Cross-level interactions vs. separated regressions for categories of the interaction variable in multilevel models

[Ariane Arbol]

Dear all,

I want to investigate which child in a sibling group takes over the care of a parent. The focus is on gender (of both the caregiving child and the siblings), but other characteristics of the children and siblings (e.g., education, employment status, own children, spatial proximity to the parent) will also be examined as influencing factors.

To do so, I use a multilevel design that first includes characteristics of the child (individual level), then characteristics of sliblings and the parent (contextual level), and finally cross-level interactions between child gender and sibling characteristics. Sibling characteristics are summary variables of the children in a family group, for example the number of full-time employed sons or the average age of all daughters in a family. The main interest in these cross-level interactions is to determine whether characteristics of male and female siblings affect a male child differently than a female child in the likelihood of assuming parental care.

However, the number of cross-level interactions is high due to a large number of variables. Therefore, I wondered if I could, in principle, compute two separate multi-level models for male children and for female children so that – as in ordinary regression models – the interaction terms are inherent. To test for significant differences between male and female children, I would compute the individual interaction terms in the overall multilevel model.

Does anyone know if that would be a correct approach? Please let me know if you need any additional information.

Thanks for any advice!

[Tom Scott]

Ariane Arbol is your outcome a binary yes/no indicator? If so, the interaction you describe would be making a strong assumption that the disturbance variance is equal across groups. A better approach is either to use a heterogeneous choice model - https://www3.nd.edu/~rwilliam/oglm/RW_Hetero_Choice.pdf - or just run an ols regression and ignore the categorical nature of the dependent variable. I'd probably do a regular logit and then an ols and compare results. Additionally, I'm not sure about the multilevel structure. Isn't your unit of observation families (1 level) and your predicting the gender of the child who cares for the parent(s) using characteristics of the parents and children. I don't see the need for multi-level modeling.

[Chul Lee]

- Having enough family sample for multilevel analysis varies with countries, but you won't have enough variance if most families in your sample have just single child or two.
- I don't know if you can conduct model fit comparison if you run separate regression for each category. Maybe other Stata users have other brilliant ideas.
C

[Ariane Arbol]

Tom Scott: Thanks for your answer. My outcome variable is the assumed care time of a child (days per year). I use a multilevel design because the individual level outcome variable should be influenced through individual level independent variables (like gender, employment status, own children, living distance from parents, ...) and through contextual level independent variables (like number of siblings, gender distribution of siblings, number of siblings with own children, number of sibling working full time, as well as parent's characteristics, like age, health status, partnership status). Children are embedded in their family context, so I have two levels in my data structure. The siblings' and parent characteristics are the same for all children of one family and the observations are not independent. Wouldn't you agree with that?

@Chul Lee: Thank you for your answer. I am not sure if I understand your point. Could you clarify what 'not enough variance' refers to? I do have 609 families with 1591 children, in a range of 2 to 7 children per family. How do I know if the variance is enough and how can I test it?

To give an example of my thoughts: Here are three outputs of two separate multilevel regressions for sons and for daughters, as well as one overall multilevel regression with an interaction term of child gender and number of sons in a family.

* Sons
. xtmixed ch_helpfreq_abs i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn ///
> c.nr_sons c.nr_daught c.sons_full_empl c.sons_part_empl c.sons_partnered c.sons_meanchild c.sons_coresiding c.sons_faraway c.sons_high_educ c.sons_childpar c.sons_parchild c.sons_meanage c
> .daught_full_empl c.daught_part_empl c.daught_partnered c.daught_meanchild c.daught_coresiding c.daught_faraway c.daught_high_educ c.daught_childpar c.daught_parchild c.daught_meanage ///
> c.r_age_z i.r_female i.r_partner i.r_educhigh c.lnr_hhincome_z c.health_lim ///
> || mergeid: if sample_mixedsibship==1 & ch_female==0, variance

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -3711.0844  
Iteration 1:   log likelihood = -3708.2362  
Iteration 2:   log likelihood = -3708.2344  
Iteration 3:   log likelihood = -3708.2344  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =        799
Group variable: mergeid                         Number of groups  =        609

                                                Obs per group:
                                                              min =          1
                                                              avg =        1.3
                                                              max =          6

