Package 'gamlss.inf'

Title: Fitting Mixed (Inflated and Adjusted) Distributions
Description: This is an add-on package to 'gamlss'. The purpose of this package is to allow users to fit GAMLSS (Generalised Additive Models for Location Scale and Shape) models when the response variable is defined either in the intervals [0,1), (0,1] and [0,1] (inflated at zero and/or one distributions), or in the positive real line including zero (zero-adjusted distributions). The mass points at zero and/or one are treated as extra parameters with the possibility to include a linear predictor for both. The package also allows transformed or truncated distributions from the GAMLSS family to be used for the continuous part of the distribution. Standard methods and GAMLSS diagnostics can be used with the resulting fitted object.
Authors: Marco Enea [aut, cre, cph], Mikis Stasinopoulos [aut], Bob Rigby [aut], Abu Hossain [aut]
Maintainer: Marco Enea <[email protected]>
License: GPL-2 | GPL-3
Version: 1.0-1
Built: 2024-09-09 06:21:08 UTC
Source: CRAN

Help Index

Models for Mixed (Inflated and Adjusted) Response Variables.

Description

This package allows mixed distribution fitting in GAMLSS. A mixed distribution is one containing both continuous and discrete parts, see Chapter 5 of Stasinopoulos et al. (2017). There are some mixed distribution in the GAMLSS implementation in R like the BEINF, BEINF0, BEINF1 for data defined on [0,1] or ZAGA, ZAIG for data defined on a positive real line but the choice is very limited. This package enhance the availability of mixed distribution within the GAMLSS framework.

For historical reasons the authors use the terminology "Inflated" for models on [0,1], "Adjusted" for models on [0,Inf]. We will follow the same terminology here. So this package allows the fit of an inflated GAMLSS model when the response variable is defined in the intervals [0,1), (0,1] and [0,1] and the fit of zero adjusted models when the response variable is defined in the positive real line, (but where there are zeros in the data).

For models with inflated proportion response variables the package provides up to two extra parameters, a mass point at zero and a mass point at one. Adding an extra inflation point at zero (or at one), is equivalent to fit two separate GAMLSS models, a GAMLSS model with a continuous distribution defined at the interval (0,1), and a logit model for zero (or ones). When both zero and one are present, i.e. [0,1], a multinomial model is needed to fit the non-(0,1) part.

For the zero adjusted models with a response defined on the positive real line (but where zeros exist in the data), the actual fitting can be achieved by fitting two separate GAMLSS models one with a distribution on the real positive line and one binomial model for the zeros and non-zeros.

This package uses the two models fitting procedures but the resulting fitted object behaves like a typical GAMLSS object so a lot of standard GAMLSS diagnostics can be used with it. It also allows transformed or truncated gamlss.family distributions to be used for the continuous part of the distribution therefore giving a great flexibility of the type of mixed distribution to be used.

The functions gamlssInf0to1() and gamlssZadj() can fit the Inflated and Adjusted models, respectively, and they are described in the two vignettes available with the package.

Details

Package: gamlss.inf
Type: Package
Version: 1.0-1
Date: 2019-03-12
License: GPL-2 | GPL-3

Author(s)

Marco Enea <[email protected]>, Mikis Stasinopoulos <[email protected]>, Bob Rigby and Abu Hossain

Maintainer: Marco Enea <[email protected]>

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.

Ospina R. and Ferrari S. L. P. (2010) Inflated beta distributions, Statistical Papers, 23, 111-126.

