GAMLSS model for a proportion response variable with point(s) mass at 0 and or 1.
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.
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, ...)y |
the proportion response variable with inflation at zero and/or one |
mu.formula |
a model formula for |
sigma.formula |
a model formula for |
nu.formula |
a model formula for |
tau.formula |
a model formula for |
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 |
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 |
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".
returns a gamlssInf0to1 object which has its own methods
Mikis Stasinopoulos, Robert Rigby, Abu Hossain and Marco Enea
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.
# 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)))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.