                                                Wald chi2(39)     =     114.47
Log likelihood = -3708.2344                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------------------
            ch_helpfreq_abs |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
              ch_employment |
        Employed part-time  |   .5489631   11.98787     0.05   0.963    -22.94683    24.04476
        Employed full-time  |   1.756799   5.868016     0.30   0.765      -9.7443     13.2579
                            |
                 ch_partner |
                    1. Yes  |  -3.876005   3.567192    -1.09   0.277    -10.86757    3.115563
                ch_nrkids_z |   .1141348    1.66041     0.07   0.945    -3.140209    3.368479
                            |
               ch_proximity |
    Lives up to 25 km away  |  -9.453456   4.247911    -2.23   0.026    -17.77921   -1.127703
Lives more than 25 km away  |   -11.1737   4.615284    -2.42   0.015    -20.21949   -2.127911
                            |
                ch_educhigh |
                    1. Yes  |   4.652283   3.420037     1.36   0.174    -2.050866    11.35543
                            |
          transfer_childpar |
                    1. Yes  |  -23.36851   18.09118    -1.29   0.196    -58.82657    12.08955
                            |
          transfer_parchild |
                    1. Yes  |   .4003016   5.103077     0.08   0.937    -9.601546    10.40215
                   ch_age_z |  -.6592975   .4291033    -1.54   0.124    -1.500324    .1817295
                            |
           ch_birthorder_yn |
                    1. Yes  |   1.751877   2.636668     0.66   0.506    -3.415897    6.919651
                    nr_sons |   .6419312   4.290005     0.15   0.881    -7.766324    9.050187
                  nr_daught |  -2.316011   2.964579    -0.78   0.435     -8.12648    3.494457
             sons_full_empl |  -.2396201   4.493694    -0.05   0.957    -9.047098    8.567858
             sons_part_empl |  -.5064474    9.71377    -0.05   0.958    -19.54509    18.53219
             sons_partnered |   .6098164    2.85247     0.21   0.831    -4.980923    6.200555
             sons_meanchild |    .233119    2.02072     0.12   0.908     -3.72742    4.193658
            sons_coresiding |  -1.064481   3.733486    -0.29   0.776    -8.381979    6.253017
               sons_faraway |  -.7549092   2.748253    -0.27   0.784    -6.141386    4.631567
             sons_high_educ |  -2.429927   2.595968    -0.94   0.349     -7.51793    2.658077
              sons_childpar |   18.02706   14.56055     1.24   0.216    -10.51109    46.56521
              sons_parchild |    5.52628   3.905462     1.42   0.157    -2.128285    13.18085
               sons_meanage |   .4314304   .4433583     0.97   0.331    -.4375358    1.300397
           daught_full_empl |   -4.02886     2.3215    -1.74   0.083    -8.578916    .5211961
           daught_part_empl |   -3.07471   2.540523    -1.21   0.226    -8.054043    1.904622
           daught_partnered |   1.527811   2.104015     0.73   0.468    -2.595982    5.651603
           daught_meanchild |  -1.599646   1.050122    -1.52   0.128    -3.657847    .4585551
          daught_coresiding |   2.673473   2.640359     1.01   0.311    -2.501536    7.848481
             daught_faraway |   4.609003    1.87217     2.46   0.014     .9396177    8.278389
           daught_high_educ |   -.234712   1.955954    -0.12   0.904    -4.068312    3.598888
            daught_childpar |  -2.559349   5.613913    -0.46   0.648    -13.56242    8.443719
            daught_parchild |  -1.335094   2.477008    -0.54   0.590     -6.18994    3.519751
             daught_meanage |   .4638818   .2646995     1.75   0.080    -.0549196    .9826833
                    r_age_z |  -.1544422   .2490918    -0.62   0.535    -.6426531    .3337687
                            |
                   r_female |
                    1. Yes  |   2.211483   2.108618     1.05   0.294    -1.921332    6.344298
                            |
                  r_partner |
                    1. Yes  |  -9.354533   3.482064    -2.69   0.007    -16.17925   -2.529812
                            |
                 r_educhigh |
                    1. Yes  |     .44917   2.437347     0.18   0.854    -4.327943    5.226283
             lnr_hhincome_z |  -.7454403   1.297822    -0.57   0.566    -3.289124    1.798243
                 health_lim |   3.605425   .5838095     6.18   0.000     2.461179     4.74967
                      _cons |  -16.46323   22.04401    -0.75   0.455    -59.66869    26.74223
---------------------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Identity            |
                  var(_cons) |   130.6422   96.72011      30.61272    557.5259
-----------------------------+------------------------------------------------
               var(Residual) |    506.107   89.18836      358.2943    714.8991
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 1.07          Prob >= chibar2 = 0.1502

.

