Force model to go through 0/0 (repeated measures mixed model)

[Fabian Fortner]

Hi
I would appreciate your help regarding this issue in a observational study (medical field). Is there a way to force this model to go through x=0 and y=0?

I want to model
the effect of a binary treatment variable: treatment
on a continuous outcome measure that starts at value = 0: measure
which is assessed repeatedly over time (time is continuous, not categorical): time
in multiple subjecs: subject_id

I did this using an approach like this:

mixed measure ///
           i.treatment##c.time_m##c.time_m ///   quadratic transformation
          || subject_id:

Then I create marginal predictions

margins  i.treatment, at(time = (0(1)9))
 
marginsplot, noci

Which results in this graph: However, as measure starts at =0 in reality, the fact that Treatment 2 start below 0 would seem odd to a reviewer or reader of the article. Is there a way to force this model to go thorugh x=0 and y=0? I thought about the noconstant option but this doesn't work.

[Clyde Schechter]

As you don't give example data, I illustrate the approach using StataCorp's example childweight data set.

. webuse childweight, clear
(Weight data on Asian children)

.
. mixed weight i.girl#c.age##c.age, nocons || id: // NOTE DISTINCTIVE USE OF # VS ##

Performing EM optimization ...

Performing gradient-based optimization:
Iteration 0:  Log likelihood = -355.61291  
Iteration 1:  Log likelihood = -355.61291  

Computing standard errors ...

Mixed-effects ML regression                         Number of obs    =     198
Group variable: id                                  Number of groups =      68
                                                    Obs per group:
                                                                 min =       1
                                                                 avg =     2.9
                                                                 max =       5
                                                    Wald chi2(4)     = 2952.42
Log likelihood = -355.61291                         Prob > chi2      =  0.0000

----------------------------------------------------------------------------------
          weight | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      girl#c.age |
           Girl  |  -1.056917   .5738161    -1.84   0.065    -2.181575    .0677423
                 |
             age |   9.174038   .3968372    23.12   0.000     8.396251    9.951824
                 |
girl#c.age#c.age |
            Boy  |  -2.135763   .1502979   -14.21   0.000    -2.430342   -1.841185
           Girl  |  -1.821343   .1577031   -11.55   0.000    -2.130435    -1.51225
----------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects parameters  |   Estimate   Std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
id: Identity                 |
                  var(_cons) |   9.937986   1.975423       6.73133    14.67222
-----------------------------+------------------------------------------------
               var(Residual) |    .554075   .0735825      .4270974    .7188035
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 83.66         Prob >= chibar2 = 0.0000

.
. margins girl, at(age = (0(0.5)2.5))

Adjusted predictions                                       Number of obs = 198

Expression: Linear prediction, fixed portion, predict()
1._at: age =   0
2._at: age =  .5
3._at: age =   1
4._at: age = 1.5
5._at: age =   2
6._at: age = 2.5

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    _at#girl |
      1#Boy  |          0  (empty)
     1#Girl  |          0  (empty)
      2#Boy  |   4.053078   .1623266    24.97   0.000     3.734924    4.371232
     2#Girl  |   3.603225   .1692095    21.29   0.000      3.27158    3.934869
      3#Boy  |   7.038274   .2541935    27.69   0.000     6.540064    7.536484
     3#Girl  |   6.295778   .2640165    23.85   0.000     5.778316    6.813241
      4#Boy  |   8.955589   .2811197    31.86   0.000     8.404605    9.506573
     4#Girl  |    8.07766    .289765    27.88   0.000     7.509731    8.645589
      5#Boy  |   9.805022   .2602134    37.68   0.000     9.295013    10.31503
     5#Girl  |   8.948871   .2635516    33.95   0.000     8.432319    9.465423
      6#Boy  |   9.586573   .2503318    38.30   0.000     9.095932    10.07721
     6#Girl  |    8.90941   .2480882    35.91   0.000     8.423166    9.395654
------------------------------------------------------------------------------

. marginsplot

Variables that uniquely identify margins: age girl

which produces the graph below. Note that there are no error bars around the (0,0) plotted points as these are forced values. (This model is not appropriate for this data, because children do not weigh 0 at age 0--but you can apply the same technique to your data to get these results.) You should not, however, represent this graph as being the output of the model that you originally ran--it is not that. And you should, in your presentation of these results, make it clear that the (0,0) point is constrained, not stochastic.

[Fabian Fortner]

Dear Clyde
Thank you very much!
Those data are very similar to mine, if we change them a little bit and try to model the weight difference from birth.

However, it fails to force through 0, when you include other fixed effects in the model (that are e.g. not also interacted with age) - is there an approach for such a case as well?
The code produces the graph below, see x=0/y=0 in the right image...

webuse childweight, clear
replace brthwt = brthwt/1000     // make it same unit as weight
gen diff = weight-brthw           // make a weight difference variable

* works as shown:
mixed diff i.girl#c.age##c.age, nocons || id:
margins i.girl, at(age = (0(0.5)2.5))
marginsplot, name(one, replace)


* adding brthwt to adjust for it (e.g. it likely is associated with weight change over time):
mixed diff i.girl#c.age##c.age brthwt, nocons || id:
margins i.girl, at(age = (0(0.5)2.5))
marginsplot, name(two, replace)

graph combine one two

[Clyde Schechter]

Offhand, I can't think of how to do that. I'll ponder a while, and if I come up with a solution, I'll get back to you. In the meantime, if somebody else knows how to do this, do chime in.

[Fabian Fortner]

Ok, I found the solution: I centered the other independent variables... example:

webuse childweight, clear
replace brthwt = brthwt/1000  // make it same unit as weight
gen diff = weight-brthw           // make a weight difference variable
egen bweight_mean = mean(brthwt)
gen bweight_center = brthw-bweight_mean

* works as shown
mixed diff i.girl#c.age##c.age, nocons || id:
margins i.girl, at(age = (0(0.5)2.5))
marginsplot, name(one, replace)

* adding brthwt
mixed diff i.girl#c.age##c.age brthwt, nocons || id:
margins i.girl, at(age = (0(0.5)2.5))
marginsplot, name(two, replace)

* adding brthwt centered instead
mixed diff i.girl#c.age##c.age bweight_center, nocons  || id:
margins i.girl, at(age = (0(0.5)2.5))
marginsplot, name(three, replace)


graph combine  one two three

[Clyde Schechter]

Very nice! And thank you for sharing your solution.