I am just learning about multilevel growth models and am still a bit confused about the random part in the model. I am used to Stata's xtreg command and find it a bit tricky to change to mixed. I am using Stata 16
My research topic: I want to compare wealth trajectories in years after divorce (0=first year after divorce, 1 = 2nd year after divorce etc). My treatment group includes first-time divorced men and women. My control groups includes a group of continuously married men and women. This group is assigned an artificial divorce date. Thus the treated group has an actual time since divorce and the control group has an artificial time since divorce.
In the growth curve model I would now like to compare wealth trajectories between the men and women in the control group to men and women in the treatment group. Additionally, I am interested in differences within the groups, so between treated men and treated women. I would expect that the four types of sample respondents (treated men, treated women, control men, control women) have different trajectories. I think it would thus make sense to allow for random intercepts and random slopes for each groups average trajectory. As I have a range of interactions (to define the groups), I am now unsure if I should add each interaction also as a random part or if it is enough to define the interactions only in the level-1 part of the model.
For simplicity I first run gender-specific models (at this point without the addition of control variables):
Code:
. mixed wealth_ind_ihsa c.divduration##i.treat || id: divduration treat if female ==1, var
> iance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -13577.383
Iteration 1: log likelihood = -13540.188 (not concave)
Iteration 2: log likelihood = -13521.659
Iteration 3: log likelihood = -13504.702
Iteration 4: log likelihood = -13504.485
Iteration 5: log likelihood = -13504.484
Computing standard errors:
Mixed-effects ML regression Number of obs = 4,156
Group variable: id Number of groups = 2,011
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(3) = 116.75
Log likelihood = -13504.484 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
divduration | .0752317 .0175084 4.30 0.000 .0409159 .1095475
|
treat |
1. yes | -3.050076 .3936666 -7.75 0.000 -3.821649 -2.278504
|
treat#c.divduration |
1. yes | .0273809 .036976 0.74 0.459 -.0450908 .0998527
|
_cons | 7.816075 .1991426 39.25 0.000 7.425762 8.206387
-------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(divdu~on) | 1.83e-14 1.84e-14 2.54e-15 1.31e-13
var(treat) | 14.18267 3.054096 9.299513 21.62996
var(_cons) | 19.10214 1.336654 16.65405 21.91008
-----------------------------+------------------------------------------------
var(Residual) | 23.55464 .7344161 22.15831 25.03896
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 611.09 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. mixed wealth_ind_ihsa c.divduration##i.treat || id: divduration treat if female ==0, var
> iance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -10978.336
Iteration 1: log likelihood = -10946.347
Iteration 2: log likelihood = -10923.592
Iteration 3: log likelihood = -10923.509
Iteration 4: log likelihood = -10923.509
Computing standard errors:
Mixed-effects ML regression Number of obs = 3,374
Group variable: id Number of groups = 1,578
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(3) = 95.10
Log likelihood = -10923.509 Prob > chi2 = 0.0000
-------------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
divduration | .0985778 .0190893 5.16 0.000 .0611634 .1359921
|
treat |
1. yes | -2.580338 .4644723 -5.56 0.000 -3.490687 -1.669989
|
treat#c.divduration |
1. yes | -.078105 .0392166 -1.99 0.046 -.1549681 -.001242
|
_cons | 8.526016 .220508 38.67 0.000 8.093828 8.958204
-------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(divdu~on) | 2.71e-17 3.31e-17 2.49e-18 2.96e-16
var(treat) | 24.9481 3.96691 18.268 34.07094
var(_cons) | 18.98301 1.459009 16.32837 22.06924
-----------------------------+------------------------------------------------
var(Residual) | 22.06696 .7535283 20.63841 23.5944
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 703.34 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.Code:
. gen divdurtreat = divduration*treat
. mixed wealth_ind_ihsa c.divduration i.treat c.divdurtreat || id: divduration treat divdurtreat if female ==1, variance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -13644.7
Iteration 1: log likelihood = -13634.069 (not concave)
Iteration 2: log likelihood = -13538.835
Iteration 3: log likelihood = -13502.249
Iteration 4: log likelihood = -13500.88
Iteration 5: log likelihood = -13500.872
Iteration 6: log likelihood = -13500.872
Computing standard errors:
Mixed-effects ML regression Number of obs = 4,156
Group variable: id Number of groups = 2,011
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(3) = 118.16
Log likelihood = -13500.872 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
divduration | .0746747 .01738 4.30 0.000 .0406106 .1087389
|
treat |
1. yes | -3.080063 .3923129 -7.85 0.000 -3.848982 -2.311144
divdurtreat | .0366243 .0399644 0.92 0.359 -.0417044 .114953
_cons | 7.816756 .1984965 39.38 0.000 7.42771 8.205802
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(divdur~n) | 2.21e-18 2.37e-15 0 .
