How to conduct Hausman-test for mixed-model with random slopes?

[Daniel Geiter]

Hi to everyone in this forum,

I am currently struggling with an issue regarding Hausman tests for multilevel models. I couldn't find any other post that would answer my questions. Still, I am a rookie to this platform and even though I read the posting advices, I might have missed out on something. So please, excuse me if I violate any points of the code of conduct. If I should correct or add something, please let me know!


My data structure looks as follows (data obtained from ISSP and WID):

* Example generated by -dataex-. For more info, type help dataex
clear
input float Likert_Prot_Env double WID_gini_NI byte left_right float(post_materialist mixed middle_edu high_edu middle_income high_income age) byte gender long encCountry float ISSP
. .426481367479445  . 0 1 0 0 0 0 3 1 1 0
. .426481367479445  1 0 1 1 0 0 0 2 2 1 0
. .426481367479445 10 1 0 0 0 0 0 2 2 1 0
. .426481367479445  5 0 1 0 0 0 0 5 2 1 0
. .426481367479445 10 0 1 0 0 0 0 5 1 1 0
. .426481367479445  1 0 1 1 0 0 0 3 2 1 0
. .426481367479445 10 0 1 0 0 0 0 4 2 1 0
. .426481367479445  8 1 0 1 0 0 0 5 1 1 0
. .426481367479445  1 0 1 0 0 0 0 6 1 1 0
. .426481367479445 10 0 1 1 0 0 0 5 2 1 0
. .426481367479445 10 0 1 0 0 0 0 6 1 1 0
. .426481367479445  8 0 1 1 0 0 0 3 1 1 0
. .426481367479445  . 1 0 0 1 0 0 2 2 1 0
. .426481367479445  . 0 0 1 0 0 0 2 1 1 0
. .426481367479445 10 0 1 0 0 0 0 6 2 1 0
. .426481367479445  5 0 1 0 0 0 0 3 2 1 0
. .426481367479445  . 0 1 1 0 0 0 2 2 1 0
. .426481367479445  3 0 0 1 0 0 0 4 1 1 0
. .426481367479445 10 0 0 0 0 0 0 6 1 1 0
. .426481367479445  7 0 1 1 0 0 0 4 2 1 0
. .426481367479445  . 0 1 1 0 0 0 5 1 1 0
. .426481367479445  1 0 1 1 0 0 0 5 1 1 0
. .426481367479445  1 0 1 1 0 0 0 6 2 1 0
. .426481367479445  5 0 1 0 0 0 0 5 2 1 0
. .426481367479445  1 0 0 0 0 0 0 5 2 1 0
. .426481367479445  5 0 1 0 0 0 0 4 2 1 0
. .426481367479445  3 0 1 1 0 0 0 4 2 1 0
. .426481367479445  3 0 0 1 0 0 0 3 2 1 0
. .426481367479445  . 0 1 0 0 0 0 5 2 1 0
. .426481367479445  . 0 1 1 0 0 0 6 1 1 0
. .426481367479445  6 0 0 0 0 0 0 5 2 1 0
. .426481367479445  5 0 1 0 0 0 0 4 2 1 0
. .426481367479445 10 0 1 1 0 0 0 1 2 1 0
. .426481367479445  8 0 0 0 0 0 0 5 2 1 0
. .426481367479445  8 0 0 0 0 0 0 1 1 1 0
. .426481367479445 10 1 0 0 0 0 0 5 2 1 0
. .426481367479445  . 0 1 0 0 0 0 4 2 1 0
. .426481367479445  4 0 0 1 0 0 0 3 2 1 0
. .426481367479445  2 0 0 1 0 0 0 3 2 1 0
. .426481367479445  9 0 1 0 0 0 0 4 2 1 0
. .426481367479445  6 0 0 0 0 0 0 2 2 1 0
. .426481367479445  . 0 1 0 0 0 0 3 2 1 0
. .426481367479445  1 0 0 1 0 0 0 2 2 1 0
. .426481367479445  . 0 1 0 0 0 0 5 1 1 0
. .426481367479445  3 0 0 0 0 0 0 4 2 1 0
. .426481367479445  3 1 0 1 0 0 0 6 2 1 0
. .426481367479445  . 0 1 1 0 0 0 2 2 1 0
. .426481367479445  . 0 1 0 0 0 0 3 2 1 0
. .426481367479445  5 0 1 1 0 0 0 6 1 1 0
. .426481367479445  1 0 1 0 0 0 0 4 2 1 0
. .426481367479445 10 0 1 1 0 0 0 5 2 1 0
. .426481367479445 10 0 1 0 0 0 0 3 2 1 0
. .426481367479445  1 0 0 1 0 0 0 5 2 1 0
. .426481367479445  . 1 0 0 0 0 0 3 1 1 0
. .426481367479445  3 0 1 1 0 0 0 6 2 1 0
. .426481367479445  7 0 1 0 0 0 0 4 2 1 0
. .426481367479445  . 0 1 1 0 0 0 3 2 1 0
. .426481367479445  . 0 1 0 0 0 0 4 1 1 0
. .426481367479445 10 0 1 0 0 0 0 6 1 1 0
. .426481367479445  1 0 1 0 0 0 0 3 2 1 0
. .426481367479445  8 0 0 1 0 0 0 2 2 1 0
. .426481367479445 10 0 1 0 0 0 0 2 1 1 0
. .426481367479445  . 0 1 1 0 0 0 1 2 1 0
. .426481367479445  1 1 0 0 0 0 0 3 2 1 0
. .426481367479445  . 0 1 0 0 0 0 2 2 1 0
. .426481367479445  1 0 0 0 0 0 0 4 1 1 0
. .426481367479445  1 0 1 1 0 0 0 4 1 1 0
. .426481367479445  . 0 0 0 0 0 0 6 2 1 0
. .426481367479445  . 0 1 0 0 0 0 3 2 1 0
. .426481367479445 10 0 1 1 0 0 0 4 2 1 0
. .426481367479445  . 0 1 1 0 0 0 4 1 1 0
. .426481367479445  1 0 1 1 0 0 0 5 2 1 0
. .426481367479445  . 0 1 1 0 0 0 5 2 1 0
. .426481367479445 10 0 0 0 0 0 0 4 2 1 0
. .426481367479445  . 0 1 1 0 0 0 1 2 1 0
. .426481367479445  5 0 1 0 0 0 0 2 2 1 0
. .426481367479445  1 0 1 1 0 0 0 3 2 1 0
. .426481367479445  5 0 0 1 0 0 0 5 2 1 0
. .426481367479445  . 0 1 0 0 0 0 6 1 1 0
. .426481367479445  2 0 1 0 0 0 0 2 1 1 0
. .426481367479445  . 0 1 1 0 0 0 5 2 1 0
. .426481367479445  . 0 1 0 0 0 0 4 2 1 0
. .426481367479445  . 0 0 1 0 0 0 5 2 1 0
. .426481367479445 10 0 0 0 1 0 0 6 1 1 0
. .426481367479445  1 0 1 1 0 0 0 6 2 1 0
. .426481367479445  1 0 1 0 0 0 0 6 2 1 0
. .426481367479445  . 0 1 0 0 0 0 6 1 1 0
. .426481367479445  . 0 1 0 0 0 0 2 2 1 0
. .426481367479445  . 0 1 1 0 0 0 3 1 1 0
. .426481367479445  1 0 0 1 0 0 0 4 1 1 0
. .426481367479445  . 0 1 0 0 0 0 6 2 1 0
. .426481367479445  5 0 0 0 0 0 0 4 2 1 0
. .426481367479445  . 0 0 0 0 0 0 4 2 1 0
. .426481367479445  1 0 1 0 0 0 0 6 2 1 0
. .426481367479445  5 0 1 0 0 0 0 3 1 1 0
. .426481367479445  . 0 1 0 0 0 0 4 1 1 0
. .426481367479445  . 0 1 1 0 0 0 4 1 1 0
. .426481367479445 10 0 1 0 0 0 0 5 1 1 0
. .426481367479445  . 0 1 0 0 0 0 3 2 1 0
. .426481367479445  . 0 1 0 1 0 0 5 2 1 0
end
label values left_right PARTY_LR
label def PARTY_LR 1 "1. Far left (communist, etc.)", modify
label def PARTY_LR 2 "2. Left / center left", modify
label def PARTY_LR 3 "3. Center / liberal", modify
label def PARTY_LR 4 "4. Right / conservative", modify
label def PARTY_LR 5 "5. Far right (fascist, etc.)", modify
label def PARTY_LR 6 "6. Other", modify
label values gender SEX
label def SEX 1 "1. Male", modify
label def SEX 2 "2. Female", modify
label values encCountry encCountry
label def encCountry 1 "Albania", modify