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. (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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

See Also

gamlss

Examples

# An artificial example using simulated data in [0,1)

# Firstly, we use function gen.Family() to create 
# the logit skew student t (logitSST) distribution which is defined in the (0,1) 
# interval. Then we use 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(300,mu=0.5,sigma=0.7,nu=0.5,tau=5,xi0=0.5,log=FALSE)
m1 <- gamlssInf0to1(y=Y,mu.formula=~1,
                    sigma.formula=~1,
                    nu.formula=~1,
                    tau.formula=~1,
                    xi0.formula=~1,
                    family=logitSST,
                    trace = TRUE)
summary(m1)

Plotting centile curves for a gamlssInf0to1 and gamlssZadj object

Description

Function centiles.Inf0to1() plots centile curves for distributions belonging to the GAMLSS family of distributions defined in the intervals (0,1],[0,1) and [0,1]. The function also tabulates the sample percentages below each centile curve (for comparison with the model percentages given by the argument cent). A restriction of the function is that it applies to models with one explanatory variable only.

Usage

centiles.Inf0to1(obj, xvar = NULL, cent = c(0.4, 2, 10, 25, 50, 75, 
    90, 98, 99.6), legend = TRUE, ylab = "y", xlab = "x", main = NULL, 
    main.gsub = "@", xleg = min(xvar), yleg = max(obj$y), xlim = range(xvar), 
    ylim = range(obj$y), save = FALSE, plot = TRUE, points = TRUE, 
    pch = 15, cex = 0.5, col = gray(0.7), col.centiles = 1:length(cent) + 
        2, lty.centiles = 1, lwd.centiles = 1, ...)
centiles.Zadj(obj, xvar = NULL, cent = c(0.4, 2, 10, 25, 50, 75, 
   90, 98, 99.6), legend = TRUE, ylab = "y", xlab = "x", main = NULL, 
   main.gsub = "@", xleg = min(xvar), yleg = max(obj$y), xlim = range(xvar), 
   ylim = range(obj$y), save = FALSE, plot = TRUE, points = TRUE, 
   pch = 15, cex = 0.5, col = gray(0.7), col.centiles = 1:length(cent) + 
   2, lty.centiles = 1, lwd.centiles = 1, ...)

Arguments

obj

a fitted gamlss object from fitting a gamlss distribution
xvar

the unique explanatory variable
cent

a vector with elements the % centile values for which the centile curves have to be evaluated
legend

whether a legend is required in the plot or not, the default is legent=TRUE

ylab

the y-variable label
xlab

the x-variable label
main

the main title here as character. If NULL the default title "centile curves using NO" (or the relevant distributions name) is shown
main.gsub

if the main.gsub (with default "@") appears in the main title then it is substituted with the default title.
xleg

position of the legend in the x-axis
yleg

position of the legend in the y-axis
xlim

the limits of the x-axis
ylim

the limits of the y-axis
save

whether to save the sample percentages or not with default equal to FALSE. In this case the sample percentages are printed but are not saved

plot

whether to plot the centiles
points

whether the data points should be plotted, default is TRUE
pch

the character to be used as the default in plotting points see par
cex

size of character see par
col

plotting colour see par
col.centiles

Plotting colours for the centile curves
lty.centiles

line type for the centile curves
lwd.centiles

The line width for the centile curves
...

for extra arguments

Details

Centiles are calculated using the fitted values in obj and xvar must correspond exactly to the predictor in obj to plot correctly.

col.centiles, lty.centiles and lwd.centiles may be vector arguments and are recycled to the length cent if necessary.

Value

A centile plot is produced and the sample centiles below each centile curve are printed (or saved)

Warning

This function is appropriate only when one continuous explanatory variable is fitted in the model

Author(s)

Mikis Stasinopoulos [email protected], Bob Rigby [email protected] with contribution from Steve Ellison

References

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.

Houssain, A., Stasinopoulos, M., Rigby, R. and Enea, M. (2015). Centile estimation for a proportion response variable. Accepted for publication on Statistics in Medicine.

