Multiplicative interaction | R Documentation |
A function of class "nonlin"
to specify a multiplicative interaction in
the formula argument to gnm
.
Mult(..., inst = NULL)
... |
a comma-separated list of two or more symbolic expressions representing the constituent multipliers in the interaction. |
inst |
a positive integer specifying the instance number of the term. |
Mult
specifies instances of a multiplicative interaction,
i.e. a product of the form
m_1 m_2 ... m_n,
where the constituent multipliers m_1, m_2, ..., m_n
are linear
or nonlinear predictors.
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"
, except that an intercept term
is not added by default. Offsets can be added to constituent
multipliers, using offset
.
The family of multiplicative interaction models include row-column association models for contingency tables (e.g., Agresti, 2002, Sec 9.6), log-multiplicative or UNIDIFF models (Erikson and Goldthorpe, 1992; Xie, 1992), and GAMMI models (van Eeuwijk, 1995).
A list with the required components of a "nonlin"
function:
predictors |
the expressions passed to |
term |
a function to create a deparsed mathematical expression of the term, given labels for the predictors. |
call |
the call to use as a prefix for parameter labels. |
Heather Turner
Agresti, A (2002). Categorical Data Analysis (2nd ed.) New York: Wiley.
Erikson, R and Goldthorpe, J H (1992). The Constant Flux. Oxford: Clarendon Press.
van Eeuwijk, F A (1995). Multiplicative interaction in generalized linear models. Biometrics 51, 1017-1032.
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.
Xie, Y (1992). The log-multiplicative layer effect model for comparing mobility tables. American Sociological Review 57, 380-395.
gnm
, formula
, instances
,
nonlin.function
, MultHomog
set.seed(1)
## Using 'Mult' with 'Exp' to constrain the first constituent multiplier
## to be non-negative
## Fit the "UNIDIFF" mobility model across education levels
unidiff <- gnm(Freq ~ educ*orig + educ*dest +
Mult(Exp(educ), orig:dest),
family = poisson, data = yaish, subset = (dest != 7))
## Not run:
## (this example can take quite a while to run)
##
## Fitting two instances of a multiplicative interaction (i.e. a
## two-component interaction))
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 +
instances(Mult(year, treatment), 2),
family = gaussian, data = wheat)
formula(bilinear2)
## yield.scaled ~ year + treatment + Mult(year, treatment, inst = 1) +
## Mult(year, treatment, inst = 2)
## End(Not run)
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