R: Robust Variance-Covariance matrix of the parameters from a...

rvcov {gamlss} | R Documentation

## Robust Variance-Covariance matrix of the parameters from a fitted GAMLSS model

### Description

The function `rvcov()` is design for providing robust standard errors for the parameters estimates of a GAMLSS fitted model. The same result can be achieved by using `vcov(fitted_model,robust=TRUE)`. The function `get.()` gets the K matrix (see details below).

### Usage

    rvcov(object, type = c("vcov", "cor", "se", "coef", "all"),
                          hessian.fun = c("R", "PB") )
    get.K(object, what = c("K", "Deriv"))

### Arguments

`object` | a GAMLSS fitted object
`type` | this argument for `rvcov()` function whether variance-covariance matrix, correlation matrix, standard errors or all of them
`what` | this an argument for the function `ket.K()` allowing to get either K or the first derivative of the likelihood with respect to the parameters (the β's in the GAMLSS notation).
`hessian.fun` | How to obtain numerically the Hessian i) using `optimHess()`, option `"R"` ii) using a function by Pinheiro and Bates taken from package `nlme`, option `"PB"`.

### Details

The robust standard errors are calculated for the robust sandwich estimator of the variance-covariance given by S=VKV where V is the standard variance-covariance matrix (the inverse of the information matrix) and K is an estimate of the variance of he first derivatives of he likelihood. The function `get.K()` is use the get the required K matrix.

### Value

A variance covariance matrix or other relevant output

### Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org, Bob Rigby and Vlasios Voudouris

### 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. (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.

(see also http://www.gamlss.org/).

### See Also

`vcov`, ~~~

### Examples

    # gererate from a gamma distribution
    Y <- rGA(200, mu=1, sigma=2)
    hist(Y)
    # fitting the wrong model i.e. sigma=1
    m1 <- gamlss(Y~1, family=EXP)
    # the conventinal se is too precise
    vcov(m1, type="se")
    # the sandwich se is wider
    rvcov(m1, type="se")
    # fitting the correct model
     m2 <- gamlss(Y~1, family=GA)
     vcov(m2, type="se")
     rvcov(m2, type="se")
    # similar stadard errors
    # also obtained using
    vcov(m2, type="se", robust=TRUE)

[Package gamlss version 5.0-2 Index]