MultHomog: Specify a Multiplicative Interaction with Homogeneous Effects in a gnm Model Formula

Description

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

Usage

MultHomog(..., inst = NULL)

Value

A list with the anticipated components of a "nonlin" function:

predictors: the factors passed to MultHomog
common: an index to specify that common effects are to be estimated across the factors
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.

Arguments

...: a comma-separated list of two or more factors.
inst: (optional) an integer specifying the instance number of the term.

Author

Heather Turner

Details

MultHomog specifies instances of a multiplicative interaction in which the constituent multipliers are the effects of two or more factors and the effects of these factors are constrained to be equal when the factor levels are equal. Thus the interaction effect would be $γ_{i} γ_{j} . . .$ for an observation with level $i$ of the first factor, level $j$ of the second factor and so on, where $γ_{l}$ is the effect for level $l$ of the homogeneous multiplicative factor.

If the factors passed to MultHomog do not have exactly the same levels, the set of levels is taken to be the union of the factor levels, sorted into increasing order.

References

Goodman, L. A. (1979) Simple Models for the Analysis of Association in Cross-Classifications having Ordered Categories. J. Am. Stat. Assoc., 74(367), 537-552.

Examples

Run this code

set.seed(1)

###  Fit an association model with homogeneous row-column effects
rc1 <- gnm(Freq ~ r + c + Diag(r,c) + MultHomog(r, c),
           family = poisson, data = friend)
rc1

if (FALSE) {
###  Extend to two-component interaction
rc2 <- update(rc1, . ~ . + MultHomog(r, c, inst = 2),
              etastart = rc1$predictors)
rc2
}

### For factors with a large number of levels, save time by
### setting diagonal elements to NA rather than fitting exactly;
### skipping start-up iterations may also save time
dat <- as.data.frame(friend)
id <- with(dat, r == c)
dat[id,] <- NA
rc2 <- gnm(Freq ~ r + c + instances(MultHomog(r, c), 2),
           family = poisson, data = dat, iterStart = 0)

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