* Daughters
. xtmixed ch_helpfreq_abs i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn ///
> c.nr_sons c.nr_daught c.sons_full_empl c.sons_part_empl c.sons_partnered c.sons_meanchild c.sons_coresiding c.sons_faraway c.sons_high_educ c.sons_childpar c.sons_parchild c.sons_meanage c
> .daught_full_empl c.daught_part_empl c.daught_partnered c.daught_meanchild c.daught_coresiding c.daught_faraway c.daught_high_educ c.daught_childpar c.daught_parchild c.daught_meanage ///
> c.r_age_z i.r_female i.r_partner i.r_educhigh c.lnr_hhincome_z c.health_lim ///
> || mergeid: if sample_mixedsibship==1 & ch_female==1, variance

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -3427.2999  
Iteration 1:   log likelihood = -3427.2903  
Iteration 2:   log likelihood = -3427.2903  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =        792
Group variable: mergeid                         Number of groups  =        609

                                                Obs per group:
                                                              min =          1
                                                              avg =        1.3
                                                              max =          4

                                                Wald chi2(39)     =     228.66
Log likelihood = -3427.2903                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------------------
            ch_helpfreq_abs |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
              ch_employment |
        Employed part-time  |  -1.722927   1.543242    -1.12   0.264    -4.747625    1.301771
        Employed full-time  |   .4696474   1.455368     0.32   0.747    -2.382821    3.322116
                            |
                 ch_partner |
                    1. Yes  |  -.9137302   1.221263    -0.75   0.454    -3.307362    1.479902
                ch_nrkids_z |   .6520454   .5672334     1.15   0.250    -.4597116    1.763802
                            |
               ch_proximity |
    Lives up to 25 km away  |  -.9600517   1.769835    -0.54   0.588    -4.428865    2.508762
Lives more than 25 km away  |  -1.563277   1.787123    -0.87   0.382    -5.065974    1.939419
                            |
                ch_educhigh |
                    1. Yes  |   1.404965   1.406267     1.00   0.318    -1.351268    4.161199
                            |
          transfer_childpar |
                    1. Yes  |   6.493479   5.131161     1.27   0.206    -3.563412    16.55037
                            |
          transfer_parchild |
                    1. Yes  |   1.636101     2.1602     0.76   0.449    -2.597814    5.870015
                   ch_age_z |    .117499   .1494363     0.79   0.432    -.1753907    .4103887
                            |
           ch_birthorder_yn |
                    1. Yes  |  -.6483175   1.130356    -0.57   0.566    -2.863774    1.567139
                    nr_sons |  -6.812667   3.223967    -2.11   0.035    -13.13153    -.493808
                  nr_daught |  -4.003401   3.018056    -1.33   0.185    -9.918683    1.911881
             sons_full_empl |    7.31318   3.014793     2.43   0.015     1.404295    13.22206
             sons_part_empl |   8.184234     8.3436     0.98   0.327    -8.168922    24.53739
             sons_partnered |  -1.286269   2.004177    -0.64   0.521    -5.214385    2.641847
             sons_meanchild |  -.2147797   1.118916    -0.19   0.848    -2.407815    1.978255
            sons_coresiding |  -4.929798   2.322037    -2.12   0.034    -9.480907   -.3786893
               sons_faraway |   .4348931   1.852258     0.23   0.814    -3.195466    4.065253
             sons_high_educ |   -.548376   1.682958    -0.33   0.745    -3.846913    2.750161
              sons_childpar |  -7.459564   7.369675    -1.01   0.311    -21.90386    6.984735
              sons_parchild |   .9031966   2.373935     0.38   0.704    -3.749631    5.556024
               sons_meanage |   .2853769   .2320614     1.23   0.219    -.1694551    .7402089
           daught_full_empl |   1.162879   2.463491     0.47   0.637    -3.665474    5.991233
           daught_part_empl |   2.173264   2.708068     0.80   0.422    -3.134452    7.480981
           daught_partnered |   .5012798   2.182889     0.23   0.818    -3.777104    4.779664
           daught_meanchild |   .5955683   1.204435     0.49   0.621     -1.76508    2.956217
          daught_coresiding |  -.5124663   2.885343    -0.18   0.859    -6.167635    5.142702
             daught_faraway |  -2.442489   1.995566    -1.22   0.221    -6.353726    1.468749
           daught_high_educ |   2.257181   2.106352     1.07   0.284    -1.871194    6.385556
            daught_childpar |   7.509555    6.29148     1.19   0.233    -4.821518    19.84063
            daught_parchild |  -4.077573   2.751644    -1.48   0.138    -9.470697     1.31555
             daught_meanage |  -.2920354   .2545915    -1.15   0.251    -.7910255    .2069547
                    r_age_z |  -.1108056   .2389284    -0.46   0.643    -.5790966    .3574854
                            |
                   r_female |
                    1. Yes  |  -1.548192   2.030893    -0.76   0.446    -5.528669    2.432285
                            |
                  r_partner |
                    1. Yes  |  -8.490553   3.308587    -2.57   0.010    -14.97526   -2.005842
                            |
                 r_educhigh |
                    1. Yes  |  -4.530716   2.310562    -1.96   0.050    -9.059335   -.0020967
             lnr_hhincome_z |   .6039895   1.219018     0.50   0.620    -1.785242    2.993221
                 health_lim |   6.776502   .5453421    12.43   0.000     5.707651    7.845353
                      _cons |   17.41661   13.32258     1.31   0.191    -8.695157    43.52838
---------------------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Identity            |
                  var(_cons) |   468.9256   29.82182      413.9719    531.1742
-----------------------------+------------------------------------------------
               var(Residual) |   44.62217   4.825609      36.09928    55.15728
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 201.27        Prob >= chibar2 = 0.0000

