Independent variables change signs when interaction is included

[Sophie Jasper]

Hey stata experts, I am currently writing my master thesis, therefore using stata. I have a question about an interpretation of my interactions. I wanna do a logistic regression, my dependent var is stock market participation (binary), my independent var are five personality traits (continuous), and my interactions are quality of government (continuous) with each trait. I also have several controls. It happens for two traits that the interaction is significant and positive, however, the respective independent variables change signs, but only for the regression in which the respective interaction is included. In all other regression with the other interactions, the sign remains the same. I have tried demeaned variables, probit, xtlogit, I have let stata calculate the interactions, and used a non-normed meancountryeqi, but results remain the same.

How is it possible to interpret these results?

This is what I regress:
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi CV, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi oqog CV, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi cqog CV, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi eqog CV, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi aqog CV, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi nqog CV, vce(robust)

This is the stata output:

	Column 1	Column 2	Column 3	Column 4	Column 5	Column 6
Openness	-.054*** (.011)	.449*** (.060)	-.054*** (.011)	-.051*** (.011)	-.051*** (.011)	-.053*** (.011)
Conscientiousness	-.101*** (.014)	-.103*** (.014)	-.114 (.070)	-.100*** (.014)	-.100*** (.014)	-.100*** (.014)
Extraversion	-.024** (.012)	-.025** (.012)	-.024** (.012)	-.427*** (.060)	-.026** (.012)	-.025** (.012)
Agreeableness	.063*** (.014)	.059*** (.014)	.063*** (.014)	.059*** (.014)	-.229*** (.072)	.063*** (.014)
Neuroticism	-.004 (.011)	-.001 (.011)	-.004 (.011)	-.000 (.012)	-.003 (.012)	.075 (.061)
QOG	.047*** (.001)	.071*** (.003)	.047*** (.004)	.027*** (.003)	.031*** (.004)	.050*** (.002)
O*QOG		-.007*** (.001)
C*QOG			.000 (.001)
E*QOG				.006*** (.001)
A*QOG					.004*** (.001)
N*QOG						-.001 (.001)

Best, Sophie

[Carlo Lazzaro]

Sophie:
welcome to this forum.
As per FAQ, please post what you typed and what Stata gave you back via CODE delimiters (otherwise, as in your post, the output is hardly readable).
You performed different regression specification: hence, no wonder that results changed.
For good reasons (see -margins- and -marginsplot-) is far better to exploit -fvvarlist- notation for creating categorical variables and interactions.
All the regression approaches that you mentioned fit different datasets and are by no means interchangeable: while -logistic- seems right if your regressand in a yes/no one, you do not say if you're dealing with cross-sectional or panel data.

[Sophie Jasper]

Thanks for your reply and sorry for that. I have an unbalanced panel with data from 2011, 2013, 2015, 2017. The independent variables are time-invariant. This is what I typed:
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi age gender maritalstatus ch001_ health incomextile unemployed secondaryeducation tertiaryeducation cf016tot GDP, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi oqog age gender maritalstatus ch001_ health incomextile unemployed secondaryeducation tertiaryeducation cf016tot GDP, vce(robust)
logit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountrynormeqi aqog age gender maritalstatus ch001_ health incomextile unemployed secondaryeducation tertiaryeducation cf016tot GDP, vce(robust)

and the output:

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -26606.692  
Iteration 2:   log pseudolikelihood = -26172.303  
Iteration 3:   log pseudolikelihood = -26169.621  
Iteration 4:   log pseudolikelihood =  -26169.62  

Logistic regression                             Number of obs     =     61,215
                                                Wald chi2(17)     =    8138.25
                                                Prob > chi2       =     0.0000
Log pseudolikelihood =  -26169.62               Pseudo R2         =     0.1652

