Greetings,

I'm running Stata 15.1 on MacOS. The dataset I'm working with was generated as follows: I pooled a number of large-sample cross-sectional surveys that featured the same question for the years 2008, 2010, 2011, 2012, 2014, 2015, 2016, and 2018. My goal is to examine whether states' google search interest in related topics (for those years) influences the proportion of state respondents giving a 'disagree' response. The variables I use (including the outcome variable) here was thus created as follows:

Code:
egen var1_state_year=mean(var1), by(state year)
Once all the necessary variables were created, I then applied the 'collapse' command:

Code:
collapse (mean) var1_state_year var2_state_year, by(state year)
My question is an attempt at clarifying an apparent inconsistency in what model the stata output suggets I run vs. what was suggested here: https://www.statalist.org/forums/for...ith-time-trend . Specifically, to capture overtime variation both within and between states, my intuition was to run a multi-level model with the xtmixed command:

Code:
. xtmixed whstate_favors indexZ  i.year  state:

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log likelihood = -1305.9038  
Iteration 1:   log likelihood = -1305.9038  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =        400
Group variable: state                           Number of groups  =         50

Obs per group:
min =          8
avg =        8.0
max =          8

Wald chi2(8)      =     275.78
Log likelihood = -1305.9038                     Prob > chi2       =     0.0000


whstate_favors       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

indexZ    1.336521    .620664     2.15   0.031     .1200416       2.553

year 
2010    -3.011593   1.064883    -2.83   0.005    -5.098725   -.9244611
2011    -.5052854   1.064613    -0.47   0.635    -2.591888    1.581317
2012    -1.860114   1.064116    -1.75   0.080    -3.945744    .2255152
2014     -1.57528   1.111708    -1.42   0.156    -3.754188    .6036278
2015     7.134012   1.239951     5.75   0.000     4.703752    9.564272
2016     2.535333   1.522316     1.67   0.096    -.4483511    5.519016
2018     6.170662   1.577615     3.91   0.000     3.078594     9.26273

_cons    17.14003   1.323791    12.95   0.000     14.54544    19.73461



Random-effects Parameters     Estimate   Std. Err.     [95% Conf. Interval]

state: Identity              
sd(_cons)    7.348734   .7864944      5.958173    9.063834

sd(Residual)     5.32021   .2012029       4.94012    5.729543

LR test vs. linear model: chibar2(01) = 280.74        Prob >= chibar2 = 0.0000
As you can see at the bottom, the lr test seems to indicate (though correct me if I'm wrong) that a multi-level model is preferable to OLS. However, in the earlier thread I linked, it was mentioned that the xt commands (whether xtreg or xtmixed) are unnecessary for pooled cross-sectional data, and that one can simply use OLS with i.year to capture time-specific effects. Can someone thus clarify how to proceed with such data?

If it helps, here is a sample of my data (whstate_favors=outcome variable, indexZ=state's average annual google search interest score):

