densityMclustBounded: Model-based mixture density estimation for bounded data

In mclustAddons: Addons for the 'mclust' Package

Model-based mixture density estimation for bounded data

Description

Density estimation for bounded data via transformation-based approach for Gaussian mixtures.

Usage

densityMclustBounded(data, 
                     G = NULL, modelNames = NULL,
                     lbound = NULL, 
                     ubound = NULL, 
                     lambda = c(-3, 3),
                     parallel = FALSE,
                     seed = NULL,
                     ...)

## S3 method for class 'densityMclustBounded'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'densityMclustBounded'
summary(object, parameters = FALSE, classification = FALSE, ...)

Arguments

data	A numeric vector, matrix, or data frame of observations. If a matrix or data frame, rows correspond to observations and columns correspond to variables.
G	An integer vector specifying the numbers of mixture components. By default G=1:3.
modelNames	A vector of character strings indicating the Gaussian mixture models to be fitted on the transformed-data space. See mclustModelNames for a descripton of available models.
lbound	Numeric vector proving lower bounds for variables.
ubound	Numeric vector proving upper bounds for variables.
lambda	A numeric vector providing the range of searched values for the transformation parameter(s).
parallel	An optional argument which allows to specify if the search over all possible models should be run sequentially (default) or in parallel. For a single machine with multiple cores, possible values are: a logical value specifying if parallel computing should be used (TRUE) or not (FALSE, default) for evaluating the fitness function; a numerical value which gives the number of cores to employ. By default, this is obtained from the function detectCores; a character string specifying the type of parallelisation to use. This depends on system OS: on Windows OS only "snow" type functionality is available, while on Unix/Linux/Mac OSX both "snow" and "multicore" (default) functionalities are available. In all the cases described above, at the end of the search the cluster is automatically stopped by shutting down the workers. If a cluster of multiple machines is available, evaluation of the fitness function can be executed in parallel using all, or a subset of, the cores available to the machines belonging to the cluster. However, this option requires more work from the user, who needs to set up and register a parallel back end. In this case the cluster must be explicitely stopped with stopCluster.
seed	An integer value containing the random number generator state. This argument can be used to replicate the result of k-means initialisation strategy. Note that if parallel computing is required, the doRNG package must be installed.
x, object	An object of class "densityMclustBounded".
digits	The number of significant digits to use for printing.
parameters	Logical; if TRUE, the parameters of mixture components are printed.
classification	Logical; if TRUE, the MAP classification/clustering of observations is printed.
...	Further arguments passed to or from other methods.

Value

Returns an object of class "densityMclustBounded".

Author(s)

Luca Scrucca

References

Scrucca L. (2019) A transformation-based approach to Gaussian mixture density estimation for bounded data. Biometrical Journal, 61:4, 873–888. https://doi.org/10.1002/bimj.201800174

See Also

predict.densityMclustBounded, plot.densityMclustBounded.

Examples

# univariate case with lower bound
x <- rchisq(200, 3)
xgrid <- seq(-2, max(x), length=1000)
f <- dchisq(xgrid, 3)  # true density
dens <- densityMclustBounded(x, lbound = 0)
summary(dens)
summary(dens, parameters = TRUE)
plot(dens, what = "BIC")
plot(dens, what = "density")
lines(xgrid, f, lty = 2)
plot(dens, what = "density", data = x, breaks = 15)

# univariate case with lower & upper bounds
x <- rbeta(200, 5, 1.5)
xgrid <- seq(-0.1, 1.1, length=1000)
f <- dbeta(xgrid, 5, 1.5)  # true density
dens <- densityMclustBounded(x, lbound = 0, ubound = 1)
summary(dens)
plot(dens, what = "BIC")
plot(dens, what = "density")
plot(dens, what = "density", data = x, breaks = 9)

# bivariate case with lower bounds
x1 <- rchisq(200, 3)
x2 <- 0.5*x1 + sqrt(1-0.5^2)*rchisq(200, 5)
x <- cbind(x1, x2)
plot(x)
dens <- densityMclustBounded(x, lbound = c(0,0))
summary(dens, parameters = TRUE)
plot(dens, what = "BIC")
plot(dens, what = "density")
plot(dens, what = "density", type = "hdr")
plot(dens, what = "density", type = "persp")

mclustAddons documentation built on Jan. 6, 2023, 5:21 p.m.