The model I want to implement:
>> mixed Likert_Prot_Env WID_gini_NI left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender if ISSP==1 || encCountry <<
with individual observations being nested in countries. All variables are on the individual level except WID_gini_NI which is the gini for each country.

If I go on to implement the following FE model:
>> reg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender i.encCountry if ISSP==1 <<
I only get negative chi2-values for Hausman:

"Test of H0: Difference in coefficients not systematic

chi2(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= -16.56

Warning: chi2 < 0 ==> model fitted on these data
fails to meet the asymptotic assumptions
of the Hausman test; see suest for a
generalized test."

Usually, this problem seems to be fixed with the "sigmamore"-option. Yet, this option is not available for "mixed"-commands, since it does not store sigma.
Another solution would be to use "xtreg, re" instead of "mixed". This is also not viable for me (if I am correct), since I include variables on the second/country level (random slopes), which is not possible for ", re".

Does any-one know a solution for this? I really tried lots of things and still, I wasn't able to find any solution for this. All help will be very, very much appreciated!

(If it is of any help to get the intuition behind the model: I am checking for a relationship between the personal willingness to pay for a green transition of the economy and the economic inequality in a country)

[JJ Kovach]

I am not clear on your question, but your mixed model is not doing what you describe, as there are no separate slopes. What you have shown is identical to xtreg, mle, which is a random effect model such that each encCountry will have a separate intercept. Your second reg model should be run using xtreg, fe or reghdfe to account for the proper degrees of freedom. But, the first model is an encCountyr random effect model whereas the second is a fixed effect model.
If you want to use the Hausman test to compare models, run both with xtreg, one with the re option and the other with the fe option.
But, the Hausman test will simply tell you if the coefficients are statistically similar such that if they are then you can use either model (since the coefficients are similar), but if they are not then you should use a fixed effect model. However, bear in mind that a fixed effect model only considers within-entity variation, whereas a random effect model combines both within and between-entity variation. For this reason, the interpretation of a random effects model is not as clear, but it is sometimes necessary due to time-invariant variables which get washed out of a fixed effect model.

[Daniel Geiter]

Dear JJ Kovach,

thanks a lot for your reply. You are probably right on the slopes thing.
To my understanding, I have to use a random effects model, since in my case, gini is basically a "time-invariant" variable: In panel data, different observations over time are the level 1 observations, while all time-invariant variables are associated with level 2 (the individual level). In my case, individuals are level 1 and country variables are level 2. In an fe model country variables would therefore be ruled out, just like time-invariant variables would be for panel data. This is also the reason I did not choose ", re" since I read that this command is not capable of including level 2 variables. Do you know, if I can do this with , mle?
I also tried running , mle and compared it with the results from mixed. The estimates and also the p-values seem to be quite different from each other.

Thanks again

[JJ Kovach]

I am trying to help, but precision in terminology is important.

"while all time-invariant variables are associated with level 2 (the individual level). In my case, individuals are level 1 and country variables are level 2." I assume you mean the second sentence as it contradicts the first?

'In an fe model country variables would therefore be ruled out, just like time-invariant variables would be for panel data.' Time invariant variables are not 'ruled out' of panel data models, only with entity specific fixed effects panel models. They are not omitted from entity random effects or entity between effects, nor are their interactions omitted from fixed effects models.

xtreg, mle will yield similar outcomes to -xtreg, re, and both handle nested data in the same way. -xtreg, mle uses maximum likelihood estimation whereas -xtreg, re uses generalized least squares, but they are both random effects models which means (among other things) that the coefficients are a weighted mix of the between and within effects. -mixed uses maximum likelihood estimation so its results can be identical to -xtreg, mle under some conditions. I tried to run the model you indicated, but the "if ISSP==1" constraint is never satisfied, as the data you show has 0s for all ISSP instances. Thus, I cannot reproduce your results. Please post the actual code showing your results so it can be evaluated.

