77    0.447     -40.07086       89.728
           3  |         -30    32.44488     -0.92    0.359     -94.89943     34.89943
           4  |    7.157143    32.44488      0.22    0.826     -57.74229     72.05657
           5  |   -7.757143    32.44488     -0.24    0.812     -72.65657     57.14229
           6  |        41.6    32.44488      1.28    0.205     -23.29943     106.4994
           7  |   -50.97143    32.44488     -1.57    0.121     -115.8709       13.928
           8  |    4.628571    32.44488      0.14    0.887     -60.27086       69.528
           9  |    22.37143    32.44488      0.69    0.493       -42.528     87.27086
          10  |    .8142857    32.44488      0.03    0.980     -64.08515     65.71372
          11  |    9.271429    32.44488      0.29    0.776       -55.628     74.17086
          12  |    21.41429    32.44488      0.66    0.512     -43.48515     86.31372
          13  |   -11.44286    32.44488     -0.35    0.726     -76.34229     53.45657
          14  |        46.1    32.44488      1.42    0.161     -18.79943     110.9994
          15  |   -15.34286    32.44488     -0.47    0.638     -80.24229     49.55657
              |
animal#c.week |
           1  |    .2285714    4.818783      0.05    0.962     -9.410431     9.867573
           2  |    15.11429    4.818783      3.14    0.003      5.475284     24.75329
           3  |    27.22857    4.818783      5.65    0.000      17.58957     36.86757
           4  |        21.5    4.818783      4.46    0.000        11.861       31.139
           5  |    16.05714    4.818783      3.33    0.001      6.418141     25.69614
           6  |    9.128571    4.818783      1.89    0.063     -.5104305     18.76757
           7  |    21.41429    4.818783      4.44    0.000      11.77528     31.05329
           8  |    23.81429    4.818783      4.94    0.000      14.17528     33.45329
           9  |    29.64286    4.818783      6.15    0.000      20.00386     39.28186
          10  |    28.77143    4.818783      5.97    0.000      19.13243     38.41043
          11  |    27.74286    4.818783      5.76    0.000      18.10386     37.38186
          12  |    15.67143    4.818783      3.25    0.002      6.032427     25.31043
          13  |        20.6    4.818783      4.27    0.000        10.961       30.239
          14  |    18.12857    4.818783      3.76    0.000      8.489569     27.76757
          15  |          16    4.818783      3.32    0.002      6.360998       25.639
              |
        _cons |    470.8429      22.942     20.52    0.000       424.952     516.7337
--------------+----------------------------------------------------------------

. matrix parms_slp=e(b)'     /* creates a column of all estimates from */

. svmat parms_slp            /* which the relevant ones must be extracted */

. preserve /* run together with next 3 lines */

. drop if _n<16 | _n>30
(75 observations deleted)

. egen float group2 = seq(), from(1) to(3) block(5)

. oneway parms_slp1 group2

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups       106.93772      2   53.4688601      0.83     0.4608
 Within groups       775.75174     12   64.6459783
------------------------------------------------------------------------
    Total            882.68946     14   63.0492471

Bartlett's test for equal variances:  chi2(2) =   1.6927  Prob>chi2 = 0.429

.
end of do-file

. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * curvature
. anova weight animal c.week#animal c.week#c.week#animal

                           Number of obs =      90     R-squared     =  0.9275
                           Root MSE      = 22.3061     Adj R-squared =  0.8566

                  Source |  Partial SS    df       MS           F     Prob > F
        -----------------+----------------------------------------------------
                   Model |  286461.824    44    6510.496      13.08     0.0000
                         |
                  animal |  9070.02977    14  647.859269       1.30     0.2439
             animal#week |  23997.0133    15  1599.80089       3.22     0.0012
        animal#week#week |  10118.6667    15  674.577778       1.36     0.2110
                         |
                Residual |  22390.2762    45  497.561693
        -----------------+----------------------------------------------------
                   Total |    308852.1    89  3470.24831

. regress

      Source |       SS       df       MS              Number of obs =      90
-------------+------------------------------           F( 44,    45) =   13.08
       Model |  286461.824    44    6510.496           Prob > F      =  0.0000
    Residual |  22390.2762    45  497.561693           R-squared     =  0.9275
-------------+------------------------------           Adj R-squared =  0.8566
       Total |    308852.1    89  3470.24831           Root MSE      =  22.306

