beta_resp {spaMM} | R Documentation |
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).
A fixed-effect residual-dispersion model can be fitted, using the resid.model
argument, which is used to specify the form of the logarithm of the precision parameter (see Examples). Thus the variance of the response become \mu(1-\mu)/(1+
exp(<specified linear expression>)
).
Usage
beta_resp(prec = stop("beta_resp's 'prec' must be specified"), link = "logit")
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 |
Details
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 weights>
). However, this feature is experimental and may be removed in the future. The fitting function's resid.model
argument may be preferred to obtain the same effect, by specifying an offset(log(<prior weights>))
in its formula (given the log link used in that model). As usual in spaMM, the offset(.) argument should be a vector and any variable necessary for evaluating it should be in the data
.
Value
A list, formally of class c("LLF", "family")
. See LL-family
for details about the structure and usage of such objects.
References
Cribari-Neto, F., & Zeileis, A. (2010). Beta Regression in R. Journal of Statistical Software, 34(2), 1-24. 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.
See Also
Further examples in LL-family
.
Examples
set.seed(123)
beta_dat <- data.frame(y=runif(100),grp=sample(2,100,replace = TRUE), x_het=runif(100))
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))
## With model for residual dispersion:
# fitme(y ~1+(1|grp), family=beta_resp(), data= beta_dat, resid.model= ~ x_het)