Improved Approximations for Multilevel Models with Binary Responses

SUMMARY This paper discusses the use of improved approximations for the estimation of generalized linear multilevel models where the response is a proportion. Simulation studies by Rodriguez and Goldman have shown that in extreme situations large biases can occur, most notably when the response is binary, the number of level 1 units per level 2 unit is small and the underlying random parameter values are large. An improved approximation is introduced which largely eliminates the biases in the situation described by Rodriguez and Goldman. Keywortis: �BINARY RESPONSE; GENERALIZED LINEAR MODEL; HIERARCHICAL DATA; MARGINAL MODEL; MULTILEVEL MODEL; QUASI-LIKELIHOOD; UNIT-SPECIFIC MODEL