See Also

gamlssInf0to1, gamlss, centiles.split , centiles.com

Examples

## Not run: 
gen.Family("SST", "logit")
gen.Inf0to1("logitSST","One") 
set.seed(30)
x <- seq(0,1,l=2000)
dat <- data.frame(x)
dat$Y <- rlogitSSTInf1(2000,mu=-3+10*x-0.7*x^2,sigma=0.9,nu=0.5,
                       tau=5,xi1=plogis(-0.5*ifelse(x>0.7,-1,13)),log=FALSE)

m1 <- gamlssInf0to1(y=Y,mu.formula=~pb(x), sigma.formula=~pb(x),
                    nu.formula=~pb(x), tau.formula=~pb(x),
                    xi1.formula=~pb(x),
                    data=dat, family=logitSST)

centiles.Inf0to1(m1,xvar= dat$x, cent=c(2,10,25,50,75,90,98),
col.centiles=c(1,7:2),
ylab="proportion", xlab="x",legend=FALSE,main="(c) Inf. logitSST")

## End(Not run)

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)))

Fitting positive real line response variable with zeros.

Description

Function gamlssZadj() allows to fit zero adjusted gamlss models when the response variable distribution is defined on the positive real line. The gamlssZadj model for adjusted positive variables is a gamlss model provides one extra parameters for the mass point at zero. This is equivalent to fit two separate models, a gamlss model for the (0,Inf) part, and a logit model for zero part versus the non-zero part. The function works similarly but provides one fitted object.

Usage

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

Arguments

y

the response variable
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 xi0
data

a data frame containing the variables occurring in the formula.
family

any gamlss distribution family defined on the rael line
weights

a vector of weights as in gamlss

trace

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

for extra arguments to pass to gamlss

Details

The default family is a gamma distribution (GA), but other distributions on the positive rael line can be used, e.g. those generated from existing continuous gamlss.family distributions using say gen.Family() with "log" or gen.trun() from package gamlss.tr

Value

. Returns a gamlssZadj object which has its own methods

Author(s)

Mikis Stasinopoulos, Robert Rigby and Marco Enea

References

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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

See Also

gamlss.family, ZAGA, ZAIG

Examples

y0 <- rZAGA(1000, mu=.3, sigma=.4, nu=.15)# p0=0.13
  g0 <- gamlss(y0~1, family=ZAGA)
 t0 <- gamlssZadj(y=y0, mu.formula=~1, family=GA, trace=TRUE)
AIC(g0,t0, k=0)

Functions to generate inflated 0-to-1 distributions from existing continuous gamlss.family distributions defined in (0,1).

Description

There are six functions here. Only the function gen.Inf0to1() should be used. The remaing five functions will be automatically created once gen.Inf0to1() has been run.

Usage

gen.Inf0to1(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...)
Inf0to1.d(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...) 
Inf0to1.p(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...) 
Inf0to1.q(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...) 
Inf0to1.r(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...) 
plotInf0to1(family = "BE", type.of.Inflation = c( "Zero&One", "Zero", "One"), 
            ...)

Arguments

family

a continuous (0,1) distribution (extremes not included) gamlss.family distribution
type.of.Inflation

the type of inflation
...

for passing extra arguments

Details

Functions Inf0to1.d, Inf0to1.p, Inf0to1.q and Inf0to1.r allow to create the density function, distribution function, quantile function and random generation, respectively. Function plotInf0to1 can be used to create the plot the distributions.

Alternatively, the function gen.Inf0to1 creates the all the standard d,p,q,r functions plus the plotting function.

For example, let us take the case of the logit SST distribution with inflation at 1. First generate the "logitSST" distribution by using gen.Family("SST", "logit"), and then, by use gen.Inf0to1("logitSST", "One"). The functins dlogitSSTInf1, plogitSSTInf1, qlogitSSTInf1, rlogitSSTInf1 and plotlogitSSTInf1 will be automatically generated. Note that gen.Inf0to1 never creates a fitting function of the type "logitSSTInf1", but the existing logitSST must be specified instead as an argument family of function gamlssInf0to1().

Value

The function gen.Inf0to1 returns the d, p, q and r functions plus the plotting function.

