Description Usage Arguments Value Author(s) References See Also Examples

This function can be used to calculate the partial effect and the elasticity of a continuous explanatory variable `x`

.

By ‘partial effect’ function we mean how `x`

is influence the parameter of interest given that the rest of explanatory terms for this parameter are on (specified) fixed values.

The function takes a GAMLSS object and for the range of the continuous variable `x`

,
(by fixing the rest of the explanatory terms at specified values),
calculates the effect that `x`

has on the specific distribution parameter (or its predictor).
The resulting function shows the effect that `x`

has on the distribution parameter.
The partial effect function which is calculated on a finite grit is then approximated using the `splinefun()`

in R and its is saved.

The saved function can be used to calculate the elasticity of `x`

. The elasticity is the first derivative of the partial effect function and shows the chance of the parameter of interest for a small change in in `x`

, by fixing the rest of the explanatory variables at specified values.

1 2 3 4 |

`obj` |
A |

`term` |
the continuous explanatory variable |

`data` |
the data.frame (not needed if is declared on |

`n.points` |
the number of points in which the influence function for |

`parameter` |
which distribution parameter |

`type` |
whether against the parameter, |

`how` |
whether for continuous variables should use the median or the last observation in the data |

`fixed.at` |
a list indicating at which values the rest of the explanatory terms should be fixed |

`plot` |
whether to the plot the influence function and its first derivatives |

A function is created which can be used to evaluate the partial effect function at different values of `x`

.

Mikis Stasinopoulos, Vlasios Voudouris, Daniil Kiose

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. and Stasinopoulos, D. M (2013) Automatic smoothing parameter selection in GAMLSS with an application to centile estimation, *Statistical methods in medical research*.

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/).

1 2 3 4 5 6 7 8 9 10 11 | ```
m1 <- gamlss(R~pb(Fl)+pb(A), data=rent, family=GA)
# getting the Partial Efect function
pef <- getPEF(obj=m1,term="A", plot=TRUE)
# the value at 1980
pef(1980)
# the first derivative at 1980
pef(1980, deriv=1)
# the second derivative at 1980
pef(1980, deriv=2)
# plotting the first derivative
curve(pef(x, deriv=1), 1900,2000)
``` |

```
Loading required package: splines
Loading required package: gamlss.data
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.0-2 **********
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 = 27923.61
GAMLSS-RS iteration 2: Global Deviance = 27923.61
new prediction
[1] 959.7969
[1] 15.78675
[1] 0.5825948
```

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