Influence diagnostics for generalized linear mixed models: a gradient-like statistic

In the literature, many influence measures proposed for Generalized Linear Mixed Models (GLMMs) require the information matrix that can be difficult to calculate. In the present paper, a known influence measure is approximated to get a simpler form, for which the information matrix is no more necessary. The proposed measure is showed to have a form similar to the gradient statistic, recently introduced. Good performances have been obtained through simulation studies