betareg {betareg} | R Documentation |
Fit beta regression models for rates and proportions via maximum likelihood using a parametrization with mean (depending through a link function on the covariates) and dispersion parameter (called phi).
betareg(formula, data, subset, na.action, weights, offset, link = c("logit", "probit", "cloglog"), control = betareg.control(...), model = TRUE, y = TRUE, x = FALSE, ...) betareg.fit(x, y, weights = NULL, offset = NULL, link = "logit", control = betareg.control())
formula |
symbolic description of the model (of type y ~ x ). |
data, subset, na.action |
arguments controlling formula processing
via model.frame . |
weights |
optional numeric vector of weights. |
offset |
optional numeric vector with an a priori known component to be included in the linear predictor. |
link |
character specification of link function. |
control |
a list of control arguments specified via
betareg.control . |
model, y, x |
logicals. If TRUE the corresponding components
of the fit (model frame, response, model matrix) are returned.
For betareg.fit , x should be a numeric regressor matrix
and y should be the numeric response vector (with values in (0,1)). |
... |
arguments passed to betareg.control . |
Beta regression as suggested by Ferrari and Cribari-Neto (2004) is implemented in betareg
.
It is useful in situations where the dependent variable is continuous and restricted to
the unit interval (0, 1), e.g., resulting from rates or proportions. It is modeled to be
beta-distributed with parametrization using mean and precision/dispersion parameter (called phi).
The mean is linked, as in generalized linear models (GLMs), to the responses through a link
function and a linear predictor. Estimation is performed by maximum likelihood (ML) via
optim
using analytical gradients and (by default) starting values from an auxiliary
linear regression of the transformed response.
The main parameters of interest are the coefficients
in the linear predictor and the additional precision/dispersion parameter phi which can either
be treated as a full model parameter (default) or as a nuisance parameter. In the latter case
the estimation does not change, only the reported information in output from print
,
summary
, or coef
(among others) will be different. See also betareg.control
.
A set of standard extractor functions for fitted model objects is available for
objects of class "betareg"
, including methods to the generic functions
print
, summary
, plot
, coef
,
vcov
, logLik
, residuals
,
predict
, terms
,
model.frame
, model.matrix
,
cooks.distance
and hatvalues
(see influence.measures
),
gleverage
(new generic), estfun
and
bread
(from the sandwich package), and
coeftest
(from the lmtest package).
See predict.betareg
, residuals.betareg
, plot.betareg
,
and summary.betareg
for more details on all methods.
betareg
returns an object of class "betareg"
, i.e., a list with components as follows.
betareg.fit
returns an unclassed list with components up to converged
.
coefficients |
vector with estimated regression coefficients and dispersion (or precision) parameter phi, |
residuals |
a vector of raw residuals (observed - fitted), |
fitted.values |
a vector of fitted means, |
optim |
output from the optim call for maximizing the log-likelihood(s), |
method |
the method argument passed to the optim call, |
control |
the control arguments passed to the optim call, |
start |
the starting values for the parameters passed to the optim call, |
weights |
the weights used (if any), |
offset |
the offset vector used (if any), |
n |
number of observations, |
df.null |
residual degrees of freedom for the null model (= n - 2 ), |
df.residual |
residual degrees of freedom for fitted model, |
phi |
logical indicating whether phi will be treated as a full model parameter
or a nuisance parameter in subsequent calls to print , summary ,
coef etc., |
loglik |
log-likelihood of the fitted model, |
vcov |
covariance matrix of all parameters in the model (including phi), |
pseudo.R.squared |
pseudo R-squared value (squared correlation of linear predictor and link-transformed response), |
link |
link object used, |
converged |
logical indicating successful convergence of optim , |
call |
the original function call, |
formula |
the original formula, |
terms |
the terms object used, |
levels |
levels of the categorical regressors, |
contrasts |
contrasts corresponding to levels , |
model |
the full model frame (if model = TRUE ), |
y |
the response proportion vector (if y = TRUE ), |
x |
the model matrix (if x = TRUE ). |
Ferrari, S.L.P., and Cribari-Neto, F. (2004). Beta Regression for Modeling Rates and Proportions. Journal of Applied Statistics, 31(7), 799–815.
summary.betareg
, predict.betareg
, residuals.betareg
## Section 4 from Ferrari and Cribari-Neto (2004) data("GasolineYield", package = "betareg") data("FoodExpenditure", package = "betareg") ## Table 1 gy <- betareg(yield ~ batch + temp, data = GasolineYield) summary(gy) ## Table 2 fe_lin <- lm(I(food/income) ~ income + persons, data = FoodExpenditure) library("lmtest") bptest(fe_lin) fe_beta <- betareg(I(food/income) ~ income + persons, data = FoodExpenditure) summary(fe_beta) ## nested model comparisons via Wald and LR tests fe_beta2 <- betareg(I(food/income) ~ income, data = FoodExpenditure) lrtest(fe_beta, fe_beta2) waldtest(fe_beta, fe_beta2)