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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