MclustBootstrap: Resampling-based Inference for Gaussian finite mixture models

In mclust: Gaussian Mixture Modelling for Model-Based Clustering, Classification, and Density Estimation

Resampling-based Inference for Gaussian finite mixture models

Description

Bootstrap or jackknife estimation of standard errors and percentile bootstrap confidence intervals for the parameters of a Gaussian mixture model.

Usage

MclustBootstrap(object, nboot = 999, 
                type = c("bs", "wlbs", "pb", "jk"),
                alpha = 1, max.nonfit = 10*nboot, 
                verbose = interactive(), ...)

Arguments

object	An object of class 'Mclust' or 'densityMclust' providing an estimated Gaussian mixture model.
nboot	The number of bootstrap replications.
type	A character string specifying the type of resampling to use: "bs" nonparametric bootstrap "wlbs" weighted likelihood bootstrap "pb" parametric bootstrap "jk" jackknife
alpha	A numerical value used when type = "wlbs" to generate weights from a Dirichlet(alpha, ..., alpha) distribution. By default alpha = 1, so weights are generated from a uniform distribution on the simplex.
max.nonfit	The maximum number of non-estimable models allowed.
verbose	A logical controlling if a text progress bar is displayed during the resampling procedure. By default is TRUE if the session is interactive, and FALSE otherwise.
...	Further arguments passed to or from other methods.

Details

For a fitted Gaussian mixture model with object$G mixture components and covariances parameterisation object$modelName, this function returns either the bootstrap distribution or the jackknife distribution of mixture parameters. In the former case, the nonparametric bootstrap or the weighted likelihood bootstrap approach could be used, so the the bootstrap procedure generates nboot bootstrap samples of the same size as the original data by resampling with replacement from the observed data. In the jackknife case, the procedure considers all the samples obtained by omitting one observation at time.

The resulting resampling distribution can then be used to obtain standard errors and percentile confidence intervals by the use of summary.MclustBootstrap function.

Value

An object of class 'MclustBootstrap' with the following components:

n	The number of observations in the data.
d	The dimension of the data.
G	A value specifying the number of mixture components.
modelName	A character string specifying the mixture model covariances parameterisation (see mclustModelNames).
parameters	A list of estimated parameters for the mixture components with the following components: pro a vector of mixing proportions. mean a matrix of means for each component. variance an array of covariance matrices for each component.
nboot	The number of bootstrap replications if type = "bs" or type = "wlbs". The sample size if type = "jk".
type	The type of resampling approach used.
nonfit	The number of resamples that did not convergence during the procedure.
pro	A matrix of dimension (nboot x G) containing the bootstrap distribution for the mixing proportion.
mean	An array of dimension (nboot x d x G), where d is the dimension of the data, containing the bootstrap distribution for the component means.
variance	An array of dimension (nboot x d x d x G), where d is the dimension of the data, containing the bootstrap distribution for the component covariances.

References

Davison, A. and Hinkley, D. (1997) Bootstrap Methods and Their Applications. Cambridge University Press.

McLachlan, G.J. and Peel, D. (2000) Finite Mixture Models. Wiley.

O'Hagan A., Murphy T. B., Gormley I. C. and Scrucca L. (2015) On Estimation of Parameter Uncertainty in Model-Based Clustering. Submitted to Computational Statistics.

See Also

summary.MclustBootstrap, plot.MclustBootstrap, Mclust, densityMclust.

Examples

data(diabetes)
X <- diabetes[,-1]
modClust <- Mclust(X) 
bootClust <- MclustBootstrap(modClust)
summary(bootClust, what = "se")
summary(bootClust, what = "ci")

data(acidity)
modDens <- densityMclust(acidity, plot = FALSE)
modDens <- MclustBootstrap(modDens)
summary(modDens, what = "se")
summary(modDens, what = "ci")

mclust documentation built on May 29, 2024, 8:06 a.m.