Mixed models are very popular and widely available in standard software, this is one of the reasons why penalized splines as mixed models have become a common approach in the smoothing context. They provide a unified approach for fitting a large class of complex models (random effects, correlated data, longitudinal analysis, etc.), and standard techniques may be used for estimation and inference.
The extension to two or more dimensions has been a subject of study in recent years, however, the development of this methodology has encounter two main drawbacks: 1) the size of the matrices used in the regression basis leads to heavy computation, and 2) the identifiability constrains needed in a multidimensional additive setting are not easy to implement.
We present a re-parametrization of multidimensional p-splines as mixed models based on the singular value decomposition of the penalty matrix. This representation allows the fit of main smooth terms and interactions avoiding identifiability problems. Array algorithms are adapted to speed up the estimation of fixed and random effects, and the smoothing parameters used in the model.
Keywords: P-splines; Mixed Models; Multidimensional smoothing; Array methods
Biography: Phd in Statistics (1999) Heriott-Watt University, UK.
Associate Prof. at the Department of Statistics, Universidad Carlos III de Madrid, Spain