Hi everyone.

I have two questions, which I would be very thankful if you could help med with. I have limited experience with panel data.

I am trying to analyze how loneliness is affecting political trust (simplified). My main variables are drawn from Likert scales, and I am using panel data with a set of controls. The panel data consists of 3 panels with a total of around 12 000 respondents (distributed differently depending on used IV).
I have done a Hausman test, which indicated an RE-model to be favorable.
I have also done a tsset that indicated that my data is "strongly balanced". Although I still have some missing data for some respondents.

Issue 1: Very low R-squared.

Why is my R-squared so low? Is it low because I have done something wrong, or is it low simply because my model doesn't explain that many variations? (The thing is, when using regular OLS the R-squared is around 0.40, although drawn from another dataset.)

I hope the table below is fairly readable. For some reason I couldn't paste the layout shown in Stata.

xtreg state_trust subj_lonli i.gender i.age i.edu i.employment i.pol_pos log_org, robust

Random-effects GLS regression
Group variable: idpers

Number of obs = 6,388
Number of groups = 3,948

R-sq:
within = 0.0184
between = 0.0520
overall = 0.0555

Obs per group:
min = 1
avg = 1.6
max = 3

.
corr(u_i, X) = 0 (assumed)

Prob > chi2 = .
Wald chi2(99) =

(Std. Err. adjusted for 3,948 clusters in idpers)
------------------------------------------------------------------------------
state_trust | Coef. | Std. Err (robust). | z | P>|z| | [95% Conf. Interval]
-------------+----------------------------------------------------------------
subj_lonli | -.044875 |.0118406 -3.79 | 0.000 | -.0680822 | -.0216677

2.gender | -.0299601 .0690845 -0.43 0.665 -.1653633 .105443


age |
15 | -.0242228 .4280639 -0.06 0.955 -.8632127 .8147671
16 | -.2432496 .3877489 -0.63 0.530 -1.003223 .5167242
17 | -.3892199 .4286725 -0.91 0.364 -1.229403 .4509628
18 | -.4196856 .4319819 -0.97 0.331 -1.266355 .4269833
19 | -.7100844 .4445975 -1.60 0.110 -1.58148 .1613107
20 | -.9919223 .4505656 -2.20 0.028 -1.875015 -.1088299
21 | -.9234081 .462765 -2.00 0.046 -1.830411 -.0164054
22 | -1.126776 .4601459 -2.45 0.014 -2.028646 -.2249067
23 | -1.225502 .4786806 -2.56 0.010 -2.163699 -.2873056
24 | -1.014845 .4787934 -2.12 0.034 -1.953263 -.0764273
25 | -.6578916 .4919066 -1.34 0.181 -1.622011 .3062276
26 | -.6735368 .5457528 -1.23 0.217 -1.743193 .3961191
27 | -.9135611 .5148083 -1.77 0.076 -1.922567 .0954446
28 | -.8806842 .4818212 -1.83 0.068 -1.825036 .063668
29 | -1.440289 .4917325 -2.93 0.003 -2.404067 -.4765108
30 | -1.279424 .5016661 -2.55 0.011 -2.262671 -.296176
31 | -1.243147 .4835396 -2.57 0.010 -2.190867 -.2954264
32 | -1.244969 .4722995 -2.64 0.008 -2.170658 -.3192786
33 | -1.391668 .4706714 -2.96 0.003 -2.314167 -.4691686
34 | -1.40175 .4667951 -3.00 0.003 -2.316652 -.4868485
35 | -1.222395 .4689766 -2.61 0.009 -2.141573 -.303218
36 | -1.209475 .457466 -2.64 0.008 -2.106092 -.3128578
37 | -.9726333 .4583795 -2.12 0.034 -1.871041 -.074226
38 | -1.084053 .4624226 -2.34 0.019 -1.990384 -.1777212
39 | -1.490873 .4564992 -3.27 0.001 -2.385595 -.5961511
40 | -1.20474 .4562663 -2.64 0.008 -2.099005 -.3104745
41 | -1.465782 .4610184 -3.18 0.001 -2.369361 -.5622025
42 | -1.181186 .4605393 -2.56 0.010 -2.083826 -.278545
43 | -1.147428 .4589952 -2.50 0.012 -2.047042 -.2478139
44 | -.9302757 .471138 -1.97 0.048 -1.853689 -.0068621
45 | -.9146044 .4630601 -1.98 0.048 -1.822185 -.0070233
46 | -1.046955 .4640126 -2.26 0.024 -1.956403 -.1375074
47 | -1.194849 .4693776 -2.55 0.011 -2.114813 -.2748862
48 | -1.458196 .4637315 -3.14 0.002 -2.367093 -.5492989
49 | -1.531758 .4588825 -3.34 0.001 -2.431151 -.6323648
50 | -1.212892 .4702986 -2.58 0.010 -2.13466 -.2911234
51 | -1.114101 .4551873 -2.45 0.014 -2.006252 -.2219502
52 | -1.201248 .4562561 -2.63 0.008 -2.095493 -.3070023
53 | -.8778564 .4590725 -1.91 0.056 -1.777622 .0219091
54 | -1.329905 .4682386 -2.84 0.005 -2.247636 -.4121743
55 | -1.353538 .4730581 -2.86 0.004 -2.280715 -.4263611
56 | -1.194882 .4638121 -2.58 0.010 -2.103937 -.285827
57 | -1.307294 .4688561 -2.79 0.005 -2.226235 -.3883531
58 | -1.186869 .4610377 -2.57 0.010 -2.090487 -.2832523
59 | -.9172123 .4672325 -1.96 0.050 -1.832971 -.0014535
60 | -.9843392 .462074 -2.13 0.033 -1.889988 -.0786908
61 | -.9555716 .4617807 -2.07 0.039 -1.860645 -.050498
62 | -1.106859 .4638763 -2.39 0.017 -2.01604 -.1976782
63 | -.977484 .4601274 -2.12 0.034 -1.879317 -.0756509
64 | -1.057566 .4593934 -2.30 0.021 -1.957961 -.1571717
65 | -.9569004 .4579375 -2.09 0.037 -1.854441 -.0593593
66 | -.9439535 .4577537 -2.06 0.039 -1.841134 -.0467726
67 | -1.182253 .4678739 -2.53 0.012 -2.09927 -.2652374
68 | -1.111331 .4620249 -2.41 0.016 -2.016883 -.2057786
69 | -1.26849 .4678471 -2.71 0.007 -2.185453 -.3515264
70 | -.6979144 .4573333 -1.53 0.127 -1.594271 .1984425
71 | -1.014777 .4735079 -2.14 0.032 -1.942835 -.0867186
72 | -.8364775 .4674897 -1.79 0.074 -1.752741 .0797855
73 | -1.100835 .4770821 -2.31 0.021 -2.035899 -.1657714
74 | -1.080575 .4966258 -2.18 0.030 -2.053944 -.1072063
75 | -.8730281 .5033653 -1.73 0.083 -1.859606 .1135498
76 | -.6902913 .4945775 -1.40 0.163 -1.659645 .2790629
77 | -1.103201 .5094065 -2.17 0.030 -2.101619 -.1047823
78 | -.4252277 .5027349 -0.85 0.398 -1.41057 .5601146
79 | -.5360097 .5036819 -1.06 0.287 -1.523208 .4511888
80 | -.6822742 .5222598 -1.31 0.191 -1.705885 .3413362
81 | -.6859098 .5459123 -1.26 0.209 -1.755878 .3840587
82 | -.5849168 .5741404 -1.02 0.308 -1.710211 .5403777
83 | -.8567249 .6325746 -1.35 0.176 -2.096548 .3830986
84 | -1.015225 .5695311 -1.78 0.075 -2.131485 .1010359
85 | -.817436 .8447003 -0.97 0.333 -2.473018 .8381461
86 | -1.716431 .8791466 -1.95 0.051 -3.439526 .006665
87 | -.9582347 .7482772 -1.28 0.200 -2.424831 .5083618
88 | -.7534905 .6502242 -1.16 0.247 -2.027906 .5209255
89 | -2.111355 1.342654 -1.57 0.116 -4.742909 .5201986
90 | -.9557962 .8015679 -1.19 0.233 -2.52684 .6152479
91 | 1.123961 .8423056 1.33 0.182 -.5269275 2.77485


