Data on multidimensional arrays are wide-spread and modelling can easily present storage and computational difficulties, even with modern computers. We present a class of regression models and a computational procedure designed specifically for such data. These models possess some remarkable storage and computational properties which lead to savings of orders of magnitude in both storage and speed over conventional methods. We call this methodology array regression. We illustrate our procedure with the analysis of a large set of count data on deaths from respiratory disease indexed by age of death, year of death and month of death.
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