The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in linear mixed models (LMMs). However, its extension to nonlinear mixed models (NLMMs) is often hampered by analytically intractable integrals. For NLMMs various estimation methods have been suggested, but they have suffered from unsatisfactory biases. In this paper we propose a statistically and computationally efficient REML procedure, based upon hierarchical likelihood. Numerical studies show that the proposed method reduces the biases in the existing methods that we studied. We also study how the current REML procedure for LMMs can be modified to compute the proposed estimators.
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