`summary.gamlss`

is the GAMLSS specific method for the generic function `summary`

which summarize
objects returned by modelling functions.

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

Print summary of a GAMLSS object

- object
a GAMLSS 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`

.- 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

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby and Calliope Akantziliotou

Using the default value `type="vcov"`

, the `vcov()`

method for gamlss 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.

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019)
*Distributions for modeling location, scale, and shape: Using GAMLSS in R*, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

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, https://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.

(see also https://www.gamlss.com/).

`gamlss`

, `deviance.gamlss`

, `fitted.gamlss`

```
data(aids)
h<-gamlss(y~poly(x,3)+qrt, family=PO, data=aids) #
summary(h)
rm(h)
```

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