Ignoring the effect of clustering in a two-level hierarchical model results in standard errors of the estimated coefficients which are too small and, consequently, P-values which are too large.
A simple regression method of dealing with clustered data is to use the cluster as the unit of investigation, aggregate the data using an appropriate numerical summary measure for each cluster, and then use this summary measure as the explanatory variable in the regression model.
It is not possible to allow for the effects of covariates which vary for level 1 units in either an aggregate level analysis using summary measures or when using robust standard errors in the regression analysis of clustered data.
The generalized estimating approach to dealing with clustered data adjusts the parameter estimates, standard errors, confidence intervals and p-values in a regression analysis to take account of the clustering of the data.
The generalized estimating equations approach to estimation makes distributional assumptions about the dependent variable in the regression model but does not assume that the between-cluster residuals are Normally distributed.