R: Specify a Product of Predictors in a gnm Model Formula

Multiplicative interaction {gnm} | R Documentation

## Specify a Product of Predictors in a gnm Model Formula

### Description

A function of class `"nonlin"` to specify a multiplicative interaction in the formula argument to `gnm`.

### Usage

    Mult(..., inst = NULL)

### Arguments

`...` | 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.

### Details

`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).

### Value

A list with the required components of a `"nonlin"` function:

`predictors` | the expressions passed to `Mult`
`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.

### Author(s)

Heather Turner

### References

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.

### See Also

`gnm`, `formula`, `instances`, `nonlin.function`, `MultHomog`

### Examples

    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)

[Package gnm version 1.0-8 Index]