Topological Interaction of Factors

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Description

Given two or more factors Topo creates an interaction factor as specified by an array of levels, which may be arbitrarily structured.

Usage

1

Arguments

...

two or more factors

spec

an array of levels, with dimensions corresponding to the number of levels of each factor in the interaction

Value

A factor of levels extracted from the levels array given in spec, using the given factors as index variables.

Author(s)

David Firth

References

Erikson, R., GoldThorpe, J. H. and Portocarero, L. (1982) Social Fluidity in Industrial Nations: England, France and Sweden. Brit. J. Sociol. 33(1), 1-34.

Xie, Y. (1992) The Log-multiplicative Layer Effect Model for Comparing Mobility Tables. Am. Sociol. Rev. 57(3), 380-395.

See Also

Symm and Diag for special cases

Examples

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set.seed(1)

### Collapse to 7 by 7 table as in Erikson (1982)

erikson <- as.data.frame(erikson)
lvl <- levels(erikson$origin)
levels(erikson$origin) <- levels(erikson$destination) <-
    c(rep(paste(lvl[1:2], collapse = " + "), 2), lvl[3],
      rep(paste(lvl[4:5], collapse = " + "), 2), lvl[6:9])
erikson <- xtabs(Freq ~ origin + destination + country, data = erikson)

### Create array of interaction levels as in Table 2 of Xie (1992)

levelMatrix <- matrix(c(2, 3, 4, 6, 5, 6, 6,
                        3, 3, 4, 6, 4, 5, 6,
                        4, 4, 2, 5, 5, 5, 5,
                        6, 6, 5, 1, 6, 5, 2,
                        4, 4, 5, 6, 3, 4, 5,
                        5, 4, 5, 5, 3, 3, 5,
                        6, 6, 5, 3, 5, 4, 1), 7, 7, byrow = TRUE)

### Fit the levels models given in Table 3 of Xie (1992)

## Null association between origin and destination
nullModel <- gnm(Freq ~ country:origin + country:destination,
                 family = poisson, data = erikson)

## Interaction specified by levelMatrix, common to all countries
commonTopo <- update(nullModel, ~ . +
                     Topo(origin, destination, spec = levelMatrix))

## Interaction specified by levelMatrix, different multiplier for
## each country
multTopo <- update(nullModel, ~ . +
                   Mult(Exp(country),
                        Topo(origin, destination, spec = levelMatrix)))

## Interaction specified by levelMatrix, different effects for
## each country
separateTopo <- update(nullModel, ~ . +
                       country:Topo(origin, destination,
                                    spec = levelMatrix))

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