------------------------------------------------------------------------------------
                   |               Robust
               smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
        bfi10_open |  -.0542844   .0111898    -4.85   0.000    -.0762161   -.0323527
       bfi10_consc |  -.1007209   .0137165    -7.34   0.000    -.1276047   -.0738371
       bfi10_extra |  -.0239048   .0117969    -2.03   0.043    -.0470263   -.0007834
       bfi10_agree |   .0634871   .0139709     4.54   0.000     .0361046    .0908695
       bfi10_neuro |  -.0036259   .0114864    -0.32   0.752    -.0261387     .018887
meancountrynormeqi |   .0473813   .0009422    50.29   0.000     .0455345     .049228
               age |   .0197396   .0012675    15.57   0.000     .0172552    .0222239
            gender |   .4089045   .0232394    17.60   0.000     .3633561    .4544529
     maritalstatus |    .226495   .0249527     9.08   0.000     .1775886    .2754013
            ch001_ |  -.0892244   .0088333   -10.10   0.000    -.1065373   -.0719115
            health |   .5623931   .0263517    21.34   0.000     .5107446    .6140415
       incomextile |   .2577227   .0108987    23.65   0.000     .2363615    .2790838
        unemployed |  -.2722945   .0422908    -6.44   0.000     -.355183   -.1894061
secondaryeducation |   .2129277   .0287005     7.42   0.000     .1566757    .2691797
 tertiaryeducation |    .628529   .0302036    20.81   0.000      .569331    .6877271
          cf016tot |   .0787095   .0058097    13.55   0.000     .0673227    .0900963
               GDP |  -.0396268   .0060792    -6.52   0.000    -.0515418   -.0277117
             _cons |  -6.967406   .1551552   -44.91   0.000    -7.271505   -6.663308
------------------------------------------------------------------------------------
(est1 stored)

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -26588.512  
Iteration 2:   log pseudolikelihood = -26134.689  
Iteration 3:   log pseudolikelihood = -26130.529  
Iteration 4:   log pseudolikelihood = -26130.526  

Logistic regression                             Number of obs     =     61,215
                                                Wald chi2(18)     =    8091.34
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -26130.526               Pseudo R2         =     0.1665

------------------------------------------------------------------------------------
                   |               Robust
               smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
        bfi10_open |   .4491226   .0603116     7.45   0.000      .330914    .5673312
       bfi10_consc |  -.1032261   .0137261    -7.52   0.000    -.1301288   -.0763233
       bfi10_extra |  -.0252594   .0118044    -2.14   0.032    -.0483957   -.0021232
       bfi10_agree |   .0588091   .0139633     4.21   0.000     .0314416    .0861766
       bfi10_neuro |  -.0005631   .0114728    -0.05   0.961    -.0230495    .0219232
meancountrynormeqi |   .0713167   .0030043    23.74   0.000     .0654284    .0772049
              oqog |  -.0072044   .0008514    -8.46   0.000    -.0088731   -.0055358
               age |   .0195976   .0012688    15.45   0.000     .0171107    .0220844
            gender |   .4112678   .0232462    17.69   0.000      .365706    .4568296
     maritalstatus |   .2259649   .0249495     9.06   0.000     .1770648     .274865
            ch001_ |  -.0885206   .0088501   -10.00   0.000    -.1058664   -.0711748
            health |   .5637663   .0263721    21.38   0.000     .5120779    .6154547
       incomextile |   .2578155   .0109171    23.62   0.000     .2364183    .2792127
        unemployed |   -.260796   .0423551    -6.16   0.000    -.3438106   -.1777815
secondaryeducation |   .2002678   .0287733     6.96   0.000     .1438732    .2566624
 tertiaryeducation |   .6201373   .0301399    20.58   0.000     .5610643    .6792104
          cf016tot |   .0774748   .0058114    13.33   0.000     .0660846    .0888649
               GDP |  -.0426493   .0060595    -7.04   0.000    -.0545258   -.0307728
             _cons |  -8.604982   .2521623   -34.12   0.000    -9.099211   -8.110753
------------------------------------------------------------------------------------
(est2 stored)

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -26600.082  
Iteration 2:   log pseudolikelihood = -26163.359  
Iteration 3:   log pseudolikelihood =  -26160.62  
Iteration 4:   log pseudolikelihood = -26160.619  

Logistic regression                             Number of obs     =     61,215
                                                Wald chi2(18)     =    8176.81
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -26160.619               Pseudo R2         =     0.1655

