Pseudo-likelihood methodology for partitioned large and complex samples

Large data sets, either coming from a large number of independent replications, or because of hierarchies in the data with large numbers of within-unit replication, may pose challenges to the data analyst up to the point of making conventional inferential methods, such as maximum likelihood, prohibitive. Based on general pseudo-likelihood concepts, we propose a method to partition such a set of data, analyze each partition member, and properly combine the inferences into a single one. It is shown that the method is fully efficient for independent partitions, while with dependent sub-samples efficiency is sometimes but not always equal to one. It is argued that, for important realistic settings, efficiency is often very high. Illustrative examples enhance insight in the method's operation, while real-data analysis underscores its power for practice.