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#' @name lr_betas
#' @rdname lr_betas
#'
#' @title Likelihood ratio for testing homogeneity constraints on beta coefficients of the SUR equations.
#'
#' @description Function \code{\link{lr_betas}} obtains a Likelihood Ratio test, LR in what follows,
#' with the purpose of testing if some of the \eqn{\beta} coefficients in the \emph{G} equations of the
#' \emph{SUR} model are equal. This function has a straightforward application, especially when \eqn{G=1},
#' to the case of testing for the existence of structural breaks in the \eqn{\beta} parameters.
#'
#' The function can test for the homogeneity of only one coefficient, of a few of them
#' or even the homogeneity of all the slope terms. The testing procedure implies, \emph{first},
#' the estimation of both a constrained and a unconstrained model and, \emph{second}, the comparison
#' of the log-likelihoods to compute the LR statistics.
#'
#' @usage lr_betas (obj, R, b)
#'
#' @inheritParams wald_betas
#'
#' @return Object of \code{htest} including the LR
#' statistic, the corresponding p-value, the degrees of
#' freedom and the values of the sample estimates.
#'
#' @author
#' \tabular{ll}{
#' Fernando Lopez \tab \email{fernando.lopez@@upct.es} \cr
#' Roman Minguez \tab \email{roman.minguez@@uclm.es} \cr
#' Jesus Mur \tab \email{jmur@@unizar.es} \cr
#' }
#'
#' @references
#' \itemize{
#' \item Mur, J., Lopez, F., and Herrera, M. (2010). Testing for spatial
#' effects in seemingly unrelated regressions.
#' \emph{Spatial Economic Analysis}, 5(4), 399-440.
#' <doi:10.1080/17421772.2010.516443>
#' \item Minguez, R., Lopez, F.A. and Mur, J. (2022).
#' spsur: An R Package for Dealing with Spatial
#' Seemingly Unrelated Regression Models.
#' \emph{Journal of Statistical Software},
#' 104(11), 1--43. <doi:10.18637/jss.v104.i11>
#'
#' }
#'
#' @seealso
#' \code{\link{spsurml}}, \code{\link{spsurtime}}, \code{\link{wald_betas}}
#'
#' @examples
#'
#' ## VIP: The output of the whole set of the examples can be examined
#' ## by executing demo(demo_lr_betas, package="spsur")
#'
#' \donttest{
#' #' #################################################
#' ######## CROSS SECTION DATA (G>1; Tm=1) ########
#' #################################################
#'
#' #### Example 1: Spatial Phillips-Curve. Anselin (1988, p. 203)
#' rm(list = ls()) # Clean memory
#' data(spc)
#' lwspc <- spdep::mat2listw(Wspc, style = "W")
#' Tformula <- WAGE83 | WAGE81 ~ UN83 + NMR83 + SMSA | UN80 + NMR80 + SMSA
#' ### H0: equal beta for SMSA in both equations.
#' R <- matrix(c(0,0,0,1,0,0,0,-1), nrow=1)
#' b <- matrix(0, ncol=1)
#' spcsur.slm <- spsurml(formula = Tformula, data = spc,
#' type = "slm", listw = lwspc)
#' summary(spcsur.slm)
#' lr_betas(spcsur.slm, R = R, b = b)
#'
#' ### Estimate restricted SUR-SLM model
#' spcsur.slmr <- spsurml(formula = Tformula, data = spc,
#' type = "slm", listw = lwspc,
#' R = R, b = b)
#' summary(spcsur.slmr)
#' }
#' @export
lr_betas <- function(obj, R, b) {
modelu <- obj
lliku <- logLik(modelu)
cat("\n Fitting restricted model by ML...\n")
modelr <- try( stats::update(modelu, R = R, b = b), silent = TRUE )
if (inherits(modelr, "try-error")) {
modelr <- spsurml(R = R, b = b, Y = modelu$Y, X = modelu$X,
G = modelu$G, N = modelu$N, Tm = modelu$Tm,
type = modelu$type, method = modelu$method,
listw = modelu$W, interval = modelu$interval,
control = list(fdHess = modelu$fdHess))
}
llikr <- logLik(modelr)
statistic <- -2*(llikr-lliku)
attr(statistic, "names") <- "Likelihood ratio"
parameter <- abs(attr(llikr, "df") - attr(lliku, "df"))
if (parameter < 1)
stop("non-positive degrees of freedom: no test possible")
attr(parameter, "names") <- "df"
p.value <- 1 - pchisq(abs(statistic), parameter)
estimate <- c(llikr, lliku)
attr(estimate, "names") <- c("Log likelihood of restricted model",
"Log likelihood of unrestricted model")
method <- "Likelihood ratio on beta parameters"
data.name <- modelu$call[[3]]
res <- list(statistic = statistic, parameter = parameter,
p.value = p.value, estimate = estimate,
method = method, data.name = data.name)
class(res) <- "htest"
res
}
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