.

* Overall with interaction term (child gender and nr sons)
. xtmixed ch_helpfreq_abs i.ch_female i.ch_employment i.ch_partner c.ch_nrkids_z i.ch_proximity i.ch_educhigh i.transfer_childpar i.transfer_parchild c.ch_age_z i.ch_birthorder_yn ///
> c.nr_sons c.nr_daught c.sons_full_empl c.sons_part_empl c.sons_partnered c.sons_meanchild c.sons_coresiding c.sons_faraway c.sons_high_educ c.sons_childpar c.sons_parchild c.sons_meanage c
> .daught_full_empl c.daught_part_empl c.daught_partnered c.daught_meanchild c.daught_coresiding c.daught_faraway c.daught_high_educ c.daught_childpar c.daught_parchild c.daught_meanage ///
> c.r_age_z i.r_female i.r_partner i.r_educhigh c.lnr_hhincome_z c.health_lim ///
> i.ch_female#c.nr_sons || mergeid: if sample_mixedsibship==1, variance

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0:   log likelihood = -7280.6901  
Iteration 1:   log likelihood = -7275.1488  
Iteration 2:   log likelihood = -7275.1292  
Iteration 3:   log likelihood =  -7275.129  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =      1,591
Group variable: mergeid                         Number of groups  =        609

                                                Obs per group:
                                                              min =          2
                                                              avg =        2.6
                                                              max =          7

