gnm: Topo – R documentation

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Topo

Topological Interaction of Factors

Description

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

Usage

Topo(..., spec = NULL)

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.

Examples

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))

gnm

Generalized Nonlinear Models

v1.1-1

GPL-2 | GPL-3

Authors

Heather Turner [aut, cre] (<https://orcid.org/0000-0002-1256-3375>), David Firth [aut] (<https://orcid.org/0000-0003-0302-2312>), Brian Ripley [ctb], Bill Venables [ctb], Douglas M. Bates [ctb], Martin Maechler [ctb] (<https://orcid.org/0000-0002-8685-9910>)

Initial release