How do you obtain predicted probabilities for the one-inflated component (nu model) of a one-inflated beta regression in
I have built the following model
zib <- gamlss(prop.abun.max ~ season + time + temp + last.rain.bom + rain + wind + cloud + re(random = ~1|site), sigma.formula = ~1, nu.formula = ~ season + time + temp + last.rain.bom + rain + wind + cloud + re(random = ~1|site), family = BEINF1, data = na.omit(subset2))
I obtain predicted probabilities for the beta distribution component of my model (the mu model) using
head(predict(zib, what = "mu", type = "response"))  0.7519171 0.7366541 0.7605794 0.6904190 0.7578658 0.7280828
This produces values in the range 0-1 which I assume are predicted probabilities.
However, similar code that references the one-inflated component of my model (the nu model) obtains values that are on the range 0.3-4.1. These values are clearly not predicted probabilities as many values are greater than 1.
head(predict(zib, what = "nu", type = "response"), n = 10)  0.6079466 0.9698540 0.7028005 0.6680394 0.6896672 0.6375064 0.6461947 0.6620159 1.2440965 0.7722830
The best post I have found on this is here. This posts asks a similar question for a zero- and one-inflated beta model in
gamlss. However, this answer is not applicable to a one-inflated beta model only (i.e without the zero-inflation) and the reference text suggested by the post no longer seems to be available.
Any advice/assistance to obtain the correct predicted probabilities for the one-inflated component (nu model) of a one-inflated beta regression in
gamlss would be very much appreciated?