summary.gamlssinf0to1 {gamlss.inf}

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 [e-mail], 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)