---------------+----------------------------------------------------------------
         weight |      Coef.    Std. Err.       t    P>|t|      [95% Con f. Interval]
---------------+----------------------------------------------------------------
        animal |
            2  |   -21.74286    51.69736     -0.42    0.676     -125.8667     82.38097
            3  |   -37.71429    51.69736     -0.73    0.469     -141.8381     66.40954
            4  |    15.87143    51.69736      0.31    0.760      -88.2524     119.9953
            5  |    38.38571    51.69736      0.74    0.462     -65.73811     142.5095
            6  |    94.45714    51.69736      1.83    0.074     -9.666686      198.581
            7  |   -2.971429    51.69736     -0.06    0.954     -107.0953     101.1524
            8  |    68.34286    51.69736      1.32    0.193     -35.78097     172.4667
            9  |    67.51429    51.69736      1.31    0.198     -36.60954     171.6381
           10  |        54.1    51.69736      1.05    0.301     -50.02383     158.2238
           11  |    26.84286    51.69736      0.52    0.606     -77.28097     130.9667
           12  |    52.12857    51.69736      1.01    0.319     -51.99526     156.2524
           13  |    27.84286    51.69736      0.54    0.593     -76.28097     131.9667
           14  |    114.5286    51.69736      2.22    0.032      10.40474     218.6524
           15  |    38.37143    51.69736      0.74    0.462      -65.7524     142.4953
               |
 animal#c.week |
            1  |    31.37143    20.01046      1.57    0.124     -8.931716     71.67457
            2  |    77.30476    20.01046      3.86    0.000      37.00162     117.6079
            3  |    63.51429    20.01046      3.17    0.003      23.21114     103.8174
            4  |    46.83333    20.01046      2.34    0.024      6.530189     87.13648
            5  |     16.4381    20.01046      0.82    0.416     -23.86505     56.74124
            6  |    5.033333    20.01046      0.25    0.803     -35.26981     45.33648
            7  |    20.55714    20.01046      1.03    0.310       -19.746     60.86029
            8  |    12.48095    20.01046      0.62    0.536     -27.82219      52.7841
            9  |    30.69048    20.01046      1.53    0.132     -9.612668     70.99362
           10  |    24.39048    20.01046      1.22    0.229     -15.91267     64.69362
           11  |    47.17143    20.01046      2.36    0.023      6.868284     87.47457
           12  |     26.3381    20.01046      1.32    0.195     -13.96505     66.64124
           13  |    25.55238    20.01046      1.28    0.208     -14.75076     65.85553
           14  |    3.652381    20.01046      0.18    0.856     -36.65076     43.95553
           15  |    11.33333    20.01046      0.57    0.574     -28.96981     51.63648
               |
 animal#c.week#|
        c.week |
            1  |   -3.892857    2.433794     -1.60    0.117      -8.79477     1.009056
            2  |    -7.77381    2.433794     -3.19    0.003     -12.67572    -2.871897
            3  |   -4.535714    2.433794     -1.86    0.069     -9.437627     .3661986
            4  |   -3.166667    2.433794     -1.30    0.200      -8.06858     1.735246
            5  |    -.047619    2.433794     -0.02    0.984     -4.949532     4.854294
            6  |    .5119048    2.433794      0.21    0.834     -4.390008     5.413818
            7  |    .1071429    2.433794      0.04    0.965      -4.79477     5.009056
            8  |    1.416667    2.433794      0.58    0.563     -3.485246      6.31858
            9  |   -.1309524    2.433794     -0.05    0.957     -5.032865      4.77096
           10  |     .547619    2.433794      0.23    0.823     -4.354294     5.449532
           11  |   -2.428571    2.433794     -1.00    0.324     -7.330484     2.473341
           12  |   -1.333333    2.433794     -0.55    0.587     -6.235246      3.56858
           13  |   -.6190476    2.433794     -0.25    0.800      -5.52096     4.282865
           14  |    1.809524    2.433794      0.74    0.461     -3.092389     6.711437
           15  |    .5833333    2.433794      0.24    0.812      -4.31858     5.485246
               |
         _cons |    424.1286    36.55555     11.60    0.000      350.5019     497.7552
---------------+----------------------------------------------------------------

