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A linear mixed-effects model (LME) is a familiar example of a multilevel parameter structure involving nuisance and structural parameters, as well as parameters that essentially control the model’s complexity. Marginalization over nuisance parameters, such as the restricted maximization likelihood method, has been the usual estimation strategy, but it can involve onerous and complex algorithms to achieve the integrations involved. Parameter cascading is described as a multicriterion optimization algorithm that is relatively simple to program and leads to fast and stable computation. The method is applied to LME, where well-developed marginalization methods are already available. Our results suggest that parameter cascading is at least as good as, if not better than, the available methods. We also extend the LME model to multicurve data smoothing by introducing a basis partitioning scheme and defining roughness penalty terms for both functional fixed effect and random effects. The results are substantially better than those obtained by using the previous LME methods. A supplemental document is available online. [ABSTRACT FROM AUTHOR]

Suppose a decision maker has asked a group of experts to assess subjective probability distributions over some space, and he wishes to find a consensus probability distribution as a function of these. The assumption that finding the consensus distribution commutes with marginalization of the distributions implies that the consensus must be found using a linear opinion pool (weighted average), provided the space being considered contains three or more points. Some of the consequences of this result are discussed. [ABSTRACT FROM AUTHOR]