------------------------------------------------------------------------------------
                   |               Robust
               smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
        bfi10_open |  -.0513248   .0112198    -4.57   0.000    -.0733151   -.0293344
       bfi10_consc |  -.0999784   .0137182    -7.29   0.000    -.1268655   -.0730912
       bfi10_extra |  -.0261673   .0118237    -2.21   0.027    -.0493413   -.0029933
       bfi10_agree |  -.2293127   .0724726    -3.16   0.002    -.3713565    -.087269
       bfi10_neuro |  -.0031551   .0115059    -0.27   0.784    -.0257062    .0193961
meancountrynormeqi |   .0311246   .0040561     7.67   0.000     .0231748    .0390745
              aqog |    .004279   .0010439     4.10   0.000     .0022329    .0063251
               age |   .0198574   .0012686    15.65   0.000      .017371    .0223438
            gender |    .411454   .0232624    17.69   0.000     .3658606    .4570475
     maritalstatus |   .2275482   .0249727     9.11   0.000     .1786027    .2764938
            ch001_ |  -.0898966   .0088472   -10.16   0.000    -.1072369   -.0725564
            health |   .5616802    .026354    21.31   0.000     .5100273    .6133331
       incomextile |   .2583767   .0109117    23.68   0.000     .2369901    .2797633
        unemployed |  -.2678391    .042318    -6.33   0.000     -.350781   -.1848973
secondaryeducation |   .2127965   .0287029     7.41   0.000     .1565397    .2690532
 tertiaryeducation |   .6262872   .0302214    20.72   0.000     .5670544      .68552
          cf016tot |   .0788237   .0058117    13.56   0.000      .067433    .0902143
               GDP |  -.0415255   .0061026    -6.80   0.000    -.0534864   -.0295647
             _cons |  -5.876958   .3049331   -19.27   0.000    -6.474616     -5.2793
------------------------------------------------------------------------------------
(est5 stored)

I hope I have presented it in the right way now, I am new to the forum.

Kind regards
Sophie

[Carlo Lazzaro]

Sophie:
thanks for providing further details and Stata outcome within CODE delimiters.
The first comment, before considering Stata outcome, refers to your -logit- choice.
If you have panel data, you should consider -xtlogit-. Moreover, you -logit- code does not take into account intraclass correlation within the same panel: you should have imposed -cluster()- for that.
Moreover: which one of the models you have tested gives the faires and truest view of the data generating process?
And, last but not least, what's your supervisor's take about the entire matter?

[Sophie Jasper]

Hi Carlo, thanks for your fast reply. Okay, I have changed my data to panel data with random effects. I have 60,215 observations from 30,286 individuals and will therefore cluster my data on individual level? I now have the following equations and outcomes, do you mean that with fvvarlist? Is there still anything wrong?

 eststo: xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountryno
> rmeqi age i.gender i.maritalstatus ch001_ i.health incomextile i.unemployed i.secondaryeduca
> tion i.tertiaryeducation cf016tot GDP, re vce(cluster mergeid)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -26606.692  
Iteration 2:   log pseudolikelihood = -26172.303  
Iteration 3:   log pseudolikelihood = -26169.621  
Iteration 4:   log pseudolikelihood =  -26169.62  

Fitting full model:

tau =  0.0     log pseudolikelihood =  -26169.62
tau =  0.1     log pseudolikelihood =  -25824.26
tau =  0.2     log pseudolikelihood = -25475.721
tau =  0.3     log pseudolikelihood =  -25129.63
tau =  0.4     log pseudolikelihood = -24794.768
tau =  0.5     log pseudolikelihood = -24485.659
tau =  0.6     log pseudolikelihood = -24228.504
tau =  0.7     log pseudolikelihood = -24076.658
tau =  0.8     log pseudolikelihood = -24159.875

Iteration 0:   log pseudolikelihood = -24076.626  
Iteration 1:   log pseudolikelihood = -22851.827  
Iteration 2:   log pseudolikelihood = -22762.731  
Iteration 3:   log pseudolikelihood = -22757.576  
Iteration 4:   log pseudolikelihood = -22757.576  (backed up)
Iteration 5:   log pseudolikelihood = -22757.146  
Iteration 6:   log pseudolikelihood = -22757.145  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =     61,215
Group variable: mergeidnew                      Number of groups  =     30,286