. matrix parms_crv=e(b)'     /* creates a column of all estimates from */

. svmat parms_crv            /* which the relevant ones must be extracted */

. preserve /* run together with next 3 lines */

. drop if _n<31 | _n>45
(75 observations deleted)

. egen float group2 = seq(), from(1) to(3) block(5)

. oneway parms_crv1 group2

                        Analysis of Variance
    Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      53.4485435      2   26.7242718      7.45     0.0079
 Within groups      43.0655887     12   3.58879906
------------------------------------------------------------------------
    Total           96.5141323     14   6.89386659

Bartlett's test for equal variances:  chi2(2) =   6.6432  Prob>chi2 = 0.036

.
end of do-file

. do "C:\Users\DEFAUL~1.SID\AppData\Local\Temp\STD00000000.tmp"

. * split-plot or hierarchical model
. anova weight group / animal|group week##group

                           Number of obs =      90     R-squared     =  0.8946
                           Root MSE      = 23.2926     Adj R-squared =  0.8437

                  Source |  Partial SS    df       MS           F     Prob > F
            -------------+----------------------------------------------------
                   Model |    276299.5    29  9527.56897      17.56     0.0000
                         |
                   group |  18548.0667     2  9274.03333       1.06     0.3782
            animal|group |    105434.2    12  8786.18333
            -------------+----------------------------------------------------
                    week |    142554.5     5     28510.9      52.55     0.0000
              week#group |  9762.73333    10  976.273333       1.80     0.0801
                         |
                Residual |     32552.6    60  542.543333
            -------------+----------------------------------------------------
                   Total |    308852.1    89  3470.24831

. mixed weight group##week || animal:, reml

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -360.02217
Iteration 1:   log restricted-likelihood = -360.02217

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    282.86
Log restricted-likelihood = -360.02217          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    27.68743      1.01    0.312     -26.26637     82.26637
          3  |        31.4    27.68743      1.13    0.257     -22.86637     85.66637
             |
        week |
          3  |          53    14.73151      3.60    0.000      24.12678     81.87322
          4  |       102.4    14.73151      6.95    0.000      73.52678     131.2732
          5  |        95.2    14.73151      6.46    0.000      66.32678     124.0732
          6  |        80.2    14.73151      5.44    0.000      51.32678     109.0732
          7  |       105.6    14.73151      7.17    0.000      76.72678     134.4732
             |
  group#week |
        2 3  |         3.6     20.8335      0.17    0.863      -37.2329      44.4329
        2 4  |       -22.6     20.8335     -1.08    0.278      -63.4329      18.2329
        2 5  |       -22.6     20.8335     -1.08    0.278      -63.4329      18.2329
        2 6  |        28.4     20.8335      1.36    0.173      -12.4329      69.2329
        2 7  |          44     20.8335      2.11    0.035      3.167097      84.8329
        3 3  |       -16.2     20.8335     -0.78    0.437      -57.0329      24.6329
        3 4  |       -20.4     20.8335     -0.98    0.327      -61.2329      20.4329
        3 5  |       -21.2     20.8335     -1.02    0.309      -62.0329      19.6329
        3 6  |        10.2     20.8335      0.49    0.624      -30.6329      51.0329
        3 7  |        19.8     20.8335      0.95    0.342      -21.0329      60.6329
             |
       _cons |       466.4    19.57797     23.82    0.000      428.0279     504.7721
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal: Identity             |
                  var(_cons) |   1373.942   598.0528      585.4031    3224.642
-----------------------------+------------------------------------------------
               var(Residual) |   542.5432   99.05438      379.3385    775.9643
-----------------------------+------------------------------------------------
LR test vs. linear regression: chibar2(01) =    57.45 Prob >= chibar2 =  0.0000

. testparm group#week /* note: P-values smaller in chi^2-distrib */


 ( 1)  [weight]2.group#3.week = 0


 ( 2)  [weight]2.group#4.week = 0


 ( 3)  [weight]2.group#5.week = 0


 ( 4)  [weight]2.group#6.week = 0


 ( 5)  [weight]2.group#7.week = 0


 ( 6)  [weight]3.group#3.week = 0


 ( 7)  [weight]3.group#4.week = 0


 ( 8)  [weight]3.group#5.week = 0


 ( 9)  [weight]3.group#6.week = 0


 (10)  [weight]3.group#7.week = 0


           chi2( 10) =   17.99
         Prob > chi2 =    0.0551

. * repeated measures ANOVA
. anova weight group / animal|group week##group, repeated(week)

