Multiplicative interaction {gnm} | R Documentation |
Mult
is a symbolic wrapper to indicate a multiplicative interaction in
the formula argument to gnm
.
Exp
is a symbolic wrapper to indicate an exponeniated multiplier
in a Mult
term.
Mult(..., multiplicity = 1) Exp(multiplier)
... |
a comma-separated list of two or more symbolic expressions, which represent the constituent multipliers in each component of the interaction. |
multiplicity |
a positive integer specifying the number of components to fit. |
multiplier |
a symbolic expression. |
A multiplicative interaction is either (if multiplicity = 1
)
a product of the form
m_1 m_2 ... m_n,
where the constituent multipliers m_1, m_2, ..., m_n are linear
predictors; or (if multiplicity
is greater than 1) a sum of
such “components”, each of which is a product of the same
linear predictors (but with different parameters).
Mult
may be used to specify a multiplicative interaction in the
formula
argument to gnm
. The desired number of
components in the interaction is specified by multiplicity
.
Models for the constituent multipliers are specified symbolically
as unspecified arguments to Mult
. These symbolic expressions
are interpreted in the same way as the right hand side of a formula in
an object of class "formula"
. In particular, an intercept term
is added by default. Offsets can be added to constituent multipliers,
using offset
.
Exp
is a companion function to Mult
, which may be used to
specify an exponentiated constituent multiplier, so that the
multiplier is constrained to be nonnegative.
Mult
returns a list of objects of class "Mult"
, with one element
for each multiplicative component. A "Mult"
object is a list of deparsed
expressions representing the factors in the multiplicative interaction.
Exp
returns an object of class "Exp"
which is a deparsed
expression representing the multiplier to be exponentiated.
These functions should only be used in formulae passed to gnm
.
Heather Turner
Vargas, M, Crossa, J, van Eeuwijk, F, Sayre, K D and Reynolds, M P (2001). Interpreting treatment by environment interaction in agronomy trials. Agronomy Journal 93, 949–960.
set.seed(1) ## Using 'Mult' with 'Exp' to constrain the first constituent multiplier data(yaish) ## Fit the "UNIDIFF" mobility model across education levels unidiff <- gnm(Freq ~ educ*orig + educ*dest + Mult(Exp(-1 + educ), -1 + orig:dest), family = poisson, data = yaish, subset = (dest != 7)) ## Not run: ## (this example can take quite a while to run) ## ## Using 'multiplicity' > 1 data(wheat) yield.scaled <- wheat$yield * sqrt(3/1000) treatment <- factor(paste(wheat$tillage, wheat$summerCrop, wheat$manure, wheat$N, sep = "")) bilinear2 <- gnm(yield.scaled ~ year + treatment + Mult(year, treatment, multiplicity = 2), family = gaussian, data = wheat) ## End(Not run)