
KolmogorovSmirnov 
ShapiroWilk 
Statistics 
df 
Sig. 
Statistics 
df 
Sig. 
 eGFR Data (figure 1)







eGFR Value 
0.054 
3776 
<0.001 
0.985 
3776 
<0.001 
 ln(eGFR) Data (figure 2)







ln(eGFR) Value 
0.101 
3776 
<0.001 
0.917 
3776 
<0.001 
In this sample of the data set, since the total number of observations number
is greater than 2000, the KolmogorovSmirnov test is used to test the normality
assumption of the dependent variable. From the Table 1 above, it can be concluded
that the statistics resulted from KolmogorovSmirnov test is significant, meaning
that H0 from the hypothesis is rejected and the sample data is assumed to be
statistically different from a normal population. The results of the ShapiroWilk
test also agreed with this. Therefore GLMM models are performed instead of LMM
models in order to model the dependent variable which does not follow a normal
distribution. However, the dependent variable should follow one of the known
distributions from the exponential family.
Even if the dependent variable (which is eGFR) is transformed to the log domain,
the distribution is still not normally distributed as can be seen from Figure 2 and
Table 1b. Therefore, eGFR itself is used in the model formulation assuming a
gamma distribution. This assumption is made in formulation of GLMM models 35. 