summary.gamlssinf0to1: Summarizes an inflated GAMLSS fitted model
In gamlss.inf: Fitting Mixed (Inflated and Adjusted) Distributions

Description Usage Arguments Details Value Author(s) References See Also Examples

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

## 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),...)

`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

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.

Print summary of a gamlssinf0to1 or a gamlssZadj object

Abu Hossain, Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby and Marco Enea

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.

gamlssInf0to1, gamlssZadj

# 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)