mkran
generates random effect terms from simple grouping
variables, for use in nonparametric mixed-effect models as described
in Gu and Ma (2005a, b). The syntax of the formula resembles that
of similar utilities for linear and nonlinear mixed-effect models,
as described in Pinheiro and Bates (2000).
Currently, mkran
takes only two kinds of basic formulas,
~1|grp2
or ~grp1|grp2
. Both grp1
and
grp2
should be factors, and for the second formula, the
levels of grp2
should be nested under those of grp1
.
The Z matrix is determined by grp2
. When observations are
ordered according to the levels of grp2
, the Z matrix is
block diagonal of 1 vectors.
The Sigma matrix is diagonal. For ~1|grp2
, it has one tuning
parameter. For ~grp1|grp2
, the number of parameters equals
the number of levels of grp1
, with each parameter shared by
the grp2
levels nested under the same grp1
level.
mkran1
adds together two independent random effects, and can
be used recursively to add more than two terms. The arguments are
of the form of the value of mkran
or mkran1
, which may
or may not be created by mkran
or mkran1
.
Multiple terms of random effects can also be specified via the likes
of mkran(~1|grp1+1|grp2,data)
, which is equivalent to
mkran1(mkran(~1|grp1,data),mkran(~1|grp2,data))
.