[Daniel Geiter]

I am sorry for not being precise enough and thank you for your patience. I will try to explain it better. Regarding your first question: Yes, you are right, I mean the second sentence. I was only trying to explain why I think I cannot use , fe or , re: Because I have variables on the second level (the country level) which would be washed out in an ,fe model and can also not be properly estimated in an , re model (if I get it right), which is why I chose mixed.

Speaking of the data I provided, I really made a mistake and only provided invalid observations. Please, excuse me. Here is another set of variables with only valid observations (not necessary any more to include the condition "ISSP==1" in the model):

* Example generated by -dataex-. For more info, type help dataex
clear
input float Likert_Prot_Env double WID_gini_NI byte left_right float(post_materialist mixed middle_edu high_edu middle_income high_income age) byte gender long encCountry
12                .  . 0 0 0 1 0 0 6 1  3
 6                .  2 0 0 0 1 1 0 3 2  3
 5                .  4 0 1 0 0 0 1 3 1  3
 .                .  . 0 0 0 1 0 0 4 2  3
11  .29771838170867  2 0 0 1 0 0 0 4 2  4
 7  .29771838170867  2 0 0 0 0 1 0 6 2  4
 6  .29771838170867  4 1 0 1 0 0 1 4 2  4
 5  .29771838170867  2 0 0 1 0 0 0 6 1  4
 3 .382910851896986  2 0 1 1 0 0 0 5 1 10
 4 .382910851896986  4 1 0 1 0 1 0 3 2 10
 7 .382910851896986 96 1 1 0 0 0 1 6 1 10
 3 .382910851896986  . 0 1 1 0 0 0 3 2 10
12 .317511502023727  3 0 1 0 1 0 0 6 1 12
 8 .317511502023727  1 0 1 0 1 1 0 4 2 12
 . .317511502023727  1 0 0 0 1 0 1 6 2 12
 9 .317511502023727  . 0 1 1 0 0 0 2 2 12
12  .31711412727492  6 1 0 0 1 0 0 2 1 14
 3  .31711412727492  4 0 1 1 0 1 0 2 1 14
 7  .31711412727492  4 0 0 0 1 0 1 2 1 14
 5  .31711412727492  4 0 0 0 1 0 0 6 2 14
 3 .315502443824087  4 0 1 0 1 0 0 3 2 15
 7 .315502443824087  3 0 1 0 1 1 0 6 2 15
10 .315502443824087  2 1 0 1 0 0 1 4 2 15
 3 .315502443824087 96 0 1 0 1 0 0 4 2 15
 4  .31880451313118  . 0 1 1 0 0 0 6 2 17
10  .31880451313118  2 0 1 1 0 1 0 6 1 17
11  .31880451313118  2 0 0 0 1 0 1 4 1 17
10  .31880451313118  1 0 0 1 0 0 0 6 1 17
 6 .347332686814582  4 0 0 0 0 0 0 6 2 19
 3 .347332686814582  . 0 0 0 0 1 0 3 2 19
13 .347332686814582  3 0 0 1 0 0 1 1 2 19
 6 .347332686814582  4 0 1 0 1 0 0 1 2 19
11 .266577932014147  . 0 0 1 0 0 0 4 1 20
11 .266577932014147  . 0 1 1 0 1 0 3 2 20
12 .273249817316092  2 0 1 0 1 0 1 4 2 20
 7 .266577932014147  . 0 1 0 1 0 0 4 1 20
 8 .480229969666585  3 0 0 0 0 0 0 6 1 21
12 .480229969666585  . 0 1 1 0 1 0 4 1 21
12 .480229969666585  3 0 1 0 1 0 1 4 2 21
14 .480229969666585  2 0 1 1 0 0 0 3 1 21
10 .410040338909816  4 1 0 0 0 0 0 6 1 22
12 .410040338909816  2 0 1 0 1 1 0 3 2 22
13 .410040338909816  4 0 1 1 0 0 1 5 1 22
 5 .410040338909816  . 1 1 1 0 0 0 5 2 22
 3 .625335378691203  2 0 1 1 0 0 0 5 1 24
 9 .625335378691203  4 0 1 0 0 1 0 5 1 24
 4 .625335378691203  . 0 0 0 1 0 1 5 1 24
 . .625335378691203  . 0 1 1 0 0 0 1 2 24
 8 .312597233641764  2 0 0 0 1 0 0 3 2 27
12 .312597233641764  2 0 1 0 1 1 0 1 2 27
10 .312597233641764  2 0 1 0 0 0 1 5 1 27
 . .312597233641764  . 1 1 0 1 0 0 4 1 27
 7 .262263788839457  2 0 1 1 0 0 0 5 1 29
 7 .262263788839457  4 0 1 0 1 1 0 3 1 29
12 .262263788839457  2 0 1 0 1 0 1 3 2 29
12 .262263788839457  2 0 1 0 1 0 0 4 2 29
 3 .479457431075552  3 0 1 1 0 0 0 5 1 33
11 .479457431075552  . 0 1 0 1 1 0 1 2 33
 7 .479457431075552  3 0 1 0 1 0 1 6 1 33
 . .479457431075552  . 1 0 0 1 0 0 5 2 33
10 .273364698905071  4 0 0 1 0 0 0 6 1 35
11 .273364698905071  3 0 1 1 0 1 0 2 1 35
 7 .273364698905071  2 0 1 1 0 0 1 4 2 35
 6 .273364698905071  4 0 0 1 0 0 0 4 1 35
 6 .293909840433564  . 1 0 0 1 0 0 2 2 36
10 .293732798472523  3 1 0 0 1 1 0 6 1 36
12 .293732798472523  4 0 1 1 0 0 1 4 1 36
 7 .293732798472523  . 0 1 1 0 0 0 2 2 36
12 .282895576374681  . 0 1 1 0 0 0 5 1 38
10 .282895576374681  4 0 0 1 0 1 0 6 1 38
 8 .282895576374681  3 0 1 1 0 0 1 4 1 38
 6 .282895576374681  . 0 1 0 1 0 0 3 2 38
14 .404394540995419  2 0 1 1 0 0 0 5 2 39
10 .404394540995419  2 0 1 0 1 1 0 2 2 39
 8 .404394540995419  4 0 1 1 0 0 1 1 1 39
 7 .404394540995419  . 0 1 0 1 0 0 3 2 39
 9                .  . 0 1 1 0 0 0 2 2 41
14                .  3 1 0 1 0 1 0 3 2 41
14                .  3 1 0 0 1 0 1 6 2 41
 9                .  . 1 1 0 0 0 0 3 2 41
end
label values left_right PARTY_LR
label def PARTY_LR 1 "1. Far left (communist, etc.)", modify
label def PARTY_LR 2 "2. Left / center left", modify
label def PARTY_LR 3 "3. Center / liberal", modify
label def PARTY_LR 4 "4. Right / conservative", modify
label def PARTY_LR 6 "6. Other", modify
label def PARTY_LR 96 "96. Invalid ballot", modify
label values gender SEX
label def SEX 1 "1. Male", modify
label def SEX 2 "2. Female", modify
label values encCountry encCountry
label def encCountry 3 "Australia", modify
label def encCountry 4 "Austria", modify
label def encCountry 10 "Croatia", modify
label def encCountry 12 "Denmark", modify
label def encCountry 14 "Finland", modify
label def encCountry 15 "France", modify
label def encCountry 17 "Germany", modify
label def encCountry 19 "Hungary", modify
label def encCountry 20 "Iceland", modify
label def encCountry 21 "Italy", modify
label def encCountry 22 "Japan", modify
label def encCountry 24 "Lithuania", modify
label def encCountry 27 "New Zealand", modify
label def encCountry 29 "Norway", modify
label def encCountry 33 "Russia", modify
label def encCountry 35 "Slovakia", modify
label def encCountry 36 "Slovenia", modify
label def encCountry 38 "Sweden", modify
label def encCountry 39 "Switzerland", modify
label def encCountry 41 "United States", modify

