gamlssInf0to1 {gamlss.inf}

GAMLSS model for a proportion response variable with point(s) mass at 0 and or 1.

Description

Function gamlssInf0to1() allows to fit inflated gamlss models when the response variable distribution is defined in the intervals [0,1), (0,1] and [0,1]. The gamlssInf0to1 model for inflated proportion variables is a gamlss model provided of up to two extra parameters for the mass point(s). In the case of inflation point at zero (one), this is equivalent to fit two separate models, a gamlss model for the (0,1) part, and a logit model for zero (one) vs non-zero (non-one) part. When both zero and one are present, a multinomial model is involved to fit the non-(0,1) part.

Usage

gamlssInf0to1(y = NULL, mu.formula = ~1, sigma.formula = ~1, 
             nu.formula = ~1,tau.formula = ~1, 
             xi0.formula = ~1,xi1.formula = ~1, data = NULL, 
             family = BE, weights = rep(1, length(Y_)), 
             trace = FALSE, ...)

Arguments

y

the proportion response variable with inflation at zero and/or one

mu.formula

a model formula for mu

sigma.formula

a model formula for sigma

nu.formula

a model formula for nu

tau.formula

a model formula for tau

xi0.formula

a model formula for the probability at zero

xi1.formula

a model formula for the probability at one

data

a data frame containing the variables occurring in the formula.

family

any gamlss distribution family defined in (0,1)

weights

a vector of weights as in gamlss

trace

logical, if TRUE information on model estimation will be printed during the fitting

...

for extra parameters

Details

The default family is a Beta distribution (BE), but other (0,1) distributions can be used, e.g. those generated from existing continuous gamlss family distributions by using gen.Family with link "logit".

Value

returns a gamlssInf0to1 object which has its own methods

Author(s)

Mikis Stasinopoulos, Robert Rigby, Abu Hossain and Marco Enea

References

Hossain, A., Stasinopoulos, M., Rigby, R. and Enea, M. (2015). Centile estimation for a proportion response variable. Statistics in Medicine, doi: 10.1002/sim.6748.

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

See Also

gamlss.family, BEINF, BE, BEo, BEZI, BEOI

Examples

# 1. An artificial example using simulated data

# Firstly, we use function gen.Family() to create the logit skew 
# student t (logitSST) distribution defined in the (0,1) interval, 
# and function gen.Inf0to1() to create the 0-inflated logitSST 
# distribution defined in [0,1).

gen.Family("SST", "logit")
gen.Inf0to1("logitSST","Zero") 

#now we can generate the data and run the model 
set.seed(10)
Y <- rlogitSSTInf0(500,mu=0.5,sigma=0.7,nu=0.5,tau=5,xi0=0.5,log=FALSE)
dat <- data.frame(Y)
dat$x <- rnorm(500)
m1 <- gamlssInf0to1(y=Y,mu.formula=~x, sigma.formula=~x,
                    nu.formula=~x, tau.formula=~x,
                    xi0.formula=~x,data=dat, family=logitSST)
summary(m1)

# 2. Example of equivalent gamlss models for an inflated-at-1 Beta distribution 

Y <- rBEINF1(500,mu=0.5,sigma=0.7,nu=0.5)
m2 <- gamlss(Y~1,sigma.formula=~1,nu.formula=~1,family=BEINF1)
m3.1 <- gamlss(Y[Y<1]~1,sigma.formula=~1,family=BE)
m3.2 <- gamlss(I(Y==1)~1,family=BI)
m4 <- gamlssInf0to1(Y,mu.formula=~1,sigma.formula=~1,xi1=~1,family=BE)
stopifnot(all.equal(deviance(m2),(deviance(m3.1)+deviance(m3.2))), 
          all.equal(deviance(m2),deviance(m4)))