I am currently using Panel data from the SOEP to analyze and compare political interest in 2013 and 2017. My final Dataset contains around 10 variables and 21,444 observations from two waves (2013 & 2017). My DV is a binary variable =1 if the individual is interested and ==0 otherwise. Below is a Description of my Variables

Code:
              storage   display    value
variable name   type    format     label      variable label
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
interested      float   %13.0g     interested
                                              Interested(0/1)
polpart         float   %9.0g      polpart    Participates (0/1)
hhinc_eqr       float   %9.0g                 Real Equivalized HH-Inc. in thousand €
female          float   %9.0g      female     Female (0/1)
age             int     %8.0g                 Age of Individual
west            float   %9.0g      west       West-Germany(0/1)
y2013           float   %9.0g      y2013      Pre crisis(0/1)
y2017           float   %9.0g      y2017      Post crisis(0/1)
unemployed      float   %10.0g     unemployed
                                              Unemployed(0/1)
edyears         float   %9.0g                 Number of Years of Education
party_pref      float   %13.0g     party_pref
                                              Party preference(0/1)
worried         float   %11.0g     worried    
hhinc_group     float   %9.0g      hhinc_group
                                              Income Groups
hhsize          byte    %8.0g                 Number of Persons in HH
persnr          long    %12.0g                Unveraenderliche Personennummer (PID)
syear           int     %12.0g                Befragungsjahr
I first ran xtlogit with a full year-dummy interaction to estimate the changes between 2013 and 2017:
Code:
. logistic interested i.y2017##c.age i.y2017##ib(2).hhinc_group i.y2017##i.west ///
> i.y2017##i.female i.y2017##i.party_pref i.y2017##i.unemployed ///
> i.y2017##i.worried i.y2017##c.edyears, vce(cluster persnr)

Logistic regression                             Number of obs     =     21,444
                                                Wald chi2(19)     =    3116.28
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -11933.143               Pseudo R2         =     0.1783

                                 (Std. Err. adjusted for 15,309 clusters in persnr)
-----------------------------------------------------------------------------------
                  |               Robust
       interested | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
            y2017 |
            2017  |   1.959571   .4097247     3.22   0.001     1.300721    2.952146
              age |   1.028058   .0016503    17.24   0.000     1.024828    1.031297
                  |
      y2017#c.age |
            2017  |   .9953376   .0017759    -2.62   0.009      .991863    .9988244
                  |
      hhinc_group |
            Poor  |    .841905   .0772755    -1.87   0.061     .7032897    1.007841
            Rich  |   1.351389   .0803104     5.07   0.000     1.202805    1.518328
                  |
y2017#hhinc_group |
       2017#Poor  |   1.102225   .1224724     0.88   0.381     .8865227     1.37041
       2017#Rich  |   .8609955   .0585903    -2.20   0.028     .7534891    .9838406
                  |
             west |
            West  |   1.097271   .0653854     1.56   0.119     .9763183    1.233207
                  |
       y2017#west |
       2017#West  |   .9534032   .0610252    -0.75   0.456     .8409944    1.080837
                  |
           female |
          Female  |   .3994588    .020074   -18.26   0.000       .36199    .4408059
                  |
     y2017#female |
     2017#Female  |   1.080646   .0578372     1.45   0.147     .9730302    1.200164
                  |
       party_pref |
      preference  |   3.502175   .1792699    24.49   0.000     3.167863    3.871767
                  |
 y2017#party_pref |
 2017#preference  |   .9004705   .0542628    -1.74   0.082     .8001578    1.013359
                  |
       unemployed |
      unemployed  |   1.166827   .1479902     1.22   0.224      .910013    1.496117
                  |
 y2017#unemployed |
 2017#unemployed  |   .8746221   .1345562    -0.87   0.384     .6469451    1.182425
                  |
          worried |
         worried  |   .8425315   .0449318    -3.21   0.001      .758913    .9353632
                  |
    y2017#worried |
    2017#worried  |   1.066966   .0755296     0.92   0.360      .928741    1.225763
                  |
          edyears |   1.206524   .0125361    18.07   0.000     1.182202    1.231346
                  |
  y2017#c.edyears |
            2017  |   .9956702   .0111172    -0.39   0.698     .9741176      1.0177
                  |
            _cons |    .010937   .0020517   -24.07   0.000     .0075722    .0157971
-----------------------------------------------------------------------------------
Note: _cons estimates baseline odds.
In order to regard the serial correlation and Panel structure of my Data, I then ran:

Code:
. xtlogit interested c.age##c.age ib(2).hhinc_group i.west i.female i.party_pref ///
> i.unemployed i.worried edyears i.y2017, re nolog or intpoints(32)