The model is now:

mixed Likert_Prot_Env WID_gini_NI left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender || encCountry
est sto me

and the FE model:

xtset encCountry
xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, fe
est sto fe
hausman fe me

My results:

. mixed Likert_Prot_Env WID_gini_NI left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender || encCountry:

Performing EM optimization ...

Performing gradient-based optimization:
Iteration 0: Log likelihood = -37530.394
Iteration 1: Log likelihood = -37530.394

Computing standard errors ...

Mixed-effects ML regression Number of obs = 15,378
Group variable: encCountry Number of groups = 18
Obs per group:
min = 291
avg = 854.3
max = 2,408
Wald chi2(10) = 878.16
Log likelihood = -37530.394 Prob > chi2 = 0.0000

----------------------------------------------------------------------------------
Likert_Prot_Env | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
WID_gini_NI | -2.890542 2.398095 -1.21 0.228 -7.590722 1.809638
left_right | -.0085881 .0018078 -4.75 0.000 -.0121314 -.0050449
post_materialist | 1.208417 .0697083 17.34 0.000 1.071791 1.345043
mixed | .392136 .0510655 7.68 0.000 .2920494 .4922227
middle_edu | .2924847 .0785446 3.72 0.000 .1385401 .4464294
high_edu | .974378 .0802422 12.14 0.000 .8171062 1.13165
middle_income | .2827749 .0547985 5.16 0.000 .1753718 .390178
high_income | .512154 .0587002 8.72 0.000 .3971037 .6272043
age | -.0106252 .0153465 -0.69 0.489 -.0407038 .0194533
gender | .3502312 .045017 7.78 0.000 .2619995 .4384629
_cons | 7.743422 .8895835 8.70 0.000 5.99987 9.486974
----------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects parameters | Estimate Std. err. [95% conf. interval]
-----------------------------+------------------------------------------------
encCountry: Identity |
var(_cons) | .8714548 .2977929 .4460391 1.702617
-----------------------------+------------------------------------------------
var(Residual) | 7.674782 .0875773 7.505039 7.848365
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 1596.01 Prob >= chibar2 = 0.0000



. xtset encCountry

Panel variable: encCountry (unbalanced)

. xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, fe

Fixed-effects (within) regression Number of obs = 17,391
Group variable: encCountry Number of groups = 20

R-squared: Obs per group:
Within = 0.0544 min = 291
Between = 0.2977 avg = 869.5
Overall = 0.0615 max = 2,408

F(9, 17362) = 110.98
corr(u_i, Xb) = 0.0668 Prob > F = 0.0000

----------------------------------------------------------------------------------
Likert_Prot_Env | Coefficient Std. err. t P>|t| [95% conf. interval]
-----------------+----------------------------------------------------------------
left_right | -.0091988 .0018224 -5.05 0.000 -.0127708 -.0056267
post_materialist | 1.140871 .0654806 17.42 0.000 1.012523 1.26922
mixed | .3621251 .0488464 7.41 0.000 .2663812 .457869
middle_edu | .2506549 .075118 3.34 0.001 .103416 .3978938
high_edu | 1.005865 .0761732 13.20 0.000 .8565581 1.155173
middle_income | .2850975 .0523331 5.45 0.000 .1825193 .3876757
high_income | .5031084 .0560738 8.97 0.000 .3931981 .6130187
age | -.0190207 .0147166 -1.29 0.196 -.0478667 .0098253
gender | .360422 .0430142 8.38 0.000 .2761099 .4447341
_cons | 7.113977 .1293089 55.02 0.000 6.860519 7.367436
-----------------+----------------------------------------------------------------
sigma_u | .99131895
sigma_e | 2.8136146
rho | .11042789 (fraction of variance due to u_i)
----------------------------------------------------------------------------------
F test that all u_i=0: F(19, 17362) = 97.45 Prob > F = 0.0000

. est sto fe

. hausman fe me
no coefficients in common; specify equations(matchlist)
for problems with different equation names.
r(498);

.

In my first post I mentioned that my problem was negative Chi2-values for the hausman test. As you can see, for some reason, I encountered another problem now, which is
"no coefficients in common; specify equations(matchlist)
for problems with different equation names.
r(498);"
for which I also haven't got any solution, yet. I guess, it occurs because of the different structures of the mixed and xtreg command. But still, I don't know why this problem occurs only now, since I haven't changed anything in the code.
So, I guess, the problem with negative Chi2-hausman-values remains.

