How can I predict the values of the dependent variable in a GAMLSS model after having predicted mu, sigma, nu and tau parameters?

Question

I am trying to predict the dependent variable of a GAMLSS function based on predicted values of mu, sigma, nu and tau parameters.

I have built a model for hospital length of stay using GAMLSS.

After training the model in a sample of patients (using BCPE) I am now trying to predict the dependent variable (length of stay) in a new dataset.

Using the "predictAll" function of the gamlss package in R I can obtain the predicted parameters for mu, sigma, nu and tau, but I don't know how can I obtain the values of the dependent variable (length of stay).

Someone can help? Thanks

Answer 1

predictAll gives you the predicted mu, sigma, nu and tau for BCPE for each new case (i.e. each new set of explanatory variable values).

Hence for a new case the predicted distribution of Y (length of stay) is

Y ~ BCPE(mu,sigma,nu,tau)

From this predicted distribution you can find the predicted median m

m <- qBCPE(0.5,mu,sigma,nu,tau)

or any p quantile of Y

q <- qBCPE(p,mu,sigma,nu,tau)

or the probability p2 that Y>c

p2 <- 1 - pBCPE(c,mu,sigma,nu,tau)