Random-effects logistic regression              Number of obs     =     21,444
Group variable: persnr                          Number of groups  =     15,309

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        1.4
                                                              max =          2

Integration method: mvaghermite                 Integration pts.  =         32

                                                Wald chi2(11)     =    1184.43
Log likelihood  = -11080.549                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
  interested | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   1.043214   .0135104     3.27   0.001     1.017068    1.070033
             |
 c.age#c.age |   1.000125   .0001226     1.02   0.308     .9998846    1.000365
             |
 hhinc_group |
       Poor  |   .7840031   .0976617    -1.95   0.051     .6141654    1.000807
       Rich  |   1.440353   .1243391     4.23   0.000     1.216154    1.705883
             |
        west |
       West  |    1.22893   .1197768     2.12   0.034     1.015232    1.487609
             |
      female |
     Female  |   .1370047   .0129937   -20.96   0.000     .1137644    .1649927
             |
  party_pref |
 preference  |   10.51701   .9246106    26.76   0.000     8.852339    12.49471
             |
  unemployed |
 unemployed  |   1.141778   .1908279     0.79   0.428     .8228457    1.584327
             |
     worried |
    worried  |   .8122069   .0655849    -2.58   0.010     .6933188    .9514815
     edyears |   1.541916   .0302456    22.08   0.000      1.48376     1.60235
             |
       y2017 |
       2017  |   1.840504   .1101531    10.19   0.000     1.636789    2.069573
       _cons |   .0000852   .0000392   -20.36   0.000     .0000346    .0002101
-------------+----------------------------------------------------------------
    /lnsig2u |   2.411774    .067891                       2.27871    2.544838
-------------+----------------------------------------------------------------
     sigma_u |   3.339721   .1133685                      3.124753    3.569477
         rho |   .7722266   .0119415                      .7479791    .7947813
------------------------------------------------------------------------------
Note: Estimates are transformed only in the first equation.
Note: _cons estimates baseline odds (conditional on zero random effects).
LR test of rho=0: chibar2(01) = 1719.38                Prob >= chibar2 = 0.000
However, I am not really sure on how to get estimate changes between 2013 and 2017 in the RE-Logit. My goal is to look at the predicted change in P(interested=1) between 2013 und 2017 for my whole sample, as well as for the three different Income Groups.
Now I am wondering, whether I should interpret this change by looking at the marginal effects of my year-dummy, or if I need to estimate separate RE-Logit for each of the three income groups (?). AFAIK the year dummies will pick up any variation in the outcome that happen over time and that is not attributed to other explanatory variables, BUT does it make sense to estimate it for different subpopulations ? If not, what other possibilities do I have to compare my two waves ?

Here is what I ran after my RE-Logit:
Code:
. margins, dydx(y2017) over(hhinc_group) coeflegend post

Average marginal effects                        Number of obs     =     21,444
Model VCE    : OIM

Expression   : Pr(interested=1), predict(pr)
dy/dx w.r.t. : 1.y2017
over         : hhinc_group

------------------------------------------------------------------------------
             |      dy/dx  Legend
-------------+----------------------------------------------------------------
0.y2017      |  (base outcome)
-------------+----------------------------------------------------------------
1.y2017      |
 hhinc_group |
       Poor  |   .0464933  _b[1.y2017:1bn.hhinc_group]
     Middle  |   .0518429  _b[1.y2017:2.hhinc_group]
       Rich  |     .05327  _b[1.y2017:3.hhinc_group]
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

.
end of do-file

. do "C:\Users\Lorenz\AppData\Local\Temp\STD1bbc_000000.tmp"

. test _b[1.y2017:1bn.hhinc_group] = _b[1.y2017:2.hhinc_group] = _b[1.y2017:3.hhinc_group]

 ( 1)  [1.y2017]1bn.hhinc_group - [1.y2017]2.hhinc_group = 0
 ( 2)  [1.y2017]1bn.hhinc_group - [1.y2017]3.hhinc_group = 0

           chi2(  2) =   50.06
         Prob > chi2 =    0.0000


Alternatively, I thought about running
Code:
xtlogit interested c.age##c.age ib(2).hhinc_group i.west i.female i.party_pref ///
i.unemployed i.worried edyears i.y2017 if hhinc_group==1, re nolog or intpoints(32)
I am unsure about the appropriateness of each of these approaches and how they differ in results and interpretation. Or should I include interaction terms with the year dummy in my RE-Logit ? I am thinking that in the case of full interaction, which is equal to estimating two separate equations for 2013 and 2017, all the within variation would be lost (?)

I am currently at undergrad level and re did my best to read all material available, but right now I cannot find an answer in regards to what I should use for my analysis.

I would very much appreciate any input.

Best regards,
Lorenz