Crossings Interaction of Factors
Crossings.Rd
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).
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.
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