                           Number of obs =      90     R-squared     =  0.8946
                           Root MSE      = 23.2926     Adj R-squared =  0.8437

                  Source |  Partial SS    df       MS           F     Prob > F
            -------------+----------------------------------------------------
                   Model |    276299.5    29  9527.56897      17.56     0.0000
                         |
                   group |  18548.0667     2  9274.03333       1.06     0.3782
            animal|group |    105434.2    12  8786.18333
            -------------+----------------------------------------------------
                    week |    142554.5     5     28510.9      52.55     0.0000
              week#group |  9762.73333    10  976.273333       1.80     0.0801
                         |
                Residual |     32552.6    60  542.543333
            -------------+----------------------------------------------------
                   Total |    308852.1    89  3470.24831


Between-subjects error term:  animal|group
                     Levels:  15        (12 df)
     Lowest b.s.e. variable:  animal
     Covariance pooled over:  group     (for repeated variable)

Repeated variable: week
                                          Huynh-Feldt epsilon        =  0.7191
                                          Greenhouse-Geisser epsilon =  0.4856
                                          Box's conservative epsilon =  0.2000

                                            ------------ Prob > F ------------
                  Source |     df      F    Regular    H-F      G-G      Box
            -------------+----------------------------------------------------
                    week |      5    52.55   0.0000   0.0000   0.0000   0.0000
              week#group |     10     1.80   0.0801   0.1103   0.1457   0.2073
                Residual |     60
            -------------+----------------------------------------------------

.
. * mixed models with correlation structure, assuming equidistant times
. gen weekeq=week+(week==1) /* equidistant time points 2-7*/

. * ar(1) autoregressive correlations
. mixed weight group##weekeq || animal:, res(ar 1, t(weekeq)) nocons reml

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -388.74541  (not concave)
Iteration 1:   log restricted-likelihood =  -354.4239
Iteration 2:   log restricted-likelihood = -354.31402
Iteration 3:   log restricted-likelihood = -354.31239
Iteration 4:   log restricted-likelihood = -354.31239

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    162.42
Log restricted-likelihood = -354.31239          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    27.20166      1.03    0.303     -25.31427     81.31427
          3  |        31.4    27.20166      1.15    0.248     -21.91427     84.71427
             |
      weekeq |
          3  |          53     11.6093      4.57    0.000      30.24619     75.75381
          4  |       102.4    15.65256      6.54    0.000      71.72154     133.0785
          5  |        95.2    18.30716      5.20    0.000      59.31863     131.0814
          6  |        80.2    20.22081      3.97    0.000      40.56794     119.8321
          7  |       105.6    21.66058      4.88    0.000      63.14605     148.0539
             |
group#weekeq |
        2 3  |         3.6    16.41803      0.22    0.826     -28.57874     35.77874
        2 4  |       -22.6    22.13606     -1.02    0.307     -65.98589     20.78589
        2 5  |       -22.6    25.89023     -0.87    0.383     -73.34392     28.14392
        2 6  |        28.4    28.59654      0.99    0.321     -27.64819     84.44819
        2 7  |          44    30.63268      1.44    0.151     -16.03895      104.039
        3 3  |       -16.2    16.41803     -0.99    0.324     -48.37874     15.97874
        3 4  |       -20.4    22.13606     -0.92    0.357     -63.78589     22.98589
        3 5  |       -21.2    25.89023     -0.82    0.413     -71.94392     29.54392
        3 6  |        10.2    28.59654      0.36    0.721     -45.84819     66.24819
        3 7  |        19.8    30.63268      0.65    0.518     -40.23895     79.83895
             |
       _cons |       466.4    19.23448     24.25    0.000      428.7011     504.0989
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal:              (empty) |
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |   .8178534   .0563492      .6732989    .9021861
                      var(e) |   1849.826    528.377       1056.81     3237.91
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(1) =    68.87   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 wcor


