The generalized linear model was an extension of the linear model y = Xβ+ ε to allow the responses y from the exponential family. The mixed effect models allowed

for a much more general treatment of ε. We now switch our attention to the linear predictor η = Xβ. We want to make this more flexible. There are a wide variety of available methods, but it is best to start with simple regression. The methods devel-

oped here form part of the solution to the multiple predictor problem.