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I am working with educational data. To do so, I am using the classic three-level hierarchical linear model (student, class and school). I am using the R software lmer package and the stata software. When I perform the residual analysis, the assumptions of homoscedasticity and normality are not met. Here is the adjusted model: m33 <- lmer(pt_ex ~ gen_alun + rep_alun + comp_alun + educ_ee + gen_prof + idad_prof + nro_alun_turm + sase_esc + reg_esc + area_esc + (1|id_esc) + (1|id_turm), REML = T, date = data)

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?

thanks in advance,

[1]: https://i.stack.imgur.com/nffjA.png

enter image description here graph Q-Q graph histogram graph residuals levels 1,2 and 3

ttnphns
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Ricardo Linhares
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Aug 04 '22 at 12:56
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    close enough to a normal –  Aug 04 '22 at 13:20
  • I disagree with @Germania. The distribution is not close to Normal as it's not symmetric. For some perspectives on the effect of skewness see here. – dipetkov Aug 07 '22 at 22:10

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