Standard deviations and correlations
for animal = 7:


Standard deviations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
sd   | 43.010    43.010    43.010    43.010    43.010    43.010


Correlations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
2   |  1.000
3   |  0.818     1.000
4   |  0.669     0.818     1.000
5   |  0.547     0.669     0.818     1.000
6   |  0.447     0.547     0.669     0.818     1.000
7   |  0.366     0.447     0.547     0.669     0.818     1.000

. * random effects and ar(1) errors
. mixed weight group##weekeq || animal:, res(ar 1, t(weekeq)) reml

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -360.02217
Iteration 1:   log restricted-likelihood =  -354.8883
Iteration 2:   log restricted-likelihood = -354.10492
Iteration 3:   log restricted-likelihood = -354.06675
Iteration 4:   log restricted-likelihood = -354.06643
Iteration 5:   log restricted-likelihood = -354.06643

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    191.08
Log restricted-likelihood = -354.06643          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    27.22117      1.03    0.304     -25.35251     81.35251
          3  |        31.4    27.22117      1.15    0.249     -21.95251     84.75251
             |
      weekeq |
          3  |          53    11.64353      4.55    0.000       30.1791      75.8209
          4  |       102.4    14.97297      6.84    0.000      73.05352     131.7465
          5  |        95.2    16.79631      5.67    0.000      62.27984     128.1202
          6  |        80.2    17.88798      4.48    0.000       45.1402     115.2598
          7  |       105.6    18.56691      5.69    0.000      69.20952     141.9905
             |
group#weekeq |
        2 3  |         3.6    16.46644      0.22    0.827     -28.67363     35.87363
        2 4  |       -22.6    21.17498     -1.07    0.286     -64.10219     18.90219
        2 5  |       -22.6    23.75357     -0.95    0.341     -69.15613     23.95613
        2 6  |        28.4    25.29743      1.12    0.262     -21.18205     77.98205
        2 7  |          44    26.25758      1.68    0.094     -7.463908     95.46391
        3 3  |       -16.2    16.46644     -0.98    0.325     -48.47363     16.07363
        3 4  |       -20.4    21.17498     -0.96    0.335     -61.90219     21.10219
        3 5  |       -21.2    23.75357     -0.89    0.372     -67.75613     25.35613
        3 6  |        10.2    25.29743      0.40    0.687     -39.38205     59.78205
        3 7  |        19.8    26.25758      0.75    0.451     -31.66391     71.26391
             |
       _cons |       466.4    19.24827     24.23    0.000      428.6741     504.1259
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal: Identity             |
                  var(_cons) |   873.8739   771.5022      154.8685    4930.995
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |   .6536608   .2213377      .0242068    .9119718
                      var(e) |    978.606   607.2897      289.9887    3302.438
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(2) =    69.36   Prob > chi2 = 0.0000


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


. estat wcor


Standard deviations and correlations
for animal = 7:


Standard deviations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
sd   | 43.040    43.040    43.040    43.040    43.040    43.040


Correlations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
2   |  1.000
3   |  0.817     1.000
4   |  0.697     0.817     1.000
5   |  0.619     0.697     0.817     1.000
6   |  0.568     0.619     0.697     0.817     1.000
7   |  0.535     0.568     0.619     0.697     0.817     1.000

. * Toeplitz
. mixed weight group##weekeq || animal:, res(toeplitz, t(weekeq)) nocons reml

Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -388.74541  (not concave)
Iteration 1:   log restricted-likelihood = -377.15901  (not concave)
Iteration 2:   log restricted-likelihood =   -370.597  (not concave)
Iteration 3:   log restricted-likelihood =  -366.6394  (not concave)
Iteration 4:   log restricted-likelihood = -363.07347  (not concave)
Iteration 5:   log restricted-likelihood = -361.39529  (not concave)
Iteration 6:   log restricted-likelihood = -359.88913
Iteration 7:   log restricted-likelihood = -355.00099  (not concave)
Iteration 8:   log restricted-likelihood = -353.35211
Iteration 9:   log restricted-likelihood = -351.18936
Iteration 10:  log restricted-likelihood = -349.84522
Iteration 11:  log restricted-likelihood =  -349.1903
Iteration 12:  log restricted-likelihood = -349.18007
Iteration 13:  log restricted-likelihood = -349.18002
Iteration 14:  log restricted-likelihood = -349.18002