Author(s)

Mikis Stasinopoulos [email protected], Bob Rigby and Marco Enea

References

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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

Examples

# 1.
gen.Inf0to1("BE","Zero&One")
rBETAInf0to1 <- Inf0to1.r("BE","Zero&One") 
all.equal(rBETAInf0to1, rBEInf0to1) 
plotBEInf0to1()
plotBEInf0to1(mu=0.3,sigma=0.35,xi0=0.5,xi1=0.3)

# 2.
gen.Family("SST", "logit")
gen.Inf0to1("logitSST","One") 
set.seed(30)

args(rlogitSSTInf1)
y <- rlogitSSTInf1(1000,mu=0.2,sigma=0.5,nu=1,tau=5,xi1=0.2)
quantile(y,c(0.1,0.25,0.5,0.75,0.9))

args(qlogitSSTInf1)
qlogitSSTInf1(p=c(0.1,0.25,0.5,0.75,0.9),mu=0.2,sigma=0.5,nu=1,tau=5,xi1=0.2)
plotlogitSSTInf1(mu=0.2,sigma=0.5,nu=1,tau=5,xi1=0.2)

Functions to generate zero adjusted distributions from existing continuous gamlss.family distributions defined on positve real line.

Description

There are six functions here. Only the function gen.Zadj() should be used. The remaing four functions will be automatically created once gen.Zadj() has been run.

Usage

gen.Zadj(family = "GA", ...)
Zadj.d(family = "GA", ...)
Zadj.p(family = "GA", ...)
Zadj.q(family = "GA", ...)
Zadj.r(family = "GA", ...)
plotZadj(family = "GA", ...)

Arguments

family

a continuous positive rael line distribution
...

for additional arguments

Details

Functions Zadj.d, Zadj.p, Zadj.q and Zadj.r allow to create the density function, distribution function, quantile function and random generation, respectively. Function plotZadj can be used to create a plot for the distribution.

Alternatively, the function gen.Zadj creates the all the standard d,p,q,r functions plus the plotting function.

Value

The function gen.Zadj returns the d, p, q and r functions plus the plotting function.

Author(s)

Mikis Stasinopoulos [email protected], Bob Rigby and Marco Enea

References

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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

See Also

gamlssZadj, ~~~

Examples

# 1.
gen.Zadj("BCT")

plotBCTZadj()
plotBCTZadj(mu=3,sigma=0.35,xi0=0.5)

# 2.
gen.Family("SST", "log")
gen.Zadj("logSST") 
 plotlogSSTZadj()

Extract Predictor Values and Standard Errors For New Data In a gamlssinf0to1 Model

Description

predict.gamlssinf0to1 is the gamlssinf0to1 specific method which produce predictors for a new data set for a specified parameter from a gamlssinf0to1 objects. The predict.gamlssinf0to1 can be used to extract the linear predictors, fitted values and specific terms in the model at new data values in the same way that the predict.lm() and predict.glm() functions can be used for lm or glm objects. Note that linear predictors, fitted values and specific terms in the model at the current data values can also be extracted using the function lpred() (which is called from predict if new data is NULL).

Usage

## S3 method for class 'gamlssinf0to1'
predict(object, parameter = c("mu", "sigma", "nu", "tau", "xi0","xi1"), 
 newdata = NULL, type = c("link", "response", "terms"),                           
   terms = NULL, se.fit = FALSE,data = NULL, ...)