                                                Wald chi2(41)     =     265.55
Log likelihood =  -7275.129                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------------------
            ch_helpfreq_abs |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------------------+----------------------------------------------------------------
                  ch_female |
                    1. Yes  |   .4456478   2.729715     0.16   0.870    -4.904495     5.79579
                            |
              ch_employment |
        Employed part-time  |   1.779429   2.932267     0.61   0.544    -3.967709    7.526568
        Employed full-time  |    1.70041   2.384047     0.71   0.476    -2.972235    6.373056
                            |
                 ch_partner |
                    1. Yes  |  -2.783383   1.888667    -1.47   0.141    -6.485102    .9183352
                ch_nrkids_z |    .697908   .7897099     0.88   0.377    -.8498949    2.245711
                            |
               ch_proximity |
    Lives up to 25 km away  |  -5.744683    2.23833    -2.57   0.010    -10.13173   -1.357638
Lives more than 25 km away  |  -10.12009    2.36278    -4.28   0.000    -14.75105   -5.489125
                            |
                ch_educhigh |
                    1. Yes  |   3.571078   1.851024     1.93   0.054    -.0568621    7.199019
                            |
          transfer_childpar |
                    1. Yes  |   16.66503   7.734952     2.15   0.031       1.5048    31.82526
                            |
          transfer_parchild |
                    1. Yes  |   2.633463   2.842403     0.93   0.354    -2.937545    8.204472
                   ch_age_z |  -.3102439   .2394077    -1.30   0.195    -.7794744    .1589866
                            |
           ch_birthorder_yn |
                    1. Yes  |   .1799993   1.704474     0.11   0.916    -3.160708    3.520707
                    nr_sons |  -1.643202    2.09047    -0.79   0.432    -5.740447    2.454043
                  nr_daught |  -2.067585    1.84727    -1.12   0.263    -5.688167    1.552997
             sons_full_empl |   2.083718   1.963467     1.06   0.289    -1.764607    5.932043
             sons_part_empl |   2.599969   4.846406     0.54   0.592    -6.898812    12.09875
             sons_partnered |  -.6474233   1.353386    -0.48   0.632    -3.300011    2.005164
             sons_meanchild |  -.1732477   .8352078    -0.21   0.836    -1.810225     1.46373
            sons_coresiding |  -1.127838   1.658009    -0.68   0.496    -4.377475    2.121799
               sons_faraway |    .493056   1.271964     0.39   0.698    -1.999947    2.986059
             sons_high_educ |  -1.141908   1.168638    -0.98   0.329    -3.432397    1.148581
              sons_childpar |  -7.985267    5.82435    -1.37   0.170    -19.40078     3.43025
              sons_parchild |   2.792214   1.791187     1.56   0.119    -.7184483    6.302877
               sons_meanage |   .2314017   .1861733     1.24   0.214    -.1334911    .5962946
           daught_full_empl |  -2.085539   1.589753    -1.31   0.190    -5.201398     1.03032
           daught_part_empl |  -1.787709   1.843065    -0.97   0.332    -5.400049    1.824631
           daught_partnered |    1.49249   1.360794     1.10   0.273    -1.174618    4.159597
           daught_meanchild |  -.5941372   .7545873    -0.79   0.431    -2.073101    .8848268
          daught_coresiding |  -.9774032   1.804738    -0.54   0.588    -4.514624    2.559818
             daught_faraway |   2.566796   1.251134     2.05   0.040     .1146183    5.018974
           daught_high_educ |  -.0576057   1.311944    -0.04   0.965    -2.628969    2.513758
            daught_childpar |  -4.067066   4.188369    -0.97   0.332    -12.27612    4.141986
            daught_parchild |  -3.057637   1.800832    -1.70   0.090    -6.587203      .47193
             daught_meanage |   .2341431   .1816325     1.29   0.197      -.12185    .5901362
                    r_age_z |  -.1035545   .1547118    -0.67   0.503    -.4067841     .199675
                            |
                   r_female |
                    1. Yes  |   .6371567   1.317004     0.48   0.629    -1.944124    3.218437
                            |
                  r_partner |
                    1. Yes  |  -8.101922   2.161736    -3.75   0.000    -12.33885   -3.864998
                            |
                 r_educhigh |
                    1. Yes  |  -1.759459   1.518839    -1.16   0.247     -4.73633    1.217411
             lnr_hhincome_z |   -.062671   .7963344    -0.08   0.937    -1.623458    1.498116
                 health_lim |   4.455586   .3587546    12.42   0.000      3.75244    5.158732
                            |
        ch_female#c.nr_sons |
                    1. Yes  |  -.3274566   1.677669    -0.20   0.845    -3.615627    2.960713
                            |
                      _cons |  -1.264141   12.96579    -0.10   0.922    -26.67662    24.14834
---------------------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
mergeid: Identity            |
                  var(_cons) |   1.39e-06   .0004813      3.7e-302    5.2e+289
-----------------------------+------------------------------------------------
               var(Residual) |   548.6588   19.51277       511.717    588.2676
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 0.00          Prob >= chibar2 = 1.0000

.

