Do I need to stick to mixed effect model when random effect is insignficant?

[Lao_feng]

I am doing a logistic regression analysis with random intercept in the model to account for within cluster correlation.There are 3 levels in my data:

Level 1: individual subject

Level 2: Family (some subjects from the same family), the variable is fam_num

Level 3: Village, the variable clu_num

The model included country, age, gender, education and marrital status.

My codes are:

proc glimmix data=work0 NOCLPRINT;
class  country (ref='Pakistan') clu_num  fam_num age4g(ref='40~49') gender edu2g mar2g ;
model comb2g(ref='0')= country age4g gender edu2g mar2g /solution Link=logit dist=binary
random int /sub=clu_num;
random int /sub=fam_num (clu_num) ;
COVTEST GLM;
run;

I used 'COVTEST GLM' to check if the outcome is independent or not within clusters. The results I got are as follow:

The P value is 0.4115, suggesting the clustering effects are not statistically significant. In such case, can I remove the random effect from model, and use standard logistic regression? Thanks

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error
Intercept	clu_num	0.01724	0.02710
Intercept	fam_n(clu_nu)	0.01920	0.1512

Tests of Covariance Parameters Based on the Residual Pseudo-Likelihood
Label	DF	-2 Res Log P-Like	ChiSq	Pr > ChiSq	Note
Independence	2	10507	0.58	0.4115	MI

[sld]

In general, I believe that the statistical model should match the design. In your study, individuals are not independent: they are clustered within families which are clustered within villages. Your model does not appear to be having any trouble with estimation. So I would keep the mixed model.

Other people may have other opinions.

[Lao_feng]

Thank you for your suggestion !