Given two ordered factors in a square, n x n frequency table, Crossings creates an n-1 column matrix corresponding to different degrees of difficulty in crossing from one level to the next, as described by Goodman (1972).

Usage

Crossings(...)

...

Two factors

Value

For two factors of n levels, returns a binary indicator matrix of n*n rows and n-1 columns.

References

Goodman, L. (1972). Some multiplicative models for the analysis of cross-classified data. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA: University of California Press, pp. 649-696.

Author

Michael Friendly and Heather Turner

glm, gnm for model fitting functions for frequency tables

Diag, Mult, Symm, Topo for similar extensions to terms in model formulas.

Examples

data(Hauser79)
# display table
structable(~Father+Son, data=Hauser79)
#>        Son UpNM LoNM  UpM  LoM Farm
#> Father
#> UpNM       1414  521  302  643   40
#> LoNM        724  524  254  703   48
#> UpM         798  648  856 1676  108
#> LoM         756  914  771 3325  237
#> Farm        409  357  441 1611 1832

hauser.indep <- gnm(Freq ~ Father + Son, data=Hauser79, family=poisson)
hauser.CR <- update(hauser.indep, ~ . + Crossings(Father,Son))
LRstats(hauser.CR)
#> Likelihood summary table:
#>              AIC    BIC LR Chisq Df Pr(>Chisq)
#> hauser.CR 318.63 334.47   89.914 12  5.131e-14 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

hauser.CRdiag <- update(hauser.indep, ~ . + Crossings(Father,Son) + Diag(Father,Son))
LRstats(hauser.CRdiag)
#> Likelihood summary table:
#>                  AIC    BIC LR Chisq Df Pr(>Chisq)
#> hauser.CRdiag 298.95 318.45   64.237  9   2.03e-10 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1