As one can see, the interaction term in the overall model is not significant, but the number of sons do have a significant effect on the care time of daughters. Would it be correct to interpret that the number of sons in a family do influence the care time of daughters negatively, but that there is no significant difference in this effect between sons and daughters?

Thanks for any further advice!

[Chul Lee]

ariane,
regarding variance decomposition ... you probably already know that null model of multilevel analysis produces two different variances if you have 2-level (individual and family) and you can calculate ICC. I will check my data set if I get low ICC.
question: in each model, gender, partner, and education are dummy variable, but employment is not. any reason?
C

[Tom Scott]

Tom Scott: Thanks for your answer. My outcome variable is the assumed care time of a child (days per year). I use a multilevel design because the individual level outcome variable should be influenced through individual level independent variables (like gender, employment status, own children, living distance from parents, ...) and through contextual level independent variables (like number of siblings, gender distribution of siblings, number of siblings with own children, number of sibling working full time, as well as parent's characteristics, like age, health status, partnership status). Children are embedded in their family context, so I have two levels in my data structure. The siblings' and parent characteristics are the same for all children of one family and the observations are not independent. Wouldn't you agree with that?

Ariane Arbol - yes, I would, assuming you have data from more than one child per family. I misunderstood your data. Out of curiosity, have you also tried treating number of kids as 5 dummy variables (3-7)?

Regarding your original question, I'm not very knowledgeable about comparing coefficients across models so hopefully you receive help from someone else

[Ariane Arbol]

@Chul Lee: The ICC of the null model is almost 9 percent and the additional LR test (comparing an empty ordinary regression model to the multilevel null model) is also significant, both suggesting that a multilevel design fits the data better. Don't you agree?

question: in each model, gender, partner, and education are dummy variable, but employment is not. any reason?

Gender (male/female) and partner (yes/no) are naturally dummy variables because there are only two categories, right? Education is only binary (high/low) because there is no further interest in more detailed categories (theoretically), while the distinction between part-time and full-time employment is interesting because of the inherent time constraints that can affect care time provided. Do you see a problem with this?

Tom Scott: I do have more than one child per family, in fact, I do have all children per family and use only mixed-gender sibships in the analysis (so there are at least two children per family).

Out of curiosity, have you also tried treating number of kids as 5 dummy variables (3-7)?

I did not and I don't think I get your idea. Which categories do you have in mind and why would that be helpful?

Thanks for your thoughts! Any further hints are appreciated!

[Tom Scott]

I did not and I don't think I get your idea. Which categories do you have in mind and why would that be helpful?

When number of kids/number of sons/number of daughters is treated as a continuous measure, you are estimating a linear effect, but the effect(s) might not be linear. Treating them as separate dummy variables will capture any nonlinear effects (e.g., threshold effects). See https://www.rhayden.us/regression-mo...variables.html for example

[Chul Lee]

Ariane,
I can't say what the cutoff point of ICC should be. It is depending on the contexts and disciplines, but I learned that 10% or higher is enough for multilevel analysis.
I saw you have 'full' and 'part-time' employment in models, so I just assumed that you have an additional category such as 'no employment.
C'

[Ariane Arbol]

Tom Scott Ah, thank you for the hint and the link!

Chul Lee At what value of ICC a multilevel analysis is appropriate is considered differently in research. For example, Hox (2010)* gives reference values between 0.05 and 0.3 for this; Nezlek (2008)** advocates a multilevel analysis independent of the ICC as soon as the data structure suggests such an analysis (and shows an example of six groups in which half of them show a positive or a negative within correlation and the intraclass correlation is 0 - if the groups were not taken into account in the modeling, a correlation of 0 would result, which would obviously not be an appropriate estimate).

I saw you have 'full' and 'part-time' employment in models, so I just assumed that you have an additional category such as 'no employment.

'no employment' is the reference category of both dummy variables.


Any further advice to my original question is still welcome!


* Hox, Joop J. (2010) Multilevel analysis: techniques and applications. New York: Routledge.
** Nezlek, John B. (2008) An Introduction to Multilevel Modeling for Social and Personality Psychology. Social and Personality Psychology Compass 2/2, 842-860.