# Rsq: Generalised (Pseudo) R-squared for GAMLSS models In gamlss: Generalised Additive Models for Location Scale and Shape

## Description

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

## Usage

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

## Arguments

 `object` a GAMLSS object `type` which definition of R squared. Can be the "Cox Snell" or the Nagelkerke, "Cragg Uhler" or "both".

## 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 d.stasinopoulos@londonmet.ac.uk

## 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.

`GAIC`

## Examples

 ```1 2 3 4``` ```data(aids) m1 <- gamlss(y~x+qrt, data=aids, family=NBI) Rsq(m1) Rsq(m1, type="both") ```

### Example output

```Loading required package: splines

Attaching package: 'gamlss.data'

The following object is masked from 'package:datasets':

sleep

**********   GAMLSS Version 5.1-3  **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

GAMLSS-RS iteration 1: Global Deviance = 492.7119
GAMLSS-RS iteration 2: Global Deviance = 492.6375
GAMLSS-RS iteration 3: Global Deviance = 492.6373
[1] 0.8095829
\$CoxSnell
[1] 0.8095829

\$CraggUhler
[1] 0.8095856
```

gamlss documentation built on March 31, 2021, 5:10 p.m.