I also tried using the ,mle option. It gave me the same error as above:

. xtset encCountry

Panel variable: encCountry (unbalanced)

. xtreg Likert_Prot_Env WID_gini_NI left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, mle

Fitting constant-only model:
Iteration 0: Log likelihood = -37958.199
Iteration 1: Log likelihood = -37957.121
Iteration 2: Log likelihood = -37957.06
Iteration 3: Log likelihood = -37957.059
Iteration 4: Log likelihood = -37957.059

Fitting full model:
Iteration 0: Log likelihood = -37546.158
Iteration 1: Log likelihood = -37530.511
Iteration 2: Log likelihood = -37530.396
Iteration 3: Log likelihood = -37530.394
Iteration 4: Log likelihood = -37530.394

Random-effects ML regression Number of obs = 15,378
Group variable: encCountry Number of groups = 18

Random effects u_i ~ Gaussian Obs per group:
min = 291
avg = 854.3
max = 2,408

LR chi2(10) = 853.33
Log likelihood = -37530.394 Prob > chi2 = 0.0000

----------------------------------------------------------------------------------
Likert_Prot_Env | Coefficient Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
WID_gini_NI | -2.890545 2.426082 -1.19 0.233 -7.645579 1.864489
left_right | -.0085881 .0018078 -4.75 0.000 -.0121314 -.0050449
post_materialist | 1.208417 .0697112 17.33 0.000 1.071786 1.345049
mixed | .392136 .0510678 7.68 0.000 .2920451 .492227
middle_edu | .2924847 .0785466 3.72 0.000 .1385363 .4464332
high_edu | .974378 .0802473 12.14 0.000 .8170963 1.13166
middle_income | .2827749 .0547994 5.16 0.000 .1753702 .3901797
high_income | .512154 .0587037 8.72 0.000 .3970968 .6272112
age | -.0106252 .0153488 -0.69 0.489 -.0407084 .019458
gender | .3502312 .045017 7.78 0.000 .2619994 .438463
_cons | 7.743423 .8989071 8.61 0.000 5.981597 9.505248
-----------------+----------------------------------------------------------------
/sigma_u | .9335162 .1595015 .6678589 1.304845
/sigma_e | 2.77034 .0158062 2.739533 2.801493
rho | .1019692 .0313107 .0531388 .1773092
----------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 1596.01 Prob >= chibar2 = 0.000

. est sto re

. xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, fe

Fixed-effects (within) regression Number of obs = 17,391
Group variable: encCountry Number of groups = 20

R-squared: Obs per group:
Within = 0.0544 min = 291
Between = 0.2977 avg = 869.5
Overall = 0.0615 max = 2,408

F(9, 17362) = 110.98
corr(u_i, Xb) = 0.0668 Prob > F = 0.0000

----------------------------------------------------------------------------------
Likert_Prot_Env | Coefficient Std. err. t P>|t| [95% conf. interval]
-----------------+----------------------------------------------------------------
left_right | -.0091988 .0018224 -5.05 0.000 -.0127708 -.0056267
post_materialist | 1.140871 .0654806 17.42 0.000 1.012523 1.26922
mixed | .3621251 .0488464 7.41 0.000 .2663812 .457869
middle_edu | .2506549 .075118 3.34 0.001 .103416 .3978938
high_edu | 1.005865 .0761732 13.20 0.000 .8565581 1.155173
middle_income | .2850975 .0523331 5.45 0.000 .1825193 .3876757
high_income | .5031084 .0560738 8.97 0.000 .3931981 .6130187
age | -.0190207 .0147166 -1.29 0.196 -.0478667 .0098253
gender | .360422 .0430142 8.38 0.000 .2761099 .4447341
_cons | 7.113977 .1293089 55.02 0.000 6.860519 7.367436
-----------------+----------------------------------------------------------------
sigma_u | .99131895
sigma_e | 2.8136146
rho | .11042789 (fraction of variance due to u_i)
----------------------------------------------------------------------------------
F test that all u_i=0: F(19, 17362) = 97.45 Prob > F = 0.0000

. est sto fe

. hausman fe re
no coefficients in common; specify equations(matchlist)
for problems with different equation names.
r(498);

.

The only thing I can say for sure, is that the problem is not that I include "WID_gini_NI" as a variable in my re model but not in the fe model.

I hope, this makes things clearer.

[JJ Kovach]

Something is amiss, as when I run the analysis with the data you generated I do not get the same results you have posted. First though, here is confirmation that the -mixed model (as you wanted to specify, but without the WID_gini_NI variable) matches an -xtreg, mle model.

Copying your generated date:

