### Abstract

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 language | English |
---|---|

Pages (from-to) | 259-280 |

Number of pages | 22 |

Journal | Journal of the Royal Statistical Society: Series B (Statistical Methodology) |

Volume | 68 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2006 |

### Fingerprint

### Keywords

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

### Cite this

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*,

*68*(2), 259-280. https://doi.org/10.1111/j.1467-9868.2006.00543.x

}

*Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, vol. 68, no. 2, pp. 259-280. https://doi.org/10.1111/j.1467-9868.2006.00543.x

**Generalized linear array models with applications to multidimensional smoothing.** / Currie, I. D.; Durban, M.; Eilers, P. H C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generalized linear array models with applications to multidimensional smoothing

AU - Currie, I. D.

AU - Durban, M.

AU - Eilers, P. H C

PY - 2006/4

Y1 - 2006/4

N2 - 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.

AB - 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.

KW - Arrays

KW - B-splines

KW - Generalized linear models

KW - Kronecker products

KW - Mixed models

KW - Penalties

KW - Smoothing

KW - Yates's algorithm

UR - http://www.scopus.com/inward/record.url?scp=33644769535&partnerID=8YFLogxK

U2 - 10.1111/j.1467-9868.2006.00543.x

DO - 10.1111/j.1467-9868.2006.00543.x

M3 - Article

VL - 68

SP - 259

EP - 280

JO - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

JF - Journal of the Royal Statistical Society: Series B (Statistical Methodology)

SN - 1369-7412

IS - 2

ER -