Generalized linear array models with applications to multidimensional smoothing

I. D. Currie, M. Durban, P. H C Eilers

Research output: Contribution to journalArticlepeer-review

135 Citations (Scopus)


Data with an array structure are common in statistics, and the design or regression matrix for analysis of such data can often be written as a Kronecker product. Factorial designs, contingency tables and smoothing of data on multidimensional grids are three such general classes of data and models. In such a setting, we develop an arithmetic of arrays which allows us to define the expectation of the data array as a sequence of nested matrix operations on a coefficient array. We show how this arithmetic leads to low storage, high speed computation in the scoring algorithm of the generalized linear model. We refer to a generalized linear array model and apply the methodology to the smoothing of multidimensional arrays. We illustrate our procedure with the analysis of three data sets: mortality data indexed by age at death and year of death, spatially varying microarray background data and disease incidence data indexed by age at death, year of death and month of death. © 2006 Royal Statistical Society.

Original languageEnglish
Pages (from-to)259-280
Number of pages22
JournalJournal of the Royal Statistical Society: Series B (Statistical Methodology)
Issue number2
Publication statusPublished - Apr 2006


  • Arrays
  • B-splines
  • Generalized linear models
  • Kronecker products
  • Mixed models
  • Penalties
  • Smoothing
  • Yates's algorithm


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