Premium
Estimation in large cross random‐effect models by data augmentation
Author(s) -
Clayton D.,
Rasbash J.
Publication year - 1999
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/1467-985x.00146
Subject(s) - categorical variable , algorithm , generalized linear mixed model , random effects model , computation , computer science , metric (unit) , macro , linear model , mixed model , generalized linear model , mathematics , machine learning , medicine , meta analysis , operations management , economics , programming language
Estimation in mixed linear models is, in general, computationally demanding, since applied problems may involve extensive data sets and large numbers of random effects. Existing computer algorithms are slow and/or require large amounts of memory. These problems are compounded in generalized linear mixed models for categorical data, since even approximate methods involve fitting of a linear mixed model within steps of an iteratively reweighted least squares algorithm. Only in models in which the random effects are hierarchically nested can the computations for fitting these models to large data sets be carried out rapidly. We describe a data augmentation approach to these computational difficulties in which we repeatedly fit an overlapping series of submodels, incorporating the missing terms in each submodel as ‘offsets’. The submodels are chosen so that they have a nested random‐effect structure, thus allowing maximum exploitation of the computational efficiency which is available in this case. Examples of the use of the algorithm for both metric and discrete responses are discussed, all calculations being carried out using macros within the MLwiN program.