library(vcdExtra)
library(gnm)
women <- subset(VisualAcuity, gender=="female", select=-gender)
indep <- glm(Freq ~ right + left, data = women, family=poisson)
mosaic(indep, residuals_type="rstandard", gp=shading_Friendly,
main="Vision data: Independence (women)" )
# Quasi-independence: ignore the diagonal cells by fitting them exactly
quasi.indep <- glm(Freq ~ right + left + Diag(right, left),
data = women, family = poisson)
mosaic(quasi.indep, residuals_type="rstandard", gp=shading_Friendly,
main="Quasi-Independence (women)" )
# Symmetry: test F[i,j] = F[j,i]. Note that the model does not include
# the 'main' effects of right and left, so assumes marginal homogeneity
symmetry <- glm(Freq ~ Symm(right, left),
data = women, family = poisson)
mosaic(symmetry, residuals_type="rstandard", gp=shading_Friendly,
main="Symmetry model (women)" )
# Quasi-symmetry: allow different marginal frequencies for left and right
quasi.symm <- glm(Freq ~ right + left + Symm(right, left),
data = women, family = poisson)
mosaic(quasi.symm, residuals_type="rstandard", gp=shading_Friendly,
main="Quasi-Symmetry model (women)")
# model comparisons: for *nested* models
anova(indep, quasi.indep, quasi.symm, test="Chisq")
anova(symmetry, quasi.symm, test="Chisq")
# model summaries, with AIC and BIC
models <- glmlist(indep, quasi.indep, symmetry, quasi.symm)
summarise(models)