R: GAM beta regression family

betar {mgcv} | R Documentation

## GAM beta regression family

### Description

Family for use with `gam`, 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.

### Usage

    betar(theta = NULL, link = "logit")

### Arguments

`theta` | the extra parameter (phi above).
`link` | The link function: one of `"logit"`, `"probit"`, `"cloglog"` and `"cauchit"`.

### Details

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.

### Value

An object of class `extended.family`.

### Author(s)

Natalya Pya (nyp20@bath.ac.uk) and Simon Wood (s.wood@r-project.org)

### Examples

    library(mgcv)
    ## Simulate some beta data...
    set.seed(3);n<-400
    dat <- gamSim(1,n=n)
    mu <- binomial()$linkinv(dat$f/4-2)
    phi <- .5
    a <- mu*phi;b <- phi - a;
    dat$y <- rbeta(n,a,b)

    bm <- gam(y~s(x0)+s(x1)+s(x2)+s(x3),family=betar(link="logit"),data=dat)

    bm
    plot(bm,pages=1)

[Package mgcv version 1.8-3 Index]