Interpretation of margins plot that not significant in slope change in Growth Curve Model

[Gayoung Choi]

Hello.
I'm a master student studying sociology.
Using the growth curve model, I examine the relationship between age discrimination and depressive symptoms in older adults and the moderating effect of social participation in the relationship.

X: age discrimination(earlyret)
Y: depressive symptoms(cesd)
Moderators: social participation(fm_v4)

My question is...

1) In my model, the slope of direct effect( social participation) was not significant ( please see the red line, fm_v4#c.c_age).
2) Also, interaction effect (social participation*age discrimination) was not significant (please see the red line, earlyret#fm_v4#c.c_age)
3) Therefore, the intercept are only significant in my model.

. mixed cesd ($indi $health i.infm_v2 i.earlyret##i.fm_v4)##c.c_age || pid: c_age, cov(un)

Performing EM optimization ...

Performing gradient-based optimization: 
Iteration 0:  Log likelihood = -17364.477  
Iteration 1:  Log likelihood = -17359.326  
Iteration 2:  Log likelihood = -17359.321  
Iteration 3:  Log likelihood = -17359.321  

Computing standard errors ...

Mixed-effects ML regression                          Number of obs    =  6,335
Group variable: pid                                  Number of groups =  1,763
                                                     Obs per group:
                                                                  min =      1
                                                                  avg =    3.6
                                                                  max =      8
                                                     Wald chi2(28)    = 351.62
Log likelihood = -17359.321                          Prob > chi2      = 0.0000

----------------------------------------------------------------------------------------
                  cesd | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------------+----------------------------------------------------------------
                 c_age |  -.0103718   .1001608    -0.10   0.918    -.2066833    .1859397
              1.female |  -.0074826    .272614    -0.03   0.978    -.5417963    .5268311
                       |
                   edu |
                    2  |  -.5330101   .2889121    -1.84   0.065    -1.099267    .0332472
                    3  |    .080262   .3877078     0.21   0.836    -.6796313    .8401552
                       |
               lg_hinc |  -.2996866   .1384337    -2.16   0.030    -.5710118   -.0283615
            1.maritalb |   -1.54429   .3369001    -4.58   0.000    -2.204602    -.883978
               0.urban |   .4072159   .3235032     1.26   0.208    -.2268386     1.04127
                1.baby |  -1.323011   .3347397    -3.95   0.000    -1.979089   -.6669336
       1.firselfhealth |    .590916   .1739587     3.40   0.001     .2499632    .9318688
               chronic |   .1370472   .1383622     0.99   0.322    -.1341378    .4082322
             1.infm_v2 |  -.9681479    .166661    -5.81   0.000    -1.294798   -.6414983
            1.earlyret |   1.726809   .4565981     3.78   0.000     .8318932    2.621725
               1.fm_v4 |  -.5888003   .2376224    -2.48   0.013    -1.054532   -.1230689
                       |
        earlyret#fm_v4 |
                  1 1  |  -1.076948   .5064372    -2.13   0.033    -2.069546   -.0843493
                       |
       c.c_age#c.c_age |  -.0061064   .0019121    -3.19   0.001    -.0098541   -.0023588
                       |
        female#c.c_age |
                    1  |  -.0322041   .0233002    -1.38   0.167    -.0778716    .0134633
                       |
           edu#c.c_age |
                    2  |  -.0242902   .0256213    -0.95   0.343    -.0745071    .0259267
                    3  |   .0378368   .0332827     1.14   0.256     -.027396    .1030697
                       |
     c.lg_hinc#c.c_age |   .0001526   .0114428     0.01   0.989    -.0222749      .02258
                       |
      maritalb#c.c_age |
                    1  |   .0060822   .0337838     0.18   0.857    -.0601327    .0722972
                       |
         urban#c.c_age |
                    0  |   .0272908   .0292365     0.93   0.351    -.0300117    .0845932
                       |
          baby#c.c_age |
                    1  |  -.1048218   .0343953    -3.05   0.002    -.1722354   -.0374082
                       |
 firselfhealth#c.c_age |
                    1  |  -.0247417   .0186391    -1.33   0.184    -.0612736    .0117902
                       |
     c.chronic#c.c_age |   -.005467   .0151906    -0.36   0.719      -.03524     .024306
                       |
       infm_v2#c.c_age |
                    1  |  -.0331699   .0167057    -1.99   0.047    -.0659125   -.0004273
                       |
      earlyret#c.c_age |
                    1  |   .0359466   .0492728     0.73   0.466    -.0606262    .1325195
                       |
         fm_v4#c.c_age |
                    1  |  -.0388203   .0235069    -1.65   0.099    -.0848929    .0072524
                       |
earlyret#fm_v4#c.c_age |
                  1 1  |  -.0780107   .0540975    -1.44   0.149    -.1840398    .0280185
                       |
                 _cons |   9.588647   1.134577     8.45   0.000     7.364916    11.81238
----------------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects parameters  |   Estimate   Std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
pid: Unstructured            |
                  var(c_age) |    .040588   .0061177      .0302064    .0545378
                  var(_cons) |   12.76785   .9137959      11.09679    14.69056
            cov(c_age,_cons) |     .58007   .0673852      .4479975    .7121425
-----------------------------+------------------------------------------------
               var(Residual) |   9.741261   .2304172       9.29996     10.2035
------------------------------------------------------------------------------
LR test vs. linear model: chi2(3) = 1032.02               Prob > chi2 = 0.0000

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

.

So I expected margins plot that there are no slope differences.
However, in my figure, there are a slope difference.
How can I explain these situation?

Thank you for reading my post!

Best,
Gayoung

[Maarten Buis]

You have an awful lot of interactions in your model. It probably means you are trying to extract more information from your data than is present in your data. Remember that not significant does not mean the effect is not there, it only means that you cannot find it.