waldtypetest {robustbetareg} | R Documentation |
Robust Wald-type Tests
Description
waldtypetest
provides Wald-type tests for both simple and composite
hypotheses for beta regression based on the robust estimators
(LSMLE, LMDPDE, SMLE, and MDPDE).
Usage
waldtypetest(object, FUN, ...)
Arguments
object |
fitted model object of class |
FUN |
function representing the null hypothesis to be tested. |
... |
further arguments to be passed to the |
Details
The function provides a robust Wald-type test for a general hypothesis
m(\theta) = \eta_0
, for a fixed \eta_0 \in R^d
, against
a two sided alternative; see Maluf et al. (2022) for details.
The argument FUN
specifies the function m(\theta) - \eta_0
,
which defines the null hypothesis. For instance, consider a model with
\theta = (\beta_1, \beta_2, \beta_3, \gamma_1)^\top
and let the
null hypothesis be \beta_2 + \beta_3 = 4
. The FUN
argument can be
FUN = function(theta) {theta[2] + theta[3] - 4}
. It is also possible to
define the function as FUN = function(theta, B) {theta[2] + theta[3] - B}
,
and pass the B
argument through the waldtypetest
function.
If no function is specified, that is, FUN=NULL
, the waldtypetest
returns a test in which the null hypothesis is that all the coefficients are
zero.
Value
waldtypetest
returns an output for the Wald-type test containing
the value of the test statistic, degrees-of-freedom and p-value.
Author(s)
Yuri S. Maluf (yurimaluf@gmail.com), Francisco F. Queiroz (ffelipeq@outlook.com) and Silvia L. P. Ferrari.
References
Maluf, Y. S., Ferrari, S. L. P., and Queiroz, F. F. (2022). Robust
beta regression through the logit transformation. arXiv:2209.11315.
Basu, A., Ghosh, A., Martin, N., and Pardo, L. (2018). Robust Wald-type
tests for non-homogeneous observations based on the minimum density
power divergence estimator. Metrika, 81:493–522.
Ribeiro, K. A. T. and Ferrari, S. L. P. (2022). Robust estimation in beta
regression via maximum Lq-likelihood. Statistical Papers.
See Also
Examples
# generating a dataset
set.seed(2022)
n <- 40
beta.coef <- c(-1, -2)
gamma.coef <- c(5)
X <- cbind(rep(1, n), x <- runif(n))
mu <- exp(X%*%beta.coef)/(1 + exp(X%*%beta.coef))
phi <- exp(gamma.coef) #Inverse Log Link Function
y <- rbeta(n, mu*phi, (1 - mu)*phi)
y[26] <- rbeta(1, ((1 + mu[26])/2)*phi, (1 - ((1 + mu[26])/2))*phi)
SimData <- as.data.frame(cbind(y, x))
colnames(SimData) <- c("y", "x")
# Fitting the MLE and the LSMLE
fit.mle <- robustbetareg(y ~ x | 1, data = SimData, alpha = 0)
fit.lsmle <- robustbetareg(y ~ x | 1, data = SimData)
# Hypothesis to be tested: (beta_1, beta_2) = c(-1, -2) against a two
# sided alternative
h0 <- function(theta){theta[1:2] - c(-1, -2)}
waldtypetest(fit.mle, h0)
waldtypetest(fit.lsmle, h0)
# Alternative way:
h0 <- function(theta, B){theta[1:2] - B}
waldtypetest(fit.mle, h0, B = c(-1, -2))
waldtypetest(fit.lsmle, h0, B = c(-1, -2))