Dear colleagues, I am working with educational data. To do so, I am using the classic three-level hierarchical linear model (student, class and school).
I'm using the stata version 17 for the analyses. . When I perform the residual analysis, the assumptions of homoscedasticity and normality are not met. Here is the adjusted model: xtmixed pt_ex_9mat gen_alun rep_alun comp_alun b4.educ_ee gen_prof b1.idad_prof nro_alun_turm b1.sase_esc b1.reg_esc area_esc||id_esc:||id_turm:,mle var

Comments:
  1. The dependent variable pt_ex (Exam Score) despite being continuous, has only discrete values ​​(0 to 100).
  2. Regarding the independent variables, with the exception of the variable nro_alun_turm (Number of students in the class), these are nominal/binary categorical.
I thought of using a GLM, namely a Poisson or Negative Binomial multilevel model, but these have infinite support. So, could you try a Gamma, since the two assumptions of the Gaussian model were not met?

can ypu help me with this? any suggestions?

thanks in advance,



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Code:
* Example generated by -dataex-. For more info, type help dataex
clear
input byte(gen_alun rep_alun comp_alun educ_ee) long gen_prof byte idad_prof float nro_alun_turm long sase_esc byte(reg_esc area_esc)
1 0 0 2 1 1 20 1 2 1
1 0 0 6 1 1 20 1 2 1
1 0 0 6 1 1 20 1 2 1
1 0 0 1 1 1 20 1 2 1
1 1 0 1 1 1 20 1 2 1
1 1 0 2 1 1 20 1 2 1
0 1 0 3 1 1 20 1 2 1
0 0 0 2 1 1 20 1 2 1
0 0 0 6 1 1 20 1 2 1
0 1 0 2 1 1 20 1 2 1
1 0 0 2 1 1 26 1 2 1
0 0 0 3 1 1 26 1 2 1
1 1 0 6 1 1 26 1 2 1
1 0 0 6 1 1 26 1 2 1
1 0 0 1 1 1 26 1 2 1
0 0 0 6 1 1 17 1 2 1
0 1 0 6 1 1 17 1 2 1
0 1 0 1 1 1 17 1 2 1
0 1 0 1 1 1 17 1 2 1
0 0 0 6 1 1 17 1 2 1
1 0 0 6 1 1 17 1 2 1
0 1 0 1 1 1 17 1 2 1
1 1 0 1 1 1 17 1 2 1
0 0 0 2 1 1 17 1 2 1
1 0 0 6 1 1 17 1 2 1
1 0 0 1 1 1 17 1 2 1
0 0 0 2 1 1 17 1 2 1
0 1 1 1 1 1 17 1 2 1
1 0 0 2 1 1 17 1 2 1
1 0 0 1 1 1 17 1 2 1
0 1 0 4 1 1 17 1 2 1
0 0 0 4 1 1 17 1 2 1
0 1 0 3 1 1 26 1 2 1
1 1 0 1 1 1 26 1 2 1
1 1 0 4 1 1 26 1 2 1
1 0 0 2 1 1 26 1 2 1
0 1 0 5 1 1 26 1 2 1
0 1 0 1 1 1 26 1 2 1
1 1 0 6 1 1 26 1 2 1
0 0 1 2 1 1 26 1 2 1
1 0 0 4 1 1 26 1 2 1
1 0 0 2 1 1 26 1 2 1
0 0 0 6 1 1 26 1 2 1
0 1 0 1 1 1 26 1 2 1
1 1 0 6 1 1 26 1 2 1
1 1 0 1 1 1 26 1 2 1
1 0 0 1 1 1 26 1 2 1
1 0 0 3 1 1 26 1 2 1
1 0 0 3 1 1 26 1 2 1