//
clear
input float Likert_Prot_Env double WID_gini_NI byte left_right float(post_materialist mixed middle_edu high_edu middle_income high_income age) byte gender long encCountry
12 . . 0 0 0 1 0 0 6 1 3
6 . 2 0 0 0 1 1 0 3 2 3
5 . 4 0 1 0 0 0 1 3 1 3
. . . 0 0 0 1 0 0 4 2 3
11 .29771838170867 2 0 0 1 0 0 0 4 2 4
7 .29771838170867 2 0 0 0 0 1 0 6 2 4
6 .29771838170867 4 1 0 1 0 0 1 4 2 4
5 .29771838170867 2 0 0 1 0 0 0 6 1 4
3 .382910851896986 2 0 1 1 0 0 0 5 1 10
4 .382910851896986 4 1 0 1 0 1 0 3 2 10
7 .382910851896986 96 1 1 0 0 0 1 6 1 10
3 .382910851896986 . 0 1 1 0 0 0 3 2 10
12 .317511502023727 3 0 1 0 1 0 0 6 1 12
8 .317511502023727 1 0 1 0 1 1 0 4 2 12
. .317511502023727 1 0 0 0 1 0 1 6 2 12
9 .317511502023727 . 0 1 1 0 0 0 2 2 12
12 .31711412727492 6 1 0 0 1 0 0 2 1 14
3 .31711412727492 4 0 1 1 0 1 0 2 1 14
7 .31711412727492 4 0 0 0 1 0 1 2 1 14
5 .31711412727492 4 0 0 0 1 0 0 6 2 14
3 .315502443824087 4 0 1 0 1 0 0 3 2 15
7 .315502443824087 3 0 1 0 1 1 0 6 2 15
10 .315502443824087 2 1 0 1 0 0 1 4 2 15
3 .315502443824087 96 0 1 0 1 0 0 4 2 15
4 .31880451313118 . 0 1 1 0 0 0 6 2 17
10 .31880451313118 2 0 1 1 0 1 0 6 1 17
11 .31880451313118 2 0 0 0 1 0 1 4 1 17
10 .31880451313118 1 0 0 1 0 0 0 6 1 17
6 .347332686814582 4 0 0 0 0 0 0 6 2 19
3 .347332686814582 . 0 0 0 0 1 0 3 2 19
13 .347332686814582 3 0 0 1 0 0 1 1 2 19
6 .347332686814582 4 0 1 0 1 0 0 1 2 19
11 .266577932014147 . 0 0 1 0 0 0 4 1 20
11 .266577932014147 . 0 1 1 0 1 0 3 2 20
12 .273249817316092 2 0 1 0 1 0 1 4 2 20
7 .266577932014147 . 0 1 0 1 0 0 4 1 20
8 .480229969666585 3 0 0 0 0 0 0 6 1 21
12 .480229969666585 . 0 1 1 0 1 0 4 1 21
12 .480229969666585 3 0 1 0 1 0 1 4 2 21
14 .480229969666585 2 0 1 1 0 0 0 3 1 21
10 .410040338909816 4 1 0 0 0 0 0 6 1 22
12 .410040338909816 2 0 1 0 1 1 0 3 2 22
13 .410040338909816 4 0 1 1 0 0 1 5 1 22
5 .410040338909816 . 1 1 1 0 0 0 5 2 22
3 .625335378691203 2 0 1 1 0 0 0 5 1 24
9 .625335378691203 4 0 1 0 0 1 0 5 1 24
4 .625335378691203 . 0 0 0 1 0 1 5 1 24
. .625335378691203 . 0 1 1 0 0 0 1 2 24
8 .312597233641764 2 0 0 0 1 0 0 3 2 27
12 .312597233641764 2 0 1 0 1 1 0 1 2 27
10 .312597233641764 2 0 1 0 0 0 1 5 1 27
. .312597233641764 . 1 1 0 1 0 0 4 1 27
7 .262263788839457 2 0 1 1 0 0 0 5 1 29
7 .262263788839457 4 0 1 0 1 1 0 3 1 29
12 .262263788839457 2 0 1 0 1 0 1 3 2 29
12 .262263788839457 2 0 1 0 1 0 0 4 2 29
3 .479457431075552 3 0 1 1 0 0 0 5 1 33
11 .479457431075552 . 0 1 0 1 1 0 1 2 33
7 .479457431075552 3 0 1 0 1 0 1 6 1 33
. .479457431075552 . 1 0 0 1 0 0 5 2 33
10 .273364698905071 4 0 0 1 0 0 0 6 1 35
11 .273364698905071 3 0 1 1 0 1 0 2 1 35
7 .273364698905071 2 0 1 1 0 0 1 4 2 35
6 .273364698905071 4 0 0 1 0 0 0 4 1 35
6 .293909840433564 . 1 0 0 1 0 0 2 2 36
10 .293732798472523 3 1 0 0 1 1 0 6 1 36
12 .293732798472523 4 0 1 1 0 0 1 4 1 36
7 .293732798472523 . 0 1 1 0 0 0 2 2 36
12 .282895576374681 . 0 1 1 0 0 0 5 1 38
10 .282895576374681 4 0 0 1 0 1 0 6 1 38
8 .282895576374681 3 0 1 1 0 0 1 4 1 38
6 .282895576374681 . 0 1 0 1 0 0 3 2 38
14 .404394540995419 2 0 1 1 0 0 0 5 2 39
10 .404394540995419 2 0 1 0 1 1 0 2 2 39
8 .404394540995419 4 0 1 1 0 0 1 1 1 39
7 .404394540995419 . 0 1 0 1 0 0 3 2 39
9 . . 0 1 1 0 0 0 2 2 41
14 . 3 1 0 1 0 1 0 3 2 41
14 . 3 1 0 0 1 0 1 6 2 41
9 . . 1 1 0 0 0 0 3 2 41
end
label values left_right PARTY_LR
label def PARTY_LR 1 "1. Far left (communist, etc.)", modify
label def PARTY_LR 2 "2. Left / center left", modify
label def PARTY_LR 3 "3. Center / liberal", modify
label def PARTY_LR 4 "4. Right / conservative", modify
label def PARTY_LR 6 "6. Other", modify
label def PARTY_LR 96 "96. Invalid ballot", modify
label values gender SEX
label def SEX 1 "1. Male", modify
label def SEX 2 "2. Female", modify
label values encCountry encCountry
label def encCountry 3 "Australia", modify
label def encCountry 4 "Austria", modify
label def encCountry 10 "Croatia", modify
label def encCountry 12 "Denmark", modify
label def encCountry 14 "Finland", modify
label def encCountry 15 "France", modify
label def encCountry 17 "Germany", modify
label def encCountry 19 "Hungary", modify
label def encCountry 20 "Iceland", modify
label def encCountry 21 "Italy", modify
label def encCountry 22 "Japan", modify
label def encCountry 24 "Lithuania", modify
label def encCountry 27 "New Zealand", modify
label def encCountry 29 "Norway", modify
label def encCountry 33 "Russia", modify
label def encCountry 35 "Slovakia", modify
label def encCountry 36 "Slovenia", modify
label def encCountry 38 "Sweden", modify
label def encCountry 39 "Switzerland", modify
label def encCountry 41 "United States", modify
//

Here is the -mixed model

. mixed Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender|| encCountry:

Performing EM optimization ...

Performing gradient-based optimization: 
Iteration 0:   log likelihood = -139.99379  
Iteration 1:   log likelihood = -139.99249  
Iteration 2:   log likelihood = -139.99249  

Computing standard errors ...

