Grouped data include repeated measures data, longitudinal data,
functional data and multilevel data as special cases. For such data,
we define SNR models as

where is the response of subject at design point , is a covariate in a general domain , is a known function of which depends on a vector of parameter and a vector of unknown non-parametric function ; and . For grouped data, usually observations are correlated within a subject but are independent between subjects. In this case W is in the form of block diagonal. Again, each function is modeled using an SS ANOVA model (). Again, assume that depends on a parsimonious set of parameters .

For model (), we denote , , , , , and . Then model () can be written in the same vector form as ().

Yuedong Wang 2004-05-19