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.0
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(17)     =    3151.89
Log pseudolikelihood  = -22757.145              Prob > chi2       =     0.0000

                                   (Std. Err. adjusted for 30,286 clusters in mergeid)
--------------------------------------------------------------------------------------
                     |               Robust
                 smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          bfi10_open |  -.0708362    .027664    -2.56   0.010    -.1250567   -.0166157
         bfi10_consc |  -.1498915   .0341088    -4.39   0.000    -.2167435   -.0830395
         bfi10_extra |  -.0649633   .0290136    -2.24   0.025    -.1218289   -.0080977
         bfi10_agree |   .1223087   .0341575     3.58   0.000     .0553613    .1892561
         bfi10_neuro |  -.0247047   .0278416    -0.89   0.375    -.0792733    .0298639
  meancountrynormeqi |   .0893142   .0023895    37.38   0.000     .0846308    .0939976
                 age |   .0255978    .002951     8.67   0.000     .0198139    .0313817
            1.gender |   .7921669   .0576142    13.75   0.000     .6792451    .9050886
     1.maritalstatus |   .5010448     .05925     8.46   0.000      .384917    .6171727
              ch001_ |  -.1561766   .0201011    -7.77   0.000    -.1955741   -.1167792
            1.health |   .7423534    .050929    14.58   0.000     .6425344    .8421725
         incomextile |   .3880567   .0221899    17.49   0.000     .3445652    .4315482
        1.unemployed |   -.423053   .0828855    -5.10   0.000    -.5855057   -.2606003
1.secondaryeducation |   .5111052   .0684194     7.47   0.000     .3770056    .6452048
 1.tertiaryeducation |   1.500836   .0763593    19.65   0.000     1.351174    1.650497
            cf016tot |   .1096531   .0113788     9.64   0.000     .0873511    .1319551
                 GDP |  -.0411016   .0104685    -3.93   0.000    -.0616195   -.0205838
               _cons |  -12.38511   .3822477   -32.40   0.000     -13.1343   -11.63592
---------------------+----------------------------------------------------------------
            /lnsig2u |   2.181268   .0365193                      2.109691    2.252844
---------------------+----------------------------------------------------------------
             sigma_u |    2.97616   .0543436                      2.871532      3.0846
                 rho |   .7291709   .0072118                      .7148064    .7430719
--------------------------------------------------------------------------------------
(est1 stored)

. eststo: xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountryno
> rmeqi c.meancountryeqi#c.bfi10_open age i.gender i.maritalstatus ch001_ i.health incomextile
>  i.unemployed i.secondaryeducation i.tertiaryeducation cf016tot GDP, re vce(cluster mergeid)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -26591.309  
Iteration 2:   log pseudolikelihood = -26139.504  
Iteration 3:   log pseudolikelihood =  -26135.47  
Iteration 4:   log pseudolikelihood = -26135.468  

Fitting full model:

tau =  0.0     log pseudolikelihood = -26135.468
tau =  0.1     log pseudolikelihood = -25790.652
tau =  0.2     log pseudolikelihood =  -25442.68
tau =  0.3     log pseudolikelihood = -25097.162
tau =  0.4     log pseudolikelihood = -24762.823
tau =  0.5     log pseudolikelihood = -24454.084
tau =  0.6     log pseudolikelihood = -24196.997
tau =  0.7     log pseudolikelihood = -24044.722
tau =  0.8     log pseudolikelihood = -24126.819

Iteration 0:   log pseudolikelihood = -24044.693  
Iteration 1:   log pseudolikelihood = -22827.205  
Iteration 2:   log pseudolikelihood = -22737.304  
Iteration 3:   log pseudolikelihood = -22732.222  
Iteration 4:   log pseudolikelihood = -22732.222  (backed up)
Iteration 5:   log pseudolikelihood =  -22731.81  
Iteration 6:   log pseudolikelihood =  -22731.81  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =     61,215
Group variable: mergeidnew                      Number of groups  =     30,286

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.0
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =    3136.87
Log pseudolikelihood  =  -22731.81              Prob > chi2       =     0.0000

