beta_resp: Beta-response family object

Description

Returns a family object for beta-response models. The model described by such a family is characterized by a linear predictor, a link function, and the beta density for the residual variation.

The precision parameter prec of this family is a positive value such that the variance of the response given its mean \(\mu\) is \(\mu(1-\mu)/(1+\)prec). prec is thus the precision parameter \(\phi\) of Ferrari & Cribari-Neto (2004) and of the betareg package (Cribari-Neto & Zeileis 2010).

Prior weights are meaningful for this family and handled as a factor of the precision parameter (as for GLM families) hence here not as a divisor of the variance (in contrast to GLM families): the variance of the response become \(\mu(1-\mu)/(1+\)prec*<prior weigths>).

Usage

beta_resp(prec = stop("beta_resp's 'prec' must be specified"), link = "logit")

Value

A list, formally of class c("LLF", "family"). See LL-family for details about the structure and usage of such objects.

Arguments

prec: Scalar (or left unspecified): precision parameter of the beta distribution.
link: logit, probit, cloglog or cauchit link, specified by any of the available ways for GLM links (name, character string, one-element character vector, or object of class link-glm as returned by make.link).

References

Cribari-Neto, F., & Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1-24. tools:::Rd_expr_doi("10.18637/jss.v034.i02")

Ferrari SLP, Cribari-Neto F (2004). “Beta Regression for Modelling Rates and Proportions.” Journal of Applied Statistics, 31(7), 799-815.

Examples

Run this code

  set.seed(123)
  beta_dat <- data.frame(y=runif(100),grp=sample(2,100,replace = TRUE))
  
  fitme(y ~1+(1|grp), family=beta_resp(), data= beta_dat)
  ## same logL, halved 'prec' when prior weights=2 are used: 
  # fitme(y ~1+(1|grp), family=beta_resp(), data= beta_dat, prior.weights=rep(2,100))