library(ordinal) # nur für die Daten
#
#

wine_ord <- wine

library(VGAM) # kennt auch ein wine, aber anders

# propodds verwendet >= 
m1 <- vglm(rating ~ contact + temp, data = wine_ord, 
           family = propodds())
coef(m1)

# cumulative mit reverse = FALSE das klassische <=
m2 <- vglm(rating ~ contact + temp, data = wine_ord, 
           family = cumulative(reverse = FALSE, parallel = TRUE))
coef(m2)

# kummulative log Chancen 
predict(m2, newdata = data.frame(contact = "no", temp ="cold"), 
        untransform = FALSE)

# kummulative Wkeiten
predict(m2, newdata = data.frame(contact = "no", temp ="cold"), 
        untransform = TRUE)
# hier wird kummuliert
exp(coef(m2)[1])/(1 + exp(coef(m2)[1]))
exp(coef(m2)[2])/(1 + exp(coef(m2)[2]))
exp(coef(m2)[3])/(1 + exp(coef(m2)[3]))
exp(coef(m2)[4])/(1 + exp(coef(m2)[4]))

# Zurückrechnen auf einzelne Wkeiten
# z.b. für Klasse 3
# Wkeit <= 3 - Wkeit <= 4
exp(coef(m2)[3])/(1 + exp(coef(m2)[3])) - exp(coef(m2)[2])/(1 + exp(coef(m2)[2]))


predict(m2, newdata = data.frame(contact = "no", temp ="cold"), 
        type = "response")

# Wkeit <= 1 bei contact yes
exp(coef(m2)[1] + coef(m2)[5])/(1 + exp(coef(m2)[1] + coef(m2)[5]))

# kummulative Wkeiten
predict(m2, newdata = data.frame(contact = "yes", temp ="cold"), 
        untransform = TRUE)

exp(coef(m2)[2] + coef(m2)[5])/(1 + exp(coef(m2)[2] + coef(m2)[5]))

# Einzel-Wkeiten
predict(m2, newdata = data.frame(contact = "yes", temp ="cold"), 
        type = "response")

#------ Sequentielles Modell

m3 <- vglm(rating ~ contact + temp, data = wine_ord, 
           family = sratio(link = "logit", parallel = TRUE))

predict(m3, newdata = data.frame(contact = "no", temp ="cold"), 
        untransform = TRUE)
# hier wird kummuliert
exp(coef(m3)[1])/(1 + exp(coef(m3)[1]))
exp(coef(m3)[2])/(1 + exp(coef(m3)[2]))
exp(coef(m3)[3])/(1 + exp(coef(m3)[3]))
exp(coef(m3)[4])/(1 + exp(coef(m3)[4]))

# vergleiche zu kumulativen Modell
predict(m2, newdata = data.frame(contact = "no", temp ="cold"), 
        untransform = TRUE)

# vergleiche wiederum zu multinomialen Modell
m4 <- vglm(rating ~ contact + temp, data = wine_ord, 
          family = multinomial())


# multinomial (am flexibelsten, Berücksichtigt nicht ordinale struktur)
predict(m4, newdata = data.frame(contact = "no", temp ="cold"), 
        type = "response")


# sequential ordinale struktur)
predict(m3, newdata = data.frame(contact = "no", temp ="cold"), 
        type = "response")

# multinomial (am flexibelsten, Berücksichtigt nicht ordinale struktur)
predict(m2, newdata = data.frame(contact = "no", temp ="cold"), 
        type = "response")