IMPROVED APPROXIMATIONS FOR MULTILEVEL MODELS WITH BINARY RESPONSES

This paper discusses the use of improved approximations for the estima tion of generalized linear multilevel models where the response is a p roportion. Simulation studies by Rodriguez and Goldman have shown that in extreme situations large biases can occur, most notably when the r esponse is binary, the number of level 1 units per level 2 unit is sma ll and the underlying random parameter values are large. An improved a pproximation is introduced which largely eliminates the biases in the situation described by Rodriguez and Goldman.