Kolmogorov-Smirnov

Shapiro-Wilk

Statistics

df

Sig.

Statistics

df

Sig.
  1. eGFR Data (figure 1)

 

 

 

 

 

 

eGFR Value

0.054

3776

<0.001

0.985

3776

<0.001
  1. 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 Kolmogorov-Smirnov 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 Kolmogorov-Smirnov 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 Shapiro-Wilk 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 3-5.
Table 2: Normality test results.
(a) for eGFR data (Figure 1) and
(b) for ln(eGFR) data (Figure 2).