0 0 0 6 1 1 26 1 2 1
0 1 0 1 1 1 26 1 2 1
1 1 1 6 1 1 26 1 2 1
1 0 0 1 1 2 20 2 2 1
0 1 0 2 1 2 20 2 2 1
1 1 0 1 1 2 20 2 2 1
1 0 0 1 1 2 20 2 2 1
1 0 0 6 1 2 20 2 2 1
1 0 0 2 1 2 20 2 2 1
1 0 0 1 1 2 20 2 2 1
1 0 0 6 1 2 20 2 2 1
1 0 0 1 1 2 20 2 2 1
0 0 0 3 1 2 20 2 2 1
0 1 0 3 1 2 20 2 2 1
1 1 0 6 1 2 20 2 2 1
0 0 0 6 1 2 20 2 2 1
0 1 0 3 1 2 20 2 2 1
1 0 0 3 1 2 20 2 2 1
1 0 0 3 1 2 20 2 2 1
1 0 0 6 1 2 20 2 2 1
1 1 0 6 1 2 20 2 2 1
1 0 0 1 1 2 20 2 2 1
0 1 0 2 1 2 20 2 2 1
0 1 0 1 0 1 21 1 2 1
0 1 0 1 0 1 21 1 2 1
0 1 1 2 0 1 21 1 2 1
1 0 0 1 0 1 21 1 2 1
0 1 0 1 0 1 21 1 2 1
0 1 0 1 0 1 21 1 2 1
1 0 0 6 0 1 21 1 2 1
1 1 0 1 0 1 21 1 2 1
1 1 0 6 0 1 21 1 2 1
1 0 0 1 0 1 21 1 2 1
1 0 1 1 0 1 21 1 2 1
1 0 0 4 0 1 21 1 2 1
0 0 0 3 0 1 21 1 2 1
1 0 1 5 0 1 21 1 2 1
1 0 0 6 0 1 21 1 2 1
1 0 0 2 0 1 21 1 2 1
1 0 0 1 0 1 21 1 2 1
0 0 0 1 0 1 21 1 2 1
1 0 0 6 0 1 21 1 2 1
0 1 0 6 0 2 21 1 2 1
0 0 0 2 0 2 21 1 2 1
0 0 0 6 0 2 21 1 2 1
0 0 0 2 0 2 21 1 2 1
1 0 0 2 0 2 21 1 2 1
1 1 0 4 0 2 21 1 2 1
1 1 0 2 0 2 21 1 2 1
0 0 0 3 0 2 21 1 2 1
1 0 0 2 0 2 21 1 2 1
end
label values gen_alun nomegen_alun
label def nomegen_alun 0 "Feminino", modify
label def nomegen_alun 1 "Masculino", modify
label values rep_alun rep_alun_2
label def rep_alun_2 0 "Não", modify
label def rep_alun_2 1 "Sim", modify
label values comp_alun comp_alun_2
label def comp_alun_2 0 "Não", modify
label def comp_alun_2 1 "Sim", modify
label values educ_ee educ_ee_nova_2
label def educ_ee_nova_2 1 "Sem habilitação", modify
label def educ_ee_nova_2 2 "1º ciclo", modify
label def educ_ee_nova_2 3 "3º ciclo", modify
label def educ_ee_nova_2 4 "Secundário", modify
label def educ_ee_nova_2 5 "Ensino superior", modify
label def educ_ee_nova_2 6 "Não sabe", modify
label values gen_prof gen_prof_2
label def gen_prof_2 0 "Feminino", modify
label def gen_prof_2 1 "Masculino", modify
label values idad_prof idad_prof_test_3
label def idad_prof_test_3 1 "Até 40 anos", modify
label def idad_prof_test_3 2 "De 40 a 50 anos", modify
label values sase_esc sase_esc_2
label def sase_esc_2 1 "Grupo 1", modify
label def sase_esc_2 2 "Grupo 2", modify
label values reg_esc nomeid_regiao
label def nomeid_regiao 2 "Nordeste", modify
label values area_esc nomeid_area
label def nomeid_area 1 "Interior", modify


Residual plot: Array Array Array Array