Code:
* Example generated by -dataex-. To install: ssc install dataex
clear
input float(whstate_favors indexZ) double(year state)
 7.680336 -1.1429285 2008  1
 24.03921  -.9920198 2008  2
 13.80334  -.7394119 2008  4
 8.201495  -.5032071 2008  5
 20.11939 -.55897766 2008  6
  18.4817 -.50976837 2008  8
22.488667   .6318882 2008  9
 22.00062 -1.3594495 2008 10
 48.47411 -.58522266 2008 11
14.984724  -.6737995 2008 12
 11.23602  -.3982272 2008 13
 28.74142  -.6180289 2008 15
 10.57713  -.4047884 2008 16
17.614655 -.18826735 2008 17
  16.9839 -.28340536 2008 18
13.688213          . 2008 19
 14.39021  -.3851047 2008 20
11.007668 -.58850324 2008 21
 13.33329  -.1981092 2008 22
21.126213 -1.1790153 2008 23
16.110003  -.6049064 2008 24
 21.99363   .4941021 2008 25
12.200358   .0971468 2008 26
17.403385 -.26700228 2008 27
  7.49368    -.83455 2008 28
 16.29431 -.50976837 2008 29
13.251606 -1.3594495 2008 30
16.155375  -.3424566 2008 31
13.729026  -.7361313 2008 32
14.480515  -.6409932 2008 33
13.202847  -.7590957 2008 34
 19.35502   -.486804 2008 35
 17.36421 -.35885975 2008 36
 9.305553 -.15546118 2008 37
 9.009853  -.9723361 2008 38
 10.74107  -.4441559 2008 39
 9.809873 -.56553894 2008 40
 25.01471  -.6049064 2008 41
 11.75892 -.20467043 2008 42
 20.31874   .5531533 2008 44
12.128377  -.1915479 2008 45
19.033066 -1.3594495 2008 46
12.045777  -.5064877 2008 47
11.860756  -.4539978 2008 48
15.495923  -.7262894 2008 49
37.404438  -.5032071 2008 50
  14.6579  -.7886212 2008 51
 23.78781 -.12265485 2008 53
 8.866741  -.9362493 2008 54
 16.52739  -.4900846 2008 55
 9.820115  -.8017437 2008 56
 6.425949 -1.0379485 2010  1
20.993994 -1.2413472 2010  2
 15.34381 -.24075733 2010  4
  4.02392  -.6049063 2010  5
 19.68124  -.7525344 2010  6
16.478086  -.1915479 2010  8
17.863935  .22509107 2010  9
17.345894 -.17842548 2010 10
20.170927 -.42447215 2010 11
10.718645 -.24075726 2010 12
 8.976017  -.3621403 2010 13
 30.34577 -1.0445098 2010 15
  11.6666   .1857236 2010 16
14.709275  .30054545 2010 17
 9.224236  -.6049063 2010 18
12.499412          . 2010 19
 8.198928   -.408069 2010 20
 13.38905  -.2243542 2010 21
 7.463886  -.6409932 2010 22
21.378126  -.5950646 2010 23
13.691906  -.4441559 2010 24
 20.93805    .172601 2010 25
10.807766  .05777933 2010 26
  16.0334  .24149424 2010 27
  3.65953  -.9362493 2010 28
13.752706  -.6705188 2010 29
 9.103647   -.850953 2010 30
 5.954556  -.1160937 2010 31
 9.344904  -.7361313 2010 32
13.878927  -.6442739 2010 33
 16.11743   -.434314 2010 34
 20.65257  -.5491358 2010 35
 14.31302  -.2374767 2010 36
13.121726 -.14233859 2010 37
11.473763    -.83455 2010 38
  9.93098  -.2276348 2010 39
11.126292  -.3030891 2010 40
  20.6783  -.6049064 2010 41
 9.692232 -.16530304 2010 42
  20.0009 -.17186426 2010 44
10.009124 -1.0707548 2010 45
4.7525783 -1.1822959 2010 46
 7.694825  -.6049064 2010 47
10.644823  -.2801248 2010 48
15.650936  -.3457372 2010 49
 31.19452  -.8607949 2010 50
10.943864 -1.0969998 2010 51
19.273506  -.3621403 2010 53
  5.90513  -1.198699 2010 54
end
label values state state
label def state 1 "Alabama", modify
label def state 2 "Alaska", modify
label def state 4 "Arizona", modify
label def state 5 "Arkansas", modify
label def state 6 "California", modify
label def state 8 "Colorado", modify
label def state 9 "Connecticut", modify
label def state 10 "Delaware", modify
label def state 11 "District of Columbia", modify
label def state 12 "Florida", modify
label def state 13 "Georgia", modify
label def state 15 "Hawaii", modify
label def state 16 "Idaho", modify
label def state 17 "Illinois", modify
label def state 18 "Indiana", modify
label def state 19 "Iowa", modify
label def state 20 "Kansas", modify
label def state 21 "Kentucky", modify
label def state 22 "Louisiana", modify
label def state 23 "Maine", modify
label def state 24 "Maryland", modify
label def state 25 "Massachusetts", modify
label def state 26 "Michigan", modify
label def state 27 "Minnesota", modify
label def state 28 "Mississippi", modify
label def state 29 "Missouri", modify
label def state 30 "Montana", modify
label def state 31 "Nebraska", modify
label def state 32 "Nevada", modify
label def state 33 "New Hampshire", modify
label def state 34 "New Jersey", modify
label def state 35 "New Mexico", modify
label def state 36 "New York", modify
label def state 37 "North Carolina", modify
label def state 38 "North Dakota", modify
label def state 39 "Ohio", modify
label def state 40 "Oklahoma", modify
label def state 41 "Oregon", modify
label def state 42 "Pennsylvania", modify
label def state 44 "Rhode Island", modify
label def state 45 "South Carolina", modify
label def state 46 "South Dakota", modify
label def state 47 "Tennessee", modify
label def state 48 "Texas", modify
label def state 49 "Utah", modify
label def state 50 "Vermont", modify
label def state 51 "Virginia", modify
label def state 53 "Washington", modify
label def state 54 "West Virginia", modify
label def state 55 "Wisconsin", modify
label def state 56 "Wyoming", modify
Thanks for your help!