Arguments

object

a gamlssinf0to1 fitted model
parameter

which distribution (or inflation) parameter is required, default parameter="mu"
newdata

a data frame containing new values for the explanatory variables used in the model
type

the default, gets the linear predictor for the specified distribution (or inflation) parameter. type="response" gets the fitted values for the parameter while type="terms" gets the fitted terms contribution
terms

if type="terms", which terms to be selected (default is all terms)
se.fit

if TRUE the approximate standard errors of the appropriate type are extracted if exist
data

the data frame used in the original fit if is not defined in the call
...

for extra arguments

Details

The predict function assumes that the object given in newdata is a data frame containing the right x-variables used in the model. This could possible cause problems if transformed variables are used in the fitting of the original model. For example, let us assume that a transformation of age is needed in the model i.e. nage<-age^.5. This could be fitted as mod<-gamlss(y~cs(age^.5),data=mydata) or as nage<-age^.5; mod<-gamlss(y~cs(nage), data=mydata). The later could more efficient if the data are in thousands rather in hundreds. In the first case, the code predict(mod,newdata=data.frame(age=c(34,56))) would produce the right results. In the second case a new data frame has to be created containing the old data plus any new transform data. This data frame has to be declared in the data option. The option newdata should contain a data.frame with the new names and the transformed values in which prediction is required, (see the last example).

Value

A vector or a matrix depending on the options.

Author(s)

Abu Hossain, Mikis Stasinopoulos [email protected], Bob Rigby 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. (2003) 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

gamlssInf0to1

Examples

gen.Family("SST", "logit")
gen.Inf0to1("logitSST","Zero") 
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)
predict(m1)

Extract Predictor Values and Standard Errors For New Data in a gamlssZadj Model

Description

predict.gamlssZadj is the specific method which produce predictors for a new data set for a specified parameter from a gamlssZadj objects. The predict.gamlssZadj can be used to extract the linear predictors, fitted values and specific terms in the model at new data values in the same way that the predict.lm() and predict.glm() functions can be used for lm or glm objects. Note that linear predictors, fitted values and specific terms in the model at the current data values can also be extracted using the function lpred() (which is called from predict if new data is NULL).

Usage

## S3 method for class 'gamlssZadj'
predict(object, parameter = c("mu", "sigma", "nu", "tau", "xi0"), 
 newdata = NULL, type = c("link", "response", "terms"),                           
   terms = NULL, se.fit = FALSE,data = NULL, ...)

Arguments

object

a gamlssZadj fitted model
parameter

which distribution (or inflation) parameter is required, default parameter="mu"
newdata

a data frame containing new values for the explanatory variables used in the model
type

the default, gets the linear predictor for the specified distribution (or inflation) parameter. type="response" gets the fitted values for the parameter while type="terms" gets the fitted terms contribution
terms

if type="terms", which terms to be selected (default is all terms)
se.fit

if TRUE the approximate standard errors of the appropriate type are extracted if exist
data

the data frame used in the original fit if is not defined in the call
...

for extra arguments

Details

The predict function assumes that the object given in newdata is a data frame containing the right x-variables used in the model. This could possible cause problems if transformed variables are used in the fitting of the original model. For example, let us assume that a transformation of age is needed in the model i.e. nage<-age^.5. This could be fitted as mod<-gamlss(y~cs(age^.5),data=mydata) or as nage<-age^.5; mod<-gamlss(y~cs(nage), data=mydata). The later could more efficient if the data are in thousands rather in hundreds. In the first case, the code predict(mod,newdata=data.frame(age=c(34,56))) would produce the right results. In the second case a new data frame has to be created containing the old data plus any new transform data. This data frame has to be declared in the data option. The option newdata should contain a data.frame with the new names and the transformed values in which prediction is required, (see the last example).

Value

A vector or a matrix depending on the options.

Author(s)

Abu Hossain, Mikis Stasinopoulos [email protected], Bob Rigby 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. (2003) 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

gamlssZadj

Examples

set.seed(3210)
x <- (runif(800)*4)-2
data(sda)
fmu <- splinefun(sda$x, sda$mu)
curve(fmu, -2,2)
fsigma <- splinefun(sda$x, sda$sigma)
curve(fsigma, -2,2)
fnu <- function(x)
  {f <- splinefun(sda$x, sda$nu)
f(x)/6
}
curve(fnu, -2,2)
set.seed(321)
y0 <- rZAGA(800, mu=fmu(x), sigma=fsigma(x), nu=fnu(x))
da <- data.frame(y0,x)
g0p <- gamlss(y0~pb(x), sigma.fo=~pb(x), nu.fo=~pb(x), data=da, family=ZAGA)
t0p <- gamlssZadj(y=y0, mu.fo=~pb(x), sigma.fo=~pb(x),data=da,
                  trace=TRUE, xi0.fo=~pb(x), family="GA")

plot(predict(g0p,"nu",type="link"),
     predict(t0p,"xi0",type="link"))

