Description Usage Arguments Details Value WARNINGS Author(s) Examples

Family for use with `gam`

or `bam`

, implementing regression for beta distributed data on (0,1).
A linear predictor controls the mean, *mu* of the beta distribution, while the variance is then
*mu(1-mu)/(1+phi)*, with parameter *phi* being estimated during
fitting, alongside the smoothing parameters.

1 |

`theta` |
the extra parameter ( |

`link` |
The link function: one of |

`eps` |
the response variable will be truncated to the interval |

These models are useful for proportions data which can not be modelled as binomial. Note the assumption that data are in
(0,1), despite the fact that for some parameter values 0 and 1 are perfectly legitimate observations. The restriction is needed to
keep the log likelihood bounded for all parameter values. Any data exactly at 0 or 1 are reset to be just above 0 or just below 1 using the `eps`

argument (in fact any observation `<eps`

is reset to `eps`

and any observation `>1-eps`

is reset to `1-eps`

). Note the effect of this resetting. If *mu*phi>1* then impossible 0s are replaced with highly improbable `eps`

values. If the inequality is reversed then 0s with infinite probability density are replaced with `eps`

values having high finite probability density. The equivalent condition for 1s is *(1-mu)*phi>1*. Clearly all types of resetting are somewhat unsatisfactory, and care is needed if data contain 0s or 1s (often it makes sense to manually reset the 0s and 1s in a manner that somehow reflects the sampling setup).

An object of class `extended.family`

.

Do read the details section if your data contain 0s and or 1s.

Natalya Pya (nat.pya@gmail.com) and Simon Wood (s.wood@r-project.org)

1 2 3 4 5 6 7 8 9 10 11 12 13 |

```
Loading required package: nlme
This is mgcv 1.8-25. For overview type 'help("mgcv-package")'.
Gu & Wahba 4 term additive model
Family: Beta regression(0.491)
Link function: logit
Formula:
y ~ s(x0) + s(x1) + s(x2) + s(x3)
Estimated degrees of freedom:
1.73 1.63 5.62 1.00 total = 10.98
REML score: -991.9735
```

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