  We present a novel method for the estimation of variance parameters in
generalised linear mixed models. The method has its roots in Harville (1977)'s
work, but it is able to deal with models that have a precision matrix for the
random-effect vector that is linear in the inverse of the variance parameters
(i.e., the precision parameters). We call the method SOP (Separation of
Overlapping Precision matrices). SOP is based on applying the method of
successive approximations to easy-to-compute estimate updates of the variance
parameters. These estimate updates have an appealing form: they are the ratio
of a (weighted) sum of squares to a quantity related to effective degrees of
freedom. We provide the sufficient and necessary conditions for these estimates
to be strictly positive. An important application field of SOP is penalised
regression estimation of models where multiple quadratic penalties act on the
same regression coefficients. We discuss in detail two of those models:
penalised splines for locally adaptive smoothness and for hierarchical curve
data. Several data examples in these settings are presented.