                                   (Std. Err. adjusted for 30,286 clusters in mergeid)
--------------------------------------------------------------------------------------
                     |               Robust
                 smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          bfi10_open |   .1020189   .0371511     2.75   0.006     .0292041    .1748337
         bfi10_consc |  -.1543348   .0341384    -4.52   0.000    -.2212449   -.0874248
         bfi10_extra |  -.0662919   .0290251    -2.28   0.022      -.12318   -.0094039
         bfi10_agree |   .1123927    .034126     3.29   0.001      .045507    .1792785
         bfi10_neuro |  -.0185169   .0278194    -0.67   0.506    -.0730419    .0360081
  meancountrynormeqi |   .1335231   .0070848    18.85   0.000     .1196371    .1474092
                     |
    c.meancountryeqi#|
        c.bfi10_open |  -.2752699   .0404522    -6.80   0.000    -.3545546   -.1959851
                     |
                 age |   .0253113    .002952     8.57   0.000     .0195255    .0310971
            1.gender |    .795764    .057634    13.81   0.000     .6828034    .9087246
     1.maritalstatus |   .4998696   .0592283     8.44   0.000     .3837844    .6159549
              ch001_ |  -.1548665    .020114    -7.70   0.000    -.1942892   -.1154438
            1.health |   .7442974   .0509628    14.60   0.000     .6444122    .8441826
         incomextile |   .3870699   .0222078    17.43   0.000     .3435435    .4305964
        1.unemployed |  -.4049214   .0829809    -4.88   0.000     -.567561   -.2422819
1.secondaryeducation |    .486414   .0685167     7.10   0.000     .3521238    .6207042
 1.tertiaryeducation |   1.486696   .0761562    19.52   0.000     1.337432    1.635959
            cf016tot |   .1080253    .011371     9.50   0.000     .0857385    .1303121
                 GDP |  -.0430037    .010446    -4.12   0.000    -.0634774   -.0225299
               _cons |  -15.29172   .5927366   -25.80   0.000    -16.45346   -14.12998
---------------------+----------------------------------------------------------------
            /lnsig2u |   2.180808   .0365854                      2.109102    2.252515
---------------------+----------------------------------------------------------------
             sigma_u |   2.975477   .0544295                      2.870686    3.084092
                 rho |   .7290802   .0072264                      .7146864     .743009
--------------------------------------------------------------------------------------
(est2 stored)

Also, which models do you mean with which one gives the fairest and truest view? Before I test the interaction efffect, I regress my personality traits on smp without the interaction variable meancountrynormeqi. This model is my baseline model, and then I try to interact meancountrynormeqi. Do you think my baseline model is then the one with the fairest view?:

 eststo: xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro age gender ma
> ritalstatus ch001_ health incomextile unemployed secondaryeducation tertiaryeducation cf016t
> ot GDP, re vce(cluster mergeid)

Fitting comparison model:

Iteration 0:   log pseudolikelihood = -31348.683  
Iteration 1:   log pseudolikelihood = -28128.419  
Iteration 2:   log pseudolikelihood = -27914.818  
Iteration 3:   log pseudolikelihood = -27914.221  
Iteration 4:   log pseudolikelihood = -27914.221  

Fitting full model:

tau =  0.0     log pseudolikelihood = -27914.221
tau =  0.1     log pseudolikelihood = -27527.051
tau =  0.2     log pseudolikelihood = -27134.029
tau =  0.3     log pseudolikelihood = -26742.092
tau =  0.4     log pseudolikelihood =  -26360.75
tau =  0.5     log pseudolikelihood = -26004.129
tau =  0.6     log pseudolikelihood = -25696.062
tau =  0.7     log pseudolikelihood = -25483.493
tau =  0.8     log pseudolikelihood = -25479.446

Iteration 0:   log pseudolikelihood = -25483.514  
Iteration 1:   log pseudolikelihood = -24105.494  
Iteration 2:   log pseudolikelihood = -23913.228  
Iteration 3:   log pseudolikelihood =  -23896.97  
Iteration 4:   log pseudolikelihood = -23896.905  
Iteration 5:   log pseudolikelihood = -23896.905  (backed up)
Iteration 6:   log pseudolikelihood = -23896.057  
Iteration 7:   log pseudolikelihood = -23896.057  

