confint method for objects of class "chandwich".
Computes confidence intervals for one or more model parameters based
on an object returned from adjust_loglik.
An object of class "chandwich", returned by
adjust_loglik.
A vector specifying the (unfixed) parameters for which confidence intervals are required. If missing, all parameters are included.
Can be either a numeric vector,
specifying indices of the components of the full parameter
vector, or a character vector of parameter names, which must be a subset
of those supplied in par_names in the call to
adjust_loglik that produced object.
parm must not have any parameters in common with
attr(object, "fixed_pars"). parm must not contain
all of the unfixed parameters, i.e. there is no point in profiling over
all the unfixed parameters.
The confidence level required. A numeric scalar in (0, 1).
A character scalar. The argument type to the function
returned by adjust_loglik, that is, the type of adjustment
made to the independence loglikelihood function.
A logical scalar. If TRUE then confidence intervals
based on an (adjusted) profile loglikelihood are returned. If
FALSE then intervals based on approximate large sample normal
theory, which are symmetric about the MLE, are returned.
Further arguments to be passed to conf_intervals.
A matrix with columns giving lower and upper confidence limits for each parameter. These will be labelled as (1 - level)/2 and 1 - (1 - level)/2 in % (by default 2.5% and 97.5%). The row names are the names of the model parameters, if these are available.
For details see the documentation for the function
conf_intervals, on which confint.chandwich is based.
The underlying function conf_intervals. If you would
like to plot the profile loglikelihood function for a parameter then call
conf_intervals directly and then use the associated plot
method. Note that in conf_intervals() a parameter choice is
specified using an argument called which_pars, not parm.
conf_region for a confidence region for
pairs of parameters.
compare_models for an adjusted likelihood ratio test
of two models.
adjust_loglik to adjust a user-supplied
loglikelihood function.
# -------------------------- GEV model, owtemps data -----------------------
# ------------ following Section 5.2 of Chandler and Bate (2007) -----------
gev_loglik <- function(pars, data) {
o_pars <- pars[c(1, 3, 5)] + pars[c(2, 4, 6)]
w_pars <- pars[c(1, 3, 5)] - pars[c(2, 4, 6)]
if (isTRUE(o_pars[2] <= 0 | w_pars[2] <= 0)) return(-Inf)
o_data <- data[, "Oxford"]
w_data <- data[, "Worthing"]
check <- 1 + o_pars[3] * (o_data - o_pars[1]) / o_pars[2]
if (isTRUE(any(check <= 0))) return(-Inf)
check <- 1 + w_pars[3] * (w_data - w_pars[1]) / w_pars[2]
if (isTRUE(any(check <= 0))) return(-Inf)
o_loglik <- log_gev(o_data, o_pars[1], o_pars[2], o_pars[3])
w_loglik <- log_gev(w_data, w_pars[1], w_pars[2], w_pars[3])
return(o_loglik + w_loglik)
}
# Initial estimates (method of moments for the Gumbel case)
sigma <- as.numeric(sqrt(6 * diag(var(owtemps))) / pi)
mu <- as.numeric(colMeans(owtemps) - 0.57722 * sigma)
init <- c(mean(mu), -diff(mu) / 2, mean(sigma), -diff(sigma) / 2, 0, 0)
# Log-likelihood adjustment of the full model
par_names <- c("mu[0]", "mu[1]", "sigma[0]", "sigma[1]", "xi[0]", "xi[1]")
large <- adjust_loglik(gev_loglik, data = owtemps, init = init,
par_names = par_names)
confint(large)
#> Waiting for profiling to be done...
#> 2.5 % 97.5 %
#> mu[0] 80.3729113 81.96020651
#> mu[1] 2.2435715 3.08287072
#> sigma[0] 3.2992230 4.25997602
#> sigma[1] 0.1611821 0.94337677
#> xi[0] -0.2740991 -0.11571585
#> xi[1] -0.1651864 -0.02001604
confint(large, profile = FALSE)
#> 2.5 % 97.5 %
#> mu[0] 80.3790976 81.96120586
#> mu[1] 2.2512784 3.08552167
#> sigma[0] 3.2536759 4.20458854
#> sigma[1] 0.1565970 0.90573598
#> xi[0] -0.2762342 -0.12166268
#> xi[1] -0.1593869 -0.01730812