edu |
8 | .2083036 .3093472 0.67 0.501 -.3980057 .8146129
9 | .0051441 .2757922 0.02 0.985 -.5353986 .5456867
10 | .3364264 .3195026 1.05 0.292 -.2897872 .9626401
12 | .2482652 .3081384 0.81 0.420 -.3556751 .8522054
13 | .8433266 .3123009 2.70 0.007 .2312281 1.455425
14 | .6817005 .4025953 1.69 0.090 -.1073717 1.470773
16 | .4819251 .3152663 1.53 0.126 -.1359855 1.099836
18 | .6971742 .3200453 2.18 0.029 .0698969 1.324451
21 | .8120132 .3573241 2.27 0.023 .1116708 1.512356


2.employment | .3522081 .057271 6.15 0.000 .239959 .4644571


pol_pos |
1 | .1049498 .2242916 0.47 0.640 -.3346535 .5445532
2 | .258274 .148335 1.74 0.082 -.0324571 .5490052
3 | .3113382 .1406105 2.21 0.027 .0357467 .5869297
4 | .3090364 .1390905 2.22 0.026 .0364239 .5816488
5 | .3087768 .1371765 2.25 0.024 .0399157 .5776378
6 | .3459819 .1514121 2.29 0.022 .0492196 .6427443
7 | .3215975 .1545897 2.08 0.037 .0186072 .6245877
8 | .0815976 .1642886 0.50 0.619 -.2404022 .4035974
9 | -.1982149 .3213479 -0.62 0.537 -.8280452 .4316154
10 | .0554127 .2384647 0.23 0.816 -.4119694 .5227949


log_org | -.1888445 .0507535 -3.72 0.000 -.2883197 -.0893694
_cons | 6.133003 .461184 13.30 0.000 5.229099 7.036907
-------------+----------------------------------------------------------------
sigma_u | 1.5854354
sigma_e | 1.3066094
rho | .59552347 (fraction of variance due to u_i)
------------------------------------------------------------------------------

.



Issue 2:
I can't seem to find what assumptions a random effects model relies on. Do my regressors and DV need to be linearly related? Do my variables need to have normal distribution? Etc. Simply: What requirements does my data need to meet (more than "passing" the Hausman test)?

Many thanks in advance.