In the original data 368 patients, measured at 18 times after
treatment with one of 7 drug treatments (including placebo), plus
a baseline measure (time=0) and one or more pre-baseline measures
(time=-1). Here for illustration we will ignore the repeated measure nature of the
data and we shall use data from time 5 only (364 observations).
The VAS scale response variable, Y, is assumed to be distributed
as `BEINF(mu,sigma,nu,tau)`

where any of the
distributional parameters `mu`

, `sigma`

, `nu`

and `tau`

are
modelled as a constant or as a function of the treatment,

`data(vas5)`

A data frame with 364 observations on the following 3 variables.

`patient`

a factor indicationg the patient

`treat`

the treatment factor with levels

`1`

`2`

`3`

`4`

`5`

`6`

`7`

`vas`

the response variable

The Visual analog scale is used to measure pain and quality of
life. For example patients are required to indicate in a scale
from 0 to 100 the amount of discomfort they have. This can be
easily translated to a value from 0 to 1 and consequently analyzed
using the beta distribution. Unfortunately if 0's or 100's are
recorded the beta distribution is not appropriate since the values
0 and 1 are not allowed in the definition of the beta
distribution. Note that the inflated beta distribution
allows values at 0 and 1. This is a mixed distribution
(continuous and discrete) having four parameters, `nu`

for
modelling the probability at zero p(Y=0) relative to p(0<Y<1), `tau`

for modelling
the probability at one p(Y=1) relative to p(0<Y<1), and `mu`

and `sigma`

for
modelling the between values, $0<Y<1$, using a beta distributed
variable `BE(mu,sigma)`

with mean `mu`

and variance
`sigma*mu*(1-mu)`

.