Generalised (Pseudo) R-squared for GAMLSS models

Description

This function gives the generalised R-squared of Nagelkerke (1991) for a GAMLSS model.

Usage

Rsq(object, type = c("Cox Snell","Cragg Uhler","both"))

Arguments

Details

The Rsq() function uses the definition for R-squared:

R-squared =1-(L(0)/L(fitted))^(2/n)

where L(0) is the null model (only a constant is fitted to all parameters) and L(fitted) is the current fitted model. This definition sometimes is referred to as the Cox & Snell R-squared. The Nagelkerke /Cragg & Uhler's definition divides the above with

1-L(0)^(2/n)

Value

The Rsq() produces a single value if type="Cox Snell" or "Cragg Uhler" and a list if type="both".

Note

The null model is fitted using the function gamlssML() which can create warning messages

Author(s)

Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org

References

Nagelkerke, N. J. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78(3), 691-692.

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

GAIC

Examples

data(aids)
m1 <- gamlss(y~x+qrt, data=aids, family=NBI)
Rsq(m1)
Rsq(m1, type="both")
rm(m1)