Mixed-effects ML regression                     Number of obs     =         56
Group variable: encCountry                      Number of groups  =         20
                                                Obs per group:
                                                              min =          1
                                                              avg =        2.8
                                                              max =          4
                                                Wald chi2(9)      =       8.87
Log likelihood = -139.99249                     Prob > chi2       =     0.4495

----------------------------------------------------------------------------------
 Likert_Prot_Env | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      left_right |  -.0287363   .0240061    -1.20   0.231    -.0757874    .0183148
post_materialist |   1.618777    1.27212     1.27   0.203    -.8745331    4.112087
           mixed |   .0626609   .9784575     0.06   0.949    -1.855081    1.980403
      middle_edu |   .7223386    1.27091     0.57   0.570      -1.7686    3.213277
        high_edu |   1.101671   1.348247     0.82   0.414    -1.540844    3.744187
   middle_income |   .5245141   .9711757     0.54   0.589    -1.378955    2.427984
     high_income |   1.616273   .9257947     1.75   0.081    -.1982511    3.430797
             age |   .0612115   .2837082     0.22   0.829    -.4948463    .6172694
          gender |   .4261422   .9052592     0.47   0.638    -1.348133    2.200417
           _cons |    6.27604   2.551256     2.46   0.014      1.27567    11.27641
----------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects parameters  |   Estimate   Std. err.     [95% conf. interval]
-----------------------------+------------------------------------------------
encCountry: Identity         |
                  var(_cons) |   2.347904   1.818804       .514395    10.71677
-----------------------------+------------------------------------------------
               var(Residual) |   6.863243   1.673667      4.255551    11.06886
------------------------------------------------------------------------------
LR test vs. linear model: chibar2(01) = 2.27          Prob >= chibar2 = 0.0659

Note how this model is not-significant (Prob > chi2 =0.4495), essentially just random noise. Now to the comparable -xtreg, mle random effect model.

. xtset encCountry

Panel variable: encCountry (balanced)

. xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, mle

Fitting constant-only model:
Iteration 0:   log likelihood = -144.10766
Iteration 1:   log likelihood = -144.09035
Iteration 2:   log likelihood = -144.09034

Fitting full model:
Iteration 0:   log likelihood = -141.31959
Iteration 1:   log likelihood = -140.55399
Iteration 2:   log likelihood =  -140.0947
Iteration 3:   log likelihood = -139.99325
Iteration 4:   log likelihood = -139.99249
Iteration 5:   log likelihood = -139.99249

Random-effects ML regression                         Number of obs    =     56
Group variable: encCountry                           Number of groups =     20

Random effects u_i ~ Gaussian                        Obs per group:
                                                                  min =      1
                                                                  avg =    2.8
                                                                  max =      4

                                                     LR chi2(9)       =   8.20
Log likelihood = -139.99249                          Prob > chi2      = 0.5146

----------------------------------------------------------------------------------
 Likert_Prot_Env | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      left_right |  -.0287363    .026459    -1.09   0.277     -.080595    .0231224
post_materialist |   1.618777    1.27223     1.27   0.203    -.8747481    4.112302
           mixed |   .0626609   .9822104     0.06   0.949    -1.862436    1.987758
      middle_edu |   .7223386   1.273088     0.57   0.570    -1.772867    3.217544
        high_edu |   1.101671   1.349133     0.82   0.414    -1.542582    3.745924
   middle_income |   .5245141   .9713213     0.54   0.589    -1.379241    2.428269
     high_income |   1.616273   .9278521     1.74   0.082    -.2022837     3.43483
             age |   .0612115   .2838473     0.22   0.829     -.495119    .6175421
          gender |   .4261422   .9062708     0.47   0.638    -1.350116      2.2024
           _cons |    6.27604    2.55131     2.46   0.014     1.275565    11.27651
-----------------+----------------------------------------------------------------
        /sigma_u |   1.532287   .5934933                      .7172134    3.273647
        /sigma_e |   2.619779    .319429                      2.062899     3.32699
             rho |   .2548981   .1719516                       .043733    .6519567
----------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 2.27               Prob >= chibar2 = 0.066

Note how the results are identical, yet this model is still not significant (Prob > chi2 = 0.5146). Here is the result of a gls random effect model. Typically, these results are very similar to those from an -xtreg, mle regression, but I suspect since these models are not significant then the coefficients from the random noise being modeled are not stable.

. xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, re

Random-effects GLS regression                   Number of obs     =         56
Group variable: encCountry                      Number of groups  =         20

R-squared:                                      Obs per group:
     Within  = 0.0942                                         min =          1
     Between = 0.3931                                         avg =        2.8
     Overall = 0.1474                                         max =          4

                                                Wald chi2(9)      =       7.52
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.5832

----------------------------------------------------------------------------------
 Likert_Prot_Env | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      left_right |  -.0349515   .0270869    -1.29   0.197    -.0880409    .0181379
post_materialist |   1.608542   1.417256     1.13   0.256    -1.169228    4.386312
           mixed |   .1136099   1.086248     0.10   0.917    -2.015398    2.242618
      middle_edu |   .6776388   1.413766     0.48   0.632    -2.093291    3.448569
        high_edu |   1.119278   1.496937     0.75   0.455    -1.814664     4.05322
   middle_income |   .5153663   1.097487     0.47   0.639    -1.635669    2.666402
     high_income |   1.650008   1.050506     1.57   0.116    -.4089457    3.708962
             age |   .0659314   .3149758     0.21   0.834    -.5514097    .6832725
          gender |   .4018984   1.001593     0.40   0.688    -1.561188    2.364985
           _cons |   6.291196   2.825679     2.23   0.026     .7529674    11.82943
-----------------+----------------------------------------------------------------
         sigma_u |  1.3325282
         sigma_e |   2.972652
             rho |  .16731838   (fraction of variance due to u_i)
----------------------------------------------------------------------------------

. estimates store re

Last, here is the fixed effect model with the associated Hausman test. Note for the Hausman command, you need to include the consistent estimate first (fixed effect), followed by the efficient estimate (random effect).

