You need to specify more. The question is very very vague. If you're interested in getting p-values after fitting the model, try using lmerTest package.

If not, specify what exactly you want.

Dear Dhritiman Chakrabarti , my question was not in getting p-value after fitting a model. In case of getting a more simpler simpler model than full model, the restricted model should be checked using different tests for its significance. One of the test is lrtest. So, Is that possible to use lrtest for comparing a Generalized linear mixed effect (GLMER) restricted and full model ? Hope you get some hint.

Only someone who is familiar with R would understand the question.

I suppose you are fitting a multilevel model in R using the lme4 package. The question is how to compare two models. Specifically, how to perform a likelihood ratio test. Correct?

Much has been written about this. Quickly two suggestions:

1. Likelihood ratio tests - If you have two nested models you can use this test. In R post lme4 lmer() or glmer() you can use anova() function to perform it. Yes it is called anova but it does likelihood ratio test which ultimately uses Chi-square test.

2. You can use change in criteria information such AIC and BIC. The goal is to reduce the AIC or BIC and a lot is written about this. These are available though the functions AIC() or BIC() or even through summary() of a fitted lmer() or glmer().

Note by default lmer() has REML = TRUE. So all the above would be incorrect. Change to REML = FALSE.

A good reference for much more is

Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models (Analytical Methods for Social Research). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511790942

That book offers more creative ways to approach multilevel regression modeling in R. So you can move beyond the above two suggestions. However, it is not a book to read fast.

I agree with Orvalho Augusto. These are the easiest methods. Just remember that to do these comparisons, you need to to Maximum likelihood (ML) method of estimation.

Dear Orvalho Augusto and Dhritiman Chakrabarti , Thank you very much!