Data for using for simulation

Description

Those data values are used to create simaulated data

Usage

data("sda")

Format

A data frame with 120 observations on the following 5 variables.

x

the explanatory variable

mu

the fitted mu

sigma

the fitted sigma

nu

the fitted nu

tau

the fitted tau

Source

The data are fitted values of model

References

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.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. https://www.crcpress.com/Flexible-Regression-and-Smoothing-Using-GAMLSS-in-R/Stasinopoulos-Rigby-Heller-Voudouris-Bastiani/p/book/9781138197909.

Examples

data(sda)
fmu <- splinefun(sda$x, sda$mu)
curve(fmu, -2,2)
fsigma <- splinefun(sda$x, sda$sigma)
curve(fsigma, -2,2)
fnu <- splinefun(sda$x, sda$nu)
curve(fnu, -2,2)
ftau <- splinefun(sda$x, sda$tau)
curve(ftau, -2,2)

Summarizes an inflated GAMLSS fitted model

Description

These are specific methods for the generic function summary which summarize objects retuned by gamlssinf0to1 or gamlssZadj.

Usage

## S3 method for class 'gamlssinf0to1'
summary(object, type = c("vcov", "qr"),
       robust=FALSE, save = FALSE, hessian.fun = c("R", "PB"), 
       digits = max(3, getOption("digits") - 3),...)

## S3 method for class 'gamlssZadj'
summary(object, type = c("vcov", "qr"),
       robust=FALSE, save = FALSE, hessian.fun = c("R", "PB"), 
       digits = max(3, getOption("digits") - 3),...)

Arguments

object

a gamlssinf0to1 or gamlssZadj fitted model
type

the default value vcov uses the vcov() method for gamlss to get the variance-covariance matrix of the estimated beta coefficients, see details below. The alternative qr is the original method used in gamlss to estimated the standard errors but it is not reliable since it do not take into the account the inter-correlation between the distributional parameters mu, sigma, nu and tau, while the inflation parameters xi0 and xi1 are uncorrelated anywway.

robust

whether robust (sandwich) standard errors are required
save

whether to save the environment of the function so to have access to its values
hessian.fun

whether when calculate the Hessian should use the "R" function optimHess() or a function based on Pinheiro and Bates nlme package, "PB".
digits

the number of digits in the output
...

for extra arguments

Details

Using the default value type="vcov", the vcov() method is used to get the variance covariance matrix (and consequently the standard errors) of the beta parameters. The variance covariance matrix is calculated using the inverse of the numerical second derivatives of the observed information matrix. This is a more reliable method since it take into the account the inter-correlation between the all the parameters. The type="qr" assumes that the parameters are fixed at the estimated values. Note that both methods are not appropriate and should be used with caution if smoothing terms are used in the fitting.

Value

Print summary of a gamlssinf0to1 or a gamlssZadj object

Author(s)

Abu Hossain, Mikis Stasinopoulos [email protected], Bob Rigby and Marco Enea

References

Houssain, A., Stasinopoulos, M., Rigby, R. and Enea, M. (2015). Centile estimation for a proportion response variable. Accepted for publication on Statistics in Medicine.