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    178.00
Log restricted-likelihood = -349.18002          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    26.79561      1.04    0.296     -24.51843     80.51843
          3  |        31.4    26.79561      1.17    0.241     -21.11843     83.91843
             |
      weekeq |
          3  |          53    11.72339      4.52    0.000      30.02259     75.97741
          4  |       102.4    13.27407      7.71    0.000      76.38329     128.4167
          5  |        95.2    17.23542      5.52    0.000      61.41919     128.9808
          6  |        80.2    18.37799      4.36    0.000      44.17981     116.2202
          7  |       105.6    22.88712      4.61    0.000      60.74207     150.4579
             |
group#weekeq |
        2 3  |         3.6    16.57937      0.22    0.828     -28.89497     36.09497
        2 4  |       -22.6    18.77238     -1.20    0.229     -59.39318     14.19318
        2 5  |       -22.6    24.37457     -0.93    0.354     -70.37328     25.17328
        2 6  |        28.4     25.9904      1.09    0.275     -22.54024     79.34024
        2 7  |          44    32.36728      1.36    0.174      -19.4387     107.4387
        3 3  |       -16.2    16.57937     -0.98    0.329     -48.69497     16.29497
        3 4  |       -20.4    18.77238     -1.09    0.277     -57.19318     16.39318
        3 5  |       -21.2    24.37457     -0.87    0.384     -68.97328     26.57328
        3 6  |        10.2     25.9904      0.39    0.695     -40.74024     61.14024
        3 7  |        19.8    32.36728      0.61    0.541      -43.6387      83.2387
             |
       _cons |       466.4    18.94736     24.62    0.000      429.2639     503.5361
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal:              (empty) |
-----------------------------+------------------------------------------------
Residual: Toeplitz(5)        |
                        cov1 |   1451.417   503.0803      465.3977    2437.436
                        cov2 |   1354.509   491.8142      390.5707    2318.447
                        cov3 |   1052.362   478.1299      115.2444    1989.479
                        cov4 |   950.6354   472.6153      24.32647    1876.944
                        cov5 |   485.4607   524.4629     -542.4678    1513.389
                      var(e) |   1795.011    510.734      1027.721    3135.157
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(5) =    79.13   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 wcor


Standard deviations and correlations
for animal = 7:


Standard deviations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
sd   | 42.368    42.368    42.368    42.368    42.368    42.368


Correlations:


weekeq   | 2    3    4    5    6    7
-------------+------------------------------------------------
2   |  1.000
3   |  0.809     1.000
4   |  0.755     0.809     1.000
5   |  0.586     0.755     0.809     1.000
6   |  0.530     0.586     0.755     0.809     1.000
7   |  0.270     0.530     0.586     0.755     0.809     1.000

. * AR(1) with non-equidistant time points (not in lecture)
. mixed weight group##week || animal:, res(ar 1, t(week)) nocons reml


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -388.74541  (not concave)
Iteration 1:   log restricted-likelihood = -355.13854
Iteration 2:   log restricted-likelihood = -354.73193
Iteration 3:   log restricted-likelihood = -354.69208
Iteration 4:   log restricted-likelihood = -354.69198
Iteration 5:   log restricted-likelihood = -354.69198

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    150.10
Log restricted-likelihood = -354.69198          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    26.75228      1.05    0.295     -24.43351     80.43351
          3  |        31.4    26.75228      1.17    0.241     -21.03351     83.83351
             |
        week |
          3  |          53    15.00046      3.53    0.000      23.59964     82.40036
          4  |       102.4    17.58992      5.82    0.000      67.92438     136.8756
          5  |        95.2    19.47517      4.89    0.000      57.02936     133.3706
          6  |        80.2    20.90792      3.84    0.000      39.22124     121.1788
          7  |       105.6    22.02381      4.79    0.000      62.43412     148.7659
             |
  group#week |
        2 3  |         3.6    21.21385      0.17    0.865     -37.97838     45.17838
        2 4  |       -22.6    24.87591     -0.91    0.364     -71.35588     26.15588
        2 5  |       -22.6    27.54205     -0.82    0.412     -76.58143     31.38143
        2 6  |        28.4    29.56826      0.96    0.337     -29.55272     86.35272
        2 7  |          44    31.14638      1.41    0.158     -17.04577     105.0458
        3 3  |       -16.2    21.21385     -0.76    0.445     -57.77838     25.37838
        3 4  |       -20.4    24.87591     -0.82    0.412     -69.15588     28.35588
        3 5  |       -21.2    27.54205     -0.77    0.441     -75.18143     32.78143
        3 6  |        10.2    29.56826      0.34    0.730     -47.75272     68.15272
        3 7  |        19.8    31.14638      0.64    0.525     -41.24577     80.84577
             |
       _cons |       466.4    18.91672     24.66    0.000      429.3239     503.4761
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal:              (empty) |
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |   .8280075   .0531303      .6913597    .9074657
                      var(e) |   1789.211   500.2773       1034.33    3095.025
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(1) =    68.11   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 wcor


