confint.moc computes confidence intervals (CI) of specified
function of the parameters based on crude Wald asymptotics. More
precise CI for the original parameters are obtained through profiling
of the likelihood function (that is evaluation of the likelihood over
a wide range of values in the parameter space). When profiling is
requested the deviance over different parameters' values is also
returned.
profiles.postCI computes data values for which the empirical
probability of observing such subject values, given mixture group,
lies between the confidence bounds (see details).
density.moc computes the estimated mixture density at data
points along some factor and optionally plot it.
# S3 method for moc
confint(object, parm = list(), level = 0.95,
profiling = c("none","simple","complete"), …)profiles.postCI(object, data = NULL, level = 0.95,
interpolate = TRUE)
# S3 method for moc
density(x, var = NULL, along = NULL,
plot = c("none","pp-plot","density","pq-plot"),
type = "l", …)
A fitted moc object.
A list of formulas beginning with ~ or expressions of the
parameters denoted \(p1,p2,\ldots\) for which confidence intervals
are requested.
For example, parm = list(~p1,~exp(p2)/(1+exp(p1+p3))).
Alpha level in the interval \((0,1)\) for the confidence
bounds \([(1-level)/2,(1+level)/2]\). In profiles.postCI, you
can also directly specify the bounds like level = c(0.02,0.98).
A string that specifies the desired type of likelihood profiling. This can be one of
(default) no profiling.
evaluate the likelihood on a grid of values, one parameters at a time holding the other parameters fixed.
fix one parameter at a time over a grid of values and re-estimate the other parameters.
An optional data.frame, matrix or vector
of length nsubject containing the values for which the
confidence limits are requested. The default is to take the original
response profile.
A logical value indicating whether interpolation of data values must be performed to achieve the probability limits. When "FALSE", the data points with the probabilities nearest to the given bounds are taken (thus using the corresponding step function).
A vector of integer values specifying the response variables for density evaluation.
A factor used to split the density estimator.
A string that specifies the kind of desired plot. Allowed values are
the default.
plot the estimated mixture cumulative probability (CDF) against its empirical counterpart.
plot the estimated CDF against the quintiles.
plot the estimated mixture distribution at observed data points.
The type of lines in the plot, see plot for
details.
Used in density.moc to pass arguments
directly to the plotting function. In confint.moc iterlim
will be passed to update.moc and offscal will change the
profiling parameters search range.
confint.moc returns a list containing a list of arrays
with likelihood deviance for each parameters configuration of the
requested profiling, a function ellip corresponding to the
asymptotic elliptic distance
$$ellip(p)=(p-\hat{p})\hat{\Sigma}^{-1}(p-\hat{p})$$
where \(\hat{p}\) is the maximum likelihood estimator of the
parameters and \(\hat{\Sigma}\) its asymptotic covariance
matrix. It also returns univariate, joint conditional and likelihood
rejection confidence intervals for the parameters (when profiling
has been requested).
profiles.postCI returns a list of array with upper and lower
bounds on data profiles for each mixture group.
density.moc returns nothing when a plot is requested, otherwise
an array with mixture density estimate and data points is returned.
The methods included here primarily exploit the empirical estimators
of the conditional expectation given mixture group for some
appropriately chosen function of the data \(g()\), that is
$$\hat{g}_k=\frac{\sum_i wt_i\,\hat{\tau}_{i,k}\,g(y_i)}{\sum_i
wt_i\,\hat{\tau}_{i,k}}.$$
Profiles confidence intervals and density estimates are defined
by choosing \(g()\) as the indicator function over appropriate sets.
See print.moc and residuals.moc.
moc, print.moc,
residuals.moc, post.moc,
loglike.moc, profilesplot