var(treat) | 13.06161 3.11551 8.18398 20.84629
var(divdur~t) | .0438225 .0199468 .0179578 .1069403
var(_cons) | 19.43964 1.345206 16.97406 22.26335
-----------------------------+------------------------------------------------
var(Residual) | 23.02648 .7503928 21.60173 24.54521
------------------------------------------------------------------------------
LR test vs. linear model: chi2(4) = 618.32 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. mixed wealth_ind_ihsa c.divduration i.treat c.divdurtreat || id: divduration treat divdurtreat if female ==0, variance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -11012.846
Iteration 1: log likelihood = -10925.717 (not concave)
Iteration 2: log likelihood = -10920.256
Iteration 3: log likelihood = -10917.022
Iteration 4: log likelihood = -10917.008
Iteration 5: log likelihood = -10917.008
Computing standard errors:
Mixed-effects ML regression Number of obs = 3,374
Group variable: id Number of groups = 1,578
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(3) = 95.03
Log likelihood = -10917.008 Prob > chi2 = 0.0000
---------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
divduration | .0972924 .0188135 5.17 0.000 .0604187 .1341662
|
treat |
1. yes | -2.556076 .4609884 -5.54 0.000 -3.459596 -1.652555
divdurtreat | -.0880446 .0443864 -1.98 0.047 -.1750404 -.0010488
_cons | 8.530427 .2191675 38.92 0.000 8.100867 8.959987
---------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(divdur~n) | 9.30e-25 1.04e-24 1.04e-25 8.33e-24
var(treat) | 22.8626 4.072005 16.12576 32.4139
var(divdur~t) | .0824965 .030153 .040301 .1688711
var(_cons) | 19.62524 1.474194 16.93851 22.73814
-----------------------------+------------------------------------------------
var(Residual) | 21.09708 .7737775 19.63373 22.6695
------------------------------------------------------------------------------
LR test vs. linear model: chi2(4) = 716.34 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.To compare between men and women in one models, I will have to add another interaction, which should look like this:
Code:
. mixed wealth_ind_ihsa c.divduration##i.treat##i.female || id: divduration treat, variance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -24557.921
Iteration 1: log likelihood = -24487.306
Iteration 2: log likelihood = -24463.858
Iteration 3: log likelihood = -24432.148
Iteration 4: log likelihood = -24431.428
Iteration 5: log likelihood = -24431.428
Computing standard errors:
Mixed-effects ML regression Number of obs = 7,530
Group variable: id Number of groups = 3,589
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(7) = 229.81
Log likelihood = -24431.428 Prob > chi2 = 0.0000
--------------------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
divduration | .0990835 .0193693 5.12 0.000 .0611204 .1370467
|
treat |
1. yes | -2.589135 .4540284 -5.70 0.000 -3.479014 -1.699256
|
treat#c.divduration |
1. yes | -.0755784 .0394343 -1.92 0.055 -.1528681 .0017114
|
female |
1. yes | -.7077551 .2977783 -2.38 0.017 -1.29139 -.1241204
|
female#c.divduration |
1. yes | -.0242395 .0259686 -0.93 0.351 -.075137 .026658
|
treat#female |
1. yes#1. yes | -.4562929 .6060581 -0.75 0.452 -1.644145 .7315592
|
treat#female#c.divduration |
1. yes#1. yes | .101074 .0540222 1.87 0.061 -.0048076 .2069555
|
_cons | 8.524302 .2230329 38.22 0.000 8.087165 8.961438
--------------------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(divdur~n) | 4.20e-15 2.93e-15 1.07e-15 1.65e-14
var(treat) | 19.06961 2.437581 14.84351 24.49893
var(_cons) | 19.06747 .985757 17.23008 21.1008
-----------------------------+------------------------------------------------
var(Residual) | 22.86307 .5261591 21.85473 23.91794
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 1308.89 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.
. margins, at(divduration=(0(1)25) treat ==(0 1) female ==(0 1)) atmeansIf I now also add all gender interactions into the random part, the random part can no longer be properly estimated:
Code:
. gen treatwomen = treat*female
. gen divdurwomen = divduration*female
. gen divdurtreat = divduration*treat
. gen divdurtreatwomen = divdurtreat*female
. mixed wealth_ind_ihsa i.treat i.treatwomen c.divduration c.divdurwomen c.divdurtreat c.di
> vdurtreatwomen || id: treat treatwomen divduration divdurwomen divdurtreat divdurtreatwom
> en, variance mle
Performing EM optimization:
Performing gradient-based optimization:
Iteration 0: log likelihood = -25048.998 (not concave)
Iteration 1: log likelihood = -24621.51
Iteration 2: log likelihood = -24430.961 (not concave)
Iteration 3: log likelihood = -24430.921 (backed up)
Iteration 4: log likelihood = -24425.776
Iteration 5: log likelihood = -24424.608
Iteration 6: log likelihood = -24424.577
Iteration 7: log likelihood = -24424.577
Computing standard errors:
Mixed-effects ML regression Number of obs = 7,530
Group variable: id Number of groups = 3,589
Obs per group:
min = 1
avg = 2.1
max = 4
Wald chi2(6) = 225.87
Log likelihood = -24424.577 Prob > chi2 = 0.0000
----------------------------------------------------------------------------------
wealth_ind_ihsa | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
treat |
1. yes | -2.168293 .4199046 -5.16 0.000 -2.99129 -1.345295
1.treatwomen | -1.223729 .5250301 -2.33 0.020 -2.252769 -.1946884
divduration | .1204012 .0167822 7.17 0.000 .0875086 .1532938
divdurwomen | -.0637083 .0196832 -3.24 0.001 -.1022866 -.0251299
divdurtreat | -.1063216 .0424442 -2.50 0.012 -.1895107 -.0231326
divdurtreatwomen | .1603849 .0572352 2.80 0.005 .048206 .2725637
_cons | 8.129163 .1472028 55.22 0.000 7.84065 8.417675
----------------------------------------------------------------------------------
------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
var(treat) | 17.49735 . . .
var(treatw~n) | 2.15e-10 . . .
var(divdu~on) | 6.16e-19 . . .
var(d~rwomen) | 7.94e-21 . . .
var(divdur~t) | .059631 . . .
var(d~twomen) | 4.09e-16 . . .
var(_cons) | 19.55695 . . .
-----------------------------+------------------------------------------------
var(Residual) | 22.16909 . . .
------------------------------------------------------------------------------
LR test vs. linear model: chi2(7) = 1327.03 Prob > chi2 = 0.0000
Note: LR test is conservative and provided only for reference.Thank,
Nicole
0 Response to Growth model (random slope & intercept) with group interaction - model specification
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