. xtreg Likert_Prot_Env left_right post_materialist mixed middle_edu high_edu middle_income high_income age gender, fe

Fixed-effects (within) regression               Number of obs     =         56
Group variable: encCountry                      Number of groups  =         20

R-squared:                                      Obs per group:
     Within  = 0.1252                                         min =          1
     Between = 0.1500                                         avg =        2.8
     Overall = 0.0800                                         max =          4

                                                F(9,27)           =       0.43
corr(u_i, Xb) = -0.0246                         Prob > F          =     0.9073

----------------------------------------------------------------------------------
 Likert_Prot_Env | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      left_right |  -.0003824    .029903    -0.01   0.990    -.0617382    .0609734
post_materialist |   1.599884    1.75132     0.91   0.369    -1.993528    5.193297
           mixed |  -.1550012   1.331419    -0.12   0.908    -2.886848    2.576846
      middle_edu |   .8216253   1.807823     0.45   0.653     -2.88772    4.530971
        high_edu |   .7097497   1.923032     0.37   0.715    -3.235987    4.655486
   middle_income |   .5793292   1.245656     0.47   0.646    -1.976545    3.135204
     high_income |   1.416785   1.146825     1.24   0.227    -.9363048    3.769875
             age |    .020078   .4091091     0.05   0.961    -.8193444    .8595005
          gender |    .503069   1.285108     0.39   0.699    -2.133754    3.139892
           _cons |   6.398284   3.499097     1.83   0.079    -.7812707    13.57784
-----------------+----------------------------------------------------------------
         sigma_u |  2.4549786
         sigma_e |   2.972652
             rho |  .40548239   (fraction of variance due to u_i)
----------------------------------------------------------------------------------
F test that all u_i=0: F(19, 27) = 1.60                      Prob > F = 0.1298

. estimates store fe

. hausman fe re

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference       Std. err.
-------------+----------------------------------------------------------------
  left_right |   -.0003824    -.0349515        .0345691        .0126683
post_mater~t |    1.599884     1.608542       -.0086577        1.028839
       mixed |   -.1550012     .1136099       -.2686111        .7698973
  middle_edu |    .8216253     .6776388        .1439865        1.126716
    high_edu |    .7097497     1.119278       -.4095284        1.207159
middle_inc~e |    .5793292     .5153663        .0639629          .58922
 high_income |    1.416785     1.650008       -.2332234        .4600476
         age |     .020078     .0659314       -.0458534        .2610757
      gender |     .503069     .4018984        .1011705        .8051789
------------------------------------------------------------------------------
                          b = Consistent under H0 and Ha; obtained from xtreg.
           B = Inconsistent under Ha, efficient under H0; obtained from xtreg.

Test of H0: Difference in coefficients not systematic

    chi2(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
            =  12.83
Prob > chi2 = 0.1706

.

The Hausman test for these two models (neither of which can be trusted/used since neither are significant) would indicate that it is fine to use random effects as the coefficients are not statistically different from those found using a fixed effect model. In this case, it is because the coefficients are so consistently insignificant.

[Daniel Geiter]

Hi again and thanks for the reply. Can you explain why you excluded WID_gini_NI from the models?

[JJ Kovach]

Hausman test is based on the coefficients of variables in both models. If additional variables are in one of the models, they will not be considered, yet their impact on the other coefficients in that model is still in play. Since you were interested in the Hausman test between fixed and random effects, I excluded the variables with no within-entity variation as they are collinear in a fixed effect model and drop out. You can include the time invariant variables if you want, and compare the models.
A few other comments:
1. Trying to understand the statistical differences between different models is difficult if none of the models fit the data. Please find a more appropriate dataset to use.
2. This dataset has 80 observations, yet only uses 52 due to missing data. This leads to a singleton problem as one of your encCountry has only 1 observation, and 5 only have 2 observations. This creates problems as noted in 1.
3. While the Hausman test is often considered a 'gold standard' in choosing between fixed and random effects, I would argue that the decision should be based on what model specification most appropriately addresses the research question. As the title in the post indicates random slopes, perhaps that is what you are really interested in examining. I am unaware of a Hausman test comparison for a random slope model, perhaps there is one. There are however tests to verify that random slopes (as well as intercepts) are different from 0.

Good luck

[Daniel Geiter]

yet their impact on the other coefficients in that model is still in play

This would be my exact problem here. I want to include the time invariant variable in my random effects/mixed model since I assume it will have an effect on the coefficients of the other variables that are also included in the fe model. But this doesn't seem to be possible with the , re command, which is why I am using mixed instead. And here I am stuck, because Stata in many cases is not able to calculate the hausman test for mixed in comparison with , fe. So if you know how to calculate hausman when the random/mixed model includes a time invariant variable, it would help me massively!

1. Trying to understand the statistical differences between different models is difficult if none of the models fit the data. Please find a more appropriate dataset to use.
2. This dataset has 80 observations, yet only uses 52 due to missing data. This leads to a singleton problem as one of your encCountry has only 1 observation, and 5 only have 2 observations. This creates problems as noted in 1.

I think, with these two points you are referring to the data example, I provided, right? It really seems like it is not very useful to only provide 100 observations (or even less) to enable someone to recalculate such a mixed model. I reckon, a lot more observations are necessary. Unfortunately, I wasn't able to attach the full dataset. Maybe because the file is too large. Can you tell me, if there is any other possibility how I can attach a longer data example without creating a post that is 2 meters long?

Thank you very much again!

[JJ Kovach]

But this doesn't seem to be possible with the , re command

Have you tried? Works just fine. Time-invariant variables can be incorporated in a random-effect model, then compared to a fixed-effect model using the Hausman test for the time-variant variables (as the time-invariant variables would not be present in the fixed-effect model and thus excluded from the Hausman test). Again though, the Hausman test in this application is simply going to tell you if the between-effects are statistically similar to the within-effects. Note that a random-effect model combines the between and within effects into a single coefficient. If the random-effect coefficient is statistically similar to the fixed-effect coefficient, then a random-effect model and a fixed-effect model will yield similar coefficients, thus either can be used. If the Hausman test is statistically significant, it means the coefficients are different such that the between-entity effects are different from the within-entity effects. If this is the case, then using a random-effect model to examine within-entity effects is not appropriate, as it is polluted by the between-entity effects which are different.

Can you tell me, if there is any other possibility how I can attach a longer data example

Have you tried one of the Stata-provided data sets? perhaps

use https://www.stata-press.com/data/r18/nlswork.dta

Or others may be more appropriate for your setting to build examples to experiment with.