linear mixed models with 2 time points

[nick sand]

Hi all,
I am studying the effect of the exposure to air pollution on brain volumes. Air pollution was assessed at baseline and brain volumes at baseline and 5 years later.
Am I right with doing a linear mixed models (with only 2 time points for the outcome?) or would it be better to do a classic linear regression with the delta between the brain volume at year 0 and at year 5.
I think mixed models are more appropriate here, that's what I would do with more than 2 time points and repeated data over time but I am a bit confused here with only 2 time points.
Thank you for your advice,
Best regards,
Nick S

[Carlo Lazzaro]

Nick:
you could also consider a panel data regression with -re- specification:

. use "https://www.stata-press.com/data/r17/nlswork.dta"
(National Longitudinal Survey of Young Women, 14-24 years old in 1968)

. xtreg ln_wage c.age##c.age, mle vce(cluster idcode)

Fitting constant-only model:
Iteration 0:   log likelihood =  -12878.37
Iteration 1:   log likelihood = -12864.036
Iteration 2:   log likelihood = -12863.892
Iteration 3:   log likelihood = -12863.892

Fitting full model:
Iteration 0:   log likelihood = -11322.802
Iteration 1:   log likelihood = -11264.949
Iteration 2:   log likelihood = -11264.776
Iteration 3:   log likelihood = -11264.776

Random-effects ML regression                        Number of obs    =  28,510
Group variable: idcode                              Number of groups =   4,710

Random effects u_i ~ Gaussian                       Obs per group:
                                                                 min =       1
                                                                 avg =     6.1
                                                                 max =      15

                                                    Wald chi2(2)     = 1261.77
Log likelihood = -11264.776                         Prob > chi2      =  0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0592303   .0041053    14.43   0.000     .0511842    .0672765
             |
 c.age#c.age |  -.0006789   .0000688    -9.87   0.000    -.0008137   -.0005441
             |
       _cons |    .545105   .0587335     9.28   0.000     .4299895    .6602205
-------------+----------------------------------------------------------------
    /sigma_u |    .357561   .0048399                      .3481996     .367174
    /sigma_e |   .3031159   .0036457                       .296054    .3103463
         rho |   .5818521   .0092125                      .5637158    .5998159
------------------------------------------------------------------------------


. mixed ln_wage c.age##c.age,vce(cluster idcode)|| idcode:

Performing EM optimization ...

Performing gradient-based optimization: 
Iteration 0:   log pseudolikelihood = -11264.776  
Iteration 1:   log pseudolikelihood = -11264.776  

Computing standard errors ...

Mixed-effects regression                        Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710
                                                Obs per group:
                                                              min =          1
                                                              avg =        6.1
                                                              max =         15
                                                Wald chi2(2)      =    1266.75
Log pseudolikelihood = -11264.776               Prob > chi2       =     0.0000

                             (Std. err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
         age |   .0592303   .0040999    14.45   0.000     .0511946    .0672661
             |
 c.age#c.age |  -.0006789   .0000687    -9.88   0.000    -.0008135   -.0005442
             |
       _cons |    .545105   .0586349     9.30   0.000     .4301826    .6600274
------------------------------------------------------------------------------

------------------------------------------------------------------------------
                             |               Robust           
  Random-effects parameters  |   Estimate   std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
idcode: Identity             |
                  var(_cons) |   .1278498   .0034804      .1212072    .1348566
-----------------------------+------------------------------------------------
               var(Residual) |   .0918793   .0022077      .0876526    .0963098
------------------------------------------------------------------------------

.

The acceptability of the "two-point in time only" issue mostly depends on tribal rules in your research field.

[nick sand]

Thank you, Carlo! I will look at this more deeply.
Best regards,
Nick