Using the LR test to discriminate between a random intercepts and a random slopes multilevel model

Hi all. I have Brazilian survey data with political and socio-economic variables. To this dataset, I added municipal-level information on whether a municipality where the survey respondent lives has one or more media outlets (binary), measured by the variable "tipo_deserto_dummy".

I want to estimate multilevel models with this data and want to know which type of model presents a better fit to the data: random intercepts or random slopes. To that end, I want to run a LR test.

The LR test's output follows below.

The questions are:

a) Does the LR test's result show that the random intercepts' model is preferred over the random slopes model?

b) Is there any problem with the LR test?

Thank you.

Code:

 quietly: mixed diff_feeling_therm_cand tipo_deserto_dummy educ party_id pol_interest intensity_follow_media retrosp_eval_socio unemployed sexo ec_casado beneficiary_bf rel_evang rel_cat color_nowhite || ibge_mun_code:
est store randint
quietly: mixed diff_feeling_therm_cand tipo_deserto_dummy educ party_id pol_interest intensity_follow_media retrosp_eval_socio unemployed sexo ec_casado beneficiary_bf rel_evang rel_cat color_nowhite || ibge_mun_code: tipo_deserto_dummy
est store randslope
lrtest randint randslope

Likelihood-ratio test                                                LR chi2(1)  =      0.01
(Assumption: randint nested in randslope)             Prob > chi2 =    0.9373

Note: The reported degrees of freedom assumes the null hypothesis is not on the boundary of the parameter space.  If this is not true, then the reported test is conservative.