Standard deviations and correlations
for animal = 7:


Standard deviations:


week   | 1    3    4    5    6    7
-------------+------------------------------------------------
sd   | 42.299    42.299    42.299    42.299    42.299    42.299


Correlations:


week   | 1    3    4    5    6    7
-------------+------------------------------------------------
1   |  1.000
3   |  0.686     1.000
4   |  0.568     0.828     1.000
5   |  0.470     0.686     0.828     1.000
6   |  0.389     0.568     0.686     0.828     1.000
7   |  0.322     0.470     0.568     0.686     0.828     1.000

. * random effects and non-equidistant AR(1) errors (not in lecture)
. mixed weight group##week || animal:, res(ar 1, t(week)) reml


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -360.02217
Iteration 1:   log restricted-likelihood = -355.18517
Iteration 2:   log restricted-likelihood =  -354.3353
Iteration 3:   log restricted-likelihood = -354.24508
Iteration 4:   log restricted-likelihood = -354.18287
Iteration 5:   log restricted-likelihood = -354.18255
Iteration 6:   log restricted-likelihood = -354.18255

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    190.16
Log restricted-likelihood = -354.18255          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    26.75314      1.05    0.295     -24.43519     80.43519
          3  |        31.4    26.75314      1.17    0.241     -21.03519     83.83519
             |
        week |
          3  |          53    14.40471      3.68    0.000      24.76728     81.23272
          4  |       102.4    16.12882      6.35    0.000      70.78809     134.0119
          5  |        95.2    17.15111      5.55    0.000      61.58444     128.8156
          6  |        80.2    17.78055      4.51    0.000      45.35075     115.0492
          7  |       105.6    18.17575      5.81    0.000      69.97618     141.2238
             |
  group#week |
        2 3  |         3.6    20.37134      0.18    0.860      -36.3271      43.5271
        2 4  |       -22.6     22.8096     -0.99    0.322     -67.30599     22.10599
        2 5  |       -22.6    24.25534     -0.93    0.351     -70.13959     24.93959
        2 6  |        28.4     25.1455      1.13    0.259     -20.88428     77.68428
        2 7  |          44     25.7044      1.71    0.087     -6.379696      94.3797
        3 3  |       -16.2    20.37134     -0.80    0.426      -56.1271      23.7271
        3 4  |       -20.4     22.8096     -0.89    0.371     -65.10599     24.30599
        3 5  |       -21.2    24.25534     -0.87    0.382     -68.73959     26.33959
        3 6  |        10.2     25.1455      0.41    0.685     -39.08428     59.48428
        3 7  |        19.8     25.7044      0.77    0.441      -30.5797      70.1797
             |
       _cons |       466.4    18.91733     24.65    0.000      429.3227     503.4773
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal: Identity             |
                  var(_cons) |   898.5255   626.2171      229.2425    3521.808
-----------------------------+------------------------------------------------
Residual: AR(1)              |
                         rho |   .6462743   .1776159      .1694174    .8779337
                      var(e) |   890.8007   418.5258      354.6988    2237.182
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(2) =    69.13   Prob > chi2 = 0.0000


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


. estat wcor


Standard deviations and correlations
for animal = 7:


Standard deviations:


week   | 1    3    4    5    6    7
-------------+------------------------------------------------
sd   | 42.300    42.300    42.300    42.300    42.300    42.300