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. (2003) 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

gamlssInf0to1, gamlssZadj

Examples

# The gamlssZadj example 
set.seed(3210)
x <- (runif(1000)*4)-2
data(sda)
fmu <- splinefun(sda$x, sda$mu)
fsigma <- splinefun(sda$x, sda$sigma)
fnu <- function(x)
  {f <- splinefun(sda$x, sda$nu)
f(x)/6
}
y0 <- rZAGA(1000, mu=fmu(x), sigma=fsigma(x), nu=fnu(x))
da <- data.frame(y0,x)
t0p <- gamlssZadj(y=y0, mu.fo=~pb(x), sigma.fo=~pb(x),data=da,
                  trace=TRUE, xi0.fo=~pb(x), family="GA")
summary(t0p)

Plot regression terms for a specified parameter of a fitted gamlssInf0to1 object

Description

This is a wrapper to function term.plot. term.plotInf0to1 produces term plots for a specified parameter from a gamlssinf0to1 object.

Usage

term.plotInf0to1(object, parameter = c("mu", "sigma", "nu", "tau", 
        "xi0", "xi1"),...)

Arguments

object

a gamlssinf0to1 fitted model
parameter

which distribution (or inflation) parameter is required, default parameter="mu"
...

extra arguments, the same of term.plot (except 'what')

Details

see function term.plot

Value

A plot of fitted terms.

Author(s)

Marco Enea, Mikis Stasinopoulos, Bob Rigby and Abu Hossain

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. (2003) 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

gamlssInf0to1

Examples

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

# term.plot for the mu parameter
term.plot(m1$dist,parameter="mu")
term.plotInf0to1(m1,parameter="mu",col.shaded = 2)

# term.plot for the binomial parameter
term.plot(m1$multinom,parameter="mu")
term.plotInf0to1(m1,parameter="xi0",col.shaded = 2)

Plot regression terms for a specified parameter of a fitted gamlssZadj object

Description

\ This is a wrapper to function term.plot. codeterm.plotZadj produces term plots for a specified parameter from a gamlssZadjobject.

Usage

term.plotZadj(object, parameter = c("mu", "sigma", "nu", "tau", "xi0"),...)

Arguments

object

a gamlssZadj fitted model
parameter

which distribution (or inflation) parameter is required, default parameter="mu"
...

extra arguments, the same of term.plot (except 'what')

Details

see function term.plot

Value

A plot of fitted terms.

Author(s)

Marco Enea, Mikis Stasinopoulos, Bob Rigby and Abu Hossain

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. (2003) 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

gamlssZadj

Examples

set.seed(3210)
x <- (runif(1000)*4)-2
data(sda)
fmu <- splinefun(sda$x, sda$mu)
curve(fmu, -2,2)
fsigma <- splinefun(sda$x, sda$sigma)
curve(fsigma, -2,2)
fnu <- function(x)
  {f <- splinefun(sda$x, sda$nu)
f(x)/6
}
curve(fnu, -2,2)
set.seed(321)
y0 <- rZAGA(1000, mu=fmu(x), sigma=fsigma(x), nu=fnu(x))
da <- data.frame(y0,x)
g0p <- gamlss(y0~pb(x), sigma.fo=~pb(x), nu.fo=~pb(x), data=da, family=ZAGA)
t0p <- gamlssZadj(y=y0, mu.fo=~pb(x), sigma.fo=~pb(x),data=da,
                  trace=TRUE, xi0.fo=~pb(x), family="GA")

# term.plot for the mu parameter
term.plot(g0p);title("gamlss")
term.plot(t0p$dist,"mu");title("gamlssZadj")
term.plotZadj(t0p,"mu",col.shaded = 3);title("gamlssZadj")



# term.plot for the sigma parameter
term.plot(g0p, "sigma");title("gamlss")
term.plot(t0p$dist,"sigma");title("gamlssZadj")
term.plotZadj(t0p,"sigma",col.shaded = 3);title("gamlssZadj")

# term.plot for the binomial parameter
term.plot(g0p, "nu");title("gamlss")
term.plot(t0p$binom,"mu");title("gamlssZadj")
term.plotZadj(t0p,"xi0",col.shaded = 3);title("gamlssZadj")