Calculating robust standard errors:

Random-effects logistic regression              Number of obs     =     61,215
Group variable: mergeidnew                      Number of groups  =     30,286

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.0
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(16)     =    2701.80
Log pseudolikelihood  = -23896.057              Prob > chi2       =     0.0000

                                 (Std. Err. adjusted for 30,286 clusters in mergeid)
------------------------------------------------------------------------------------
                   |               Robust
               smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------------+----------------------------------------------------------------
        bfi10_open |  -.2476276    .028503    -8.69   0.000    -.3034924   -.1917628
       bfi10_consc |  -.0476146   .0350198    -1.36   0.174    -.1162521    .0210229
       bfi10_extra |   .0967788   .0299448     3.23   0.001      .038088    .1554696
       bfi10_agree |   .3094504    .035304     8.77   0.000     .2402559    .3786449
       bfi10_neuro |  -.1364359   .0287281    -4.75   0.000    -.1927418   -.0801299
               age |   .0313484   .0029949    10.47   0.000     .0254785    .0372184
            gender |   .9076036   .0575142    15.78   0.000     .7948779    1.020329
     maritalstatus |   .4199228   .0593549     7.07   0.000     .3035894    .5362563
            ch001_ |  -.1061121   .0201479    -5.27   0.000    -.1456013   -.0666228
            health |   .8794781   .0509739    17.25   0.000     .7795711     .979385
       incomextile |   .2980869   .0218804    13.62   0.000     .2552021    .3409716
        unemployed |  -.5488034   .0832166    -6.59   0.000     -.711905   -.3857019
secondaryeducation |   1.043227   .0679658    15.35   0.000     .9100161    1.176437
 tertiaryeducation |   2.397791   .0793968    30.20   0.000     2.242177    2.553406
          cf016tot |   .1662276   .0114159    14.56   0.000     .1438528    .1886024
               GDP |  -.0678701    .009567    -7.09   0.000     -.086621   -.0491192
             _cons |  -8.682553   .3539683   -24.53   0.000    -9.376318   -7.988788
-------------------+----------------------------------------------------------------
          /lnsig2u |   2.311664    .037046                      2.239056    2.384273
-------------------+----------------------------------------------------------------
           sigma_u |   3.176666   .0588414                      3.063407    3.294112
               rho |   .7541402   .0068688                      .7404307    .7673532
------------------------------------------------------------------------------------
(est2 stored)

Kind regards,
Sophie

[Carlo Lazzaro]

Sophie:
- your code for interaction code is incomplete,as it shoud have been (see examples under -help fvvarlist-):

c.meancountryeqi##c.bfi10_open

;
- with fairest and truest model I meant what the model that accounts for all predictors considered in the literature of your research field for the topic you're studying;
- while imposing clustered standard errors is manadatory if you go pooled -logit- (as you did in your first example), clustered standard errors in -xtlogit- make sense if you detected/suspected heteroskedasticity and/or autocorrelation in your dataset. Otherwise, you can stay with default standard errors.

[Sophie Jasper]

Thanks a lot, this is probably very basic stuff but helps a lot. The fairest model is:
xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro age i.gender i.maritalstatus ch001_ i.health incomextile i.unemployed i.secondaryeducation i.tertiaryeducation cf016tot GDP, re
or with the interaction variable (that hasnt been done before in this way):
xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro age i.gender i.maritalstatus ch001_ i.health incomextile i.unemployed i.secondaryeducation i.tertiaryeducation cf016tot GDP meancountrynormeqi, re

[Sophie Jasper]

Is there anything else I need to do? In order to have same datasets?

[Carlo Lazzaro]

Sophie:
what do you mean by

In order to have same datasets?

As an aside, I recommend you to discuss with your supervisor any choice related to regression model (that I assume is one of the pivotal parts of your master thesis).

[Marcos Almeida]

Just a side note: using margins followed by marginsplot will give you an insightful display of the influence concerning interaction terms.