Correlations:


week   | 1    3    4    5    6    7
-------------+------------------------------------------------
1   |  1.000
3   |  0.710     1.000
4   |  0.637     0.824     1.000
5   |  0.589     0.710     0.824     1.000
6   |  0.558     0.637     0.710     0.824     1.000
7   |  0.538     0.589     0.637     0.710     0.824     1.000

. * Toeplitz with non-equidistant times (not in lecture)
. mixed weight group##week || animal:, res(toeplitz, t(week)) nocons reml


Note: time gaps exist in the
estimation data


Obtaining starting values by EM:

Performing gradient-based optimization:

Iteration 0:   log restricted-likelihood = -388.74541  (not concave)
Iteration 1:   log restricted-likelihood =  -358.3441  (not concave)
Iteration 2:   log restricted-likelihood = -349.02093
Iteration 3:   log restricted-likelihood = -347.98691  (not concave)
Iteration 4:   log restricted-likelihood = -347.49485
Iteration 5:   log restricted-likelihood = -346.33452
Iteration 6:   log restricted-likelihood = -345.91953
Iteration 7:   log restricted-likelihood = -345.77675
Iteration 8:   log restricted-likelihood = -345.75095
Iteration 9:   log restricted-likelihood = -345.75087
Iteration 10:  log restricted-likelihood = -345.75087

Computing standard errors:

Mixed-effects REML regression                   Number of obs      =        90
Group variable: animal                          Number of groups   =        15

                                                Obs per group: min =         6
                                                               avg =       6.0
                                                               max =         6


                                                Wald chi2(17)      =    157.51
Log restricted-likelihood = -345.75087          Prob > chi2        =    0.0000

-------------+----------------------------------------------------------------
       weight |      Coef.    Std. Err.       z    P>|z|      [95% Con f. Interval]
-------------+----------------------------------------------------------------
       group |
          2  |          28    25.70936      1.09    0.276     -22.38942     78.38942
          3  |        31.4    25.70936      1.22    0.222     -18.98942     81.78942
             |
        week |
          3  |          53    13.37436      3.96    0.000      26.78674     79.21326
          4  |       102.4    18.22204      5.62    0.000      66.68545     138.1145
          5  |        95.2    18.35964      5.19    0.000      59.21576     131.1842
          6  |        80.2    22.02868      3.64    0.000      37.02458     123.3754
          7  |       105.6    25.53153      4.14    0.000      55.55913     155.6409
             |
  group#week |
        2 3  |         3.6     18.9142      0.19    0.849     -33.47115     40.67115
        2 4  |       -22.6    25.76986     -0.88    0.380       -73.108       27.908
        2 5  |       -22.6    25.96446     -0.87    0.384      -73.4894      28.2894
        2 6  |        28.4    31.15326      0.91    0.362     -32.65927     89.45927
        2 7  |          44    36.10703      1.22    0.223     -26.76848     114.7685
        3 3  |       -16.2     18.9142     -0.86    0.392     -53.27115     20.87115
        3 4  |       -20.4    25.76986     -0.79    0.429       -70.908       30.108
        3 5  |       -21.2    25.96446     -0.82    0.414      -72.0894      29.6894
        3 6  |        10.2    31.15326      0.33    0.743     -50.85927     71.25927
        3 7  |        19.8    36.10703      0.55    0.583     -50.96848     90.56848
             |
       _cons |       466.4    18.17926     25.66    0.000      430.7693     502.0307
-------------+----------------------------------------------------------------

-----------------------------+------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
animal:              (empty) |
-----------------------------+------------------------------------------------
Residual: Toeplitz(6)        |
                        cov1 |   1281.657   422.5398      453.4943     2109.82
                        cov2 |   1205.244   411.8058      398.1196    2012.369
                        cov3 |   822.3207    370.414      96.32258    1548.319
                        cov4 |   809.7366   295.2776      231.0031     1388.47
                        cov5 |   439.2707   308.6206     -165.6145    1044.156
                        cov6 |   22.78057   283.9943      -533.838    579.3991
                      var(e) |   1652.428   435.7838      985.4641    2770.794
-----------------------------+------------------------------------------------
LR test vs. linear regression:       chi2(6) =    85.99   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.


.
end of do-file

. exit, clear