gamlss (version 5.4-12)

Rsq: 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"))

Value

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

Arguments

object

a GAMLSS object

type

which definition of R squared. Can be the "Cox Snell" or the Nagelkerke, "Cragg Uhler" or "both".

Author

Mikis Stasinopoulos

Details

The Rsq() function uses the definition for R-squared: $$R^2=1- \left(\frac{L(0)}{L(\hat{\theta})}\right)^(2/n)$$ where \(L(0)\) is the null model (only a constant is fitted to all parameters) and \(L(\hat{\theta})\) 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 $$1- L(0)^(2/n)$$

References

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

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/).

See Also

GAIC

Examples

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