[Sophie Jasper]

thanks for all the help. I'd like to ask one more question. This is my stata output:

. eststo: xtlogit smp bfi10_open bfi10_consc bfi10_extra bfi10_agree bfi10_neuro meancountryno
> rmeqi age i.gender i.maritalstatus ch001_ i.health incomextile i.unemployed i.secondaryeduca
> tion i.tertiaryeducation cf016tot GDP, re

Fitting comparison model:

Iteration 0:   log likelihood = -31348.683  
Iteration 1:   log likelihood = -26606.692  
Iteration 2:   log likelihood = -26172.303  
Iteration 3:   log likelihood = -26169.621  
Iteration 4:   log likelihood =  -26169.62  

Fitting full model:

tau =  0.0     log likelihood =  -26169.62
tau =  0.1     log likelihood =  -25824.26
tau =  0.2     log likelihood = -25475.721
tau =  0.3     log likelihood =  -25129.63
tau =  0.4     log likelihood = -24794.768
tau =  0.5     log likelihood = -24485.659
tau =  0.6     log likelihood = -24228.504
tau =  0.7     log likelihood = -24076.658
tau =  0.8     log likelihood = -24159.875

Iteration 0:   log likelihood = -24076.626  
Iteration 1:   log likelihood = -22851.827  
Iteration 2:   log likelihood = -22762.731  
Iteration 3:   log likelihood = -22757.576  
Iteration 4:   log likelihood = -22757.576  (backed up)
Iteration 5:   log likelihood = -22757.146  
Iteration 6:   log likelihood = -22757.145  

Random-effects logistic regression              Number of obs     =     61,215
Group variable: mergeidnew                      Number of groups  =     30,286

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.0
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(17)     =    3207.56
Log likelihood  = -22757.145                    Prob > chi2       =     0.0000

--------------------------------------------------------------------------------------
                 smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
          bfi10_open |  -.0708362   .0279704    -2.53   0.011    -.1256573   -.0160151
         bfi10_consc |  -.1498915   .0345134    -4.34   0.000    -.2175366   -.0822465
         bfi10_extra |  -.0649633   .0296218    -2.19   0.028    -.1230209   -.0069057
         bfi10_agree |   .1223087   .0343919     3.56   0.000     .0549018    .1897156
         bfi10_neuro |  -.0247047     .02828    -0.87   0.382    -.0801324    .0307231
  meancountrynormeqi |   .0893142   .0022403    39.87   0.000     .0849233    .0937051
                 age |   .0255978   .0030169     8.48   0.000     .0196849    .0315108
            1.gender |   .7921669   .0577119    13.73   0.000     .6790537      .90528
     1.maritalstatus |   .5010448    .059325     8.45   0.000     .3847699    .6173198
              ch001_ |  -.1561766   .0206171    -7.58   0.000    -.1965853   -.1157679
            1.health |   .7423534   .0504947    14.70   0.000     .6433856    .8413213
         incomextile |   .3880567   .0222795    17.42   0.000     .3443897    .4317237
        1.unemployed |   -.423053   .0814924    -5.19   0.000    -.5827752   -.2633308
1.secondaryeducation |   .5111052   .0682887     7.48   0.000     .3772618    .6449487
 1.tertiaryeducation |   1.500836   .0759614    19.76   0.000     1.351954    1.649717
            cf016tot |   .1096531   .0114142     9.61   0.000     .0872816    .1320246
                 GDP |  -.0411016   .0104534    -3.93   0.000    -.0615899   -.0206134
               _cons |  -12.38511   .3818587   -32.43   0.000    -13.13354   -11.63668
---------------------+----------------------------------------------------------------
            /lnsig2u |   2.181268   .0352956                      2.112089    2.250446
---------------------+----------------------------------------------------------------
             sigma_u |    2.97616   .0525227                      2.874977    3.080903
                 rho |   .7291709   .0069702                      .7152951    .7426138
--------------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 6824.95                Prob >= chibar2 = 0.000
(est1 stored)

.
. eststo: xtlogit smp bfi10_open bfi10_consc bfi10_agree bfi10_neuro c.meancountrynormeqi##c.b
> fi10_extra age i.gender i.maritalstatus ch001_ i.health incomextile i.unemployed i.secondary
> education i.tertiaryeducation cf016tot GDP, re

Fitting comparison model:

Iteration 0:   log likelihood = -31348.683  
Iteration 1:   log likelihood = -26587.059  
Iteration 2:   log likelihood = -26148.257  
Iteration 3:   log likelihood = -26145.465  
Iteration 4:   log likelihood = -26145.464  

Fitting full model:

tau =  0.0     log likelihood = -26145.464
tau =  0.1     log likelihood = -25800.877
tau =  0.2     log likelihood =  -25453.19
tau =  0.3     log likelihood = -25108.059
tau =  0.4     log likelihood = -24774.289
tau =  0.5     log likelihood = -24466.424
tau =  0.6     log likelihood = -24210.678
tau =  0.7     log likelihood = -24060.411
tau =  0.8     log likelihood = -24145.432

Iteration 0:   log likelihood = -24060.395  
Iteration 1:   log likelihood = -22835.042  
Iteration 2:   log likelihood = -22748.502  
Iteration 3:   log likelihood = -22743.408  
Iteration 4:   log likelihood = -22743.408  (backed up)
Iteration 5:   log likelihood =  -22742.99  
Iteration 6:   log likelihood =  -22742.99  

Random-effects logistic regression              Number of obs     =     61,215
Group variable: mergeidnew                      Number of groups  =     30,286

Random effects u_i ~ Gaussian                   Obs per group:
                                                              min =          1
                                                              avg =        2.0
                                                              max =          4

Integration method: mvaghermite                 Integration pts.  =         12

                                                Wald chi2(18)     =    3214.16
Log likelihood  =  -22742.99                    Prob > chi2       =     0.0000

---------------------------------------------------------------------------------------
                  smp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------+----------------------------------------------------------------
           bfi10_open |  -.0654562   .0279893    -2.34   0.019    -.1203143   -.0105981
          bfi10_consc |  -.1466294   .0344997    -4.25   0.000    -.2142475   -.0790112
          bfi10_agree |   .1149852   .0343945     3.34   0.001     .0475733    .1823972
          bfi10_neuro |  -.0179483   .0283008    -0.63   0.526    -.0734169    .0375203
   meancountrynormeqi |   .0531095   .0070284     7.56   0.000     .0393341    .0668849
          bfi10_extra |  -.7557818   .1326727    -5.70   0.000    -1.015815   -.4957481
                      |
 c.meancountrynormeqi#|
        c.bfi10_extra |   .0103843    .001943     5.34   0.000     .0065761    .0141926
                      |
                  age |   .0256358    .003016     8.50   0.000     .0197245    .0315471
             1.gender |   .7941819     .05769    13.77   0.000     .6811115    .9072523
      1.maritalstatus |   .4976177   .0593004     8.39   0.000     .3813912    .6138443
               ch001_ |  -.1564929   .0206128    -7.59   0.000    -.1968932   -.1160926
             1.health |   .7386956   .0504871    14.63   0.000     .6397428    .8376484
          incomextile |     .38772    .022277    17.40   0.000     .3440579    .4313822
         1.unemployed |  -.4170344   .0814684    -5.12   0.000    -.5767096   -.2573592
 1.secondaryeducation |   .5075014     .06827     7.43   0.000     .3736945    .6413082
  1.tertiaryeducation |    1.49563   .0759425    19.69   0.000     1.346785    1.644474
             cf016tot |    .110062   .0114133     9.64   0.000     .0876923    .1324316
                  GDP |  -.0394278   .0104552    -3.77   0.000    -.0599197   -.0189359
                _cons |  -10.01745   .5752783   -17.41   0.000    -11.14497   -8.889921
----------------------+----------------------------------------------------------------
             /lnsig2u |   2.178962   .0353249                      2.109727    2.248198
----------------------+----------------------------------------------------------------
              sigma_u |   2.972731   .0525057                      2.871583    3.077442
                  rho |   .7287154   .0069834                      .7148137    .7421839
---------------------------------------------------------------------------------------
LR test of rho=0: chibar2(01) = 6804.95                Prob >= chibar2 = 0.000
(est2 stored)

Can someone help me interpreting the interaction term? And as an additional question: can and when yes how do I interpret the interaction term when the independent variable is not significant? For example, if bfi10_erxtra is not significant in model 2.

Thank you a lot and kind regards,
Sophie