MoE_dens: Density for MoEClust Mixture Models

In MoEClust: Gaussian Parsimonious Clustering Models with Covariates and a Noise Component

Density for MoEClust Mixture Models

Description

Computes densities (or log-densities) of observations in MoEClust mixture models.

Usage

MoE_dens(data,
         mus,
         sigs,
         log.tau = 0L,
         Vinv = NULL,
         logarithm = TRUE)

Arguments

data	If there are no expert network covariates, data should be a numeric matrix or data frame, wherein rows correspond to observations (n) and columns correspond to variables (d). If there are expert network covariates, this should be a list of length G containing matrices/data.frames of (multivariate) WLS residuals for each component.
mus	The mean for each of G components. If there is more than one component, this is a matrix whose k-th column is the mean of the k-th component of the mixture model. For the univariate models, this is a G-vector of means. In the presence of expert network covariates, all values should be equal to 0.
sigs	The variance component in the parameters list from the output to e.g. MoE_clust. The components of this list depend on the specification of modelName (see mclustVariance for details). The number of components G, the number of variables d, and the modelName are inferred from sigs.
log.tau	If covariates enter the gating network, an n times G matrix of mixing proportions, otherwise a G-vector of mixing proportions for the components of the mixture. Must be on the log-scale in both cases. The default of 0 effectively means densities (or log-densities) aren't scaled by the mixing proportions.
Vinv	An estimate of the reciprocal hypervolume of the data region. See the function noise_vol. Used only if an initial guess as to which observations are noise is supplied. Mixing proportion(s) must be included for the noise component also.
logarithm	A logical value indicating whether or not the logarithm of the component densities should be returned. This defaults to TRUE, otherwise component densities are returned, obtained from the component log-densities by exponentiation. The log-densities can be passed to MoE_estep or MoE_cstep.

Value

A numeric matrix whose [i,k]-th entry is the density or log-density of observation i in component k, scaled by the mixing proportions. These densities are unnormalised.

Note

This function is intended for joint use with MoE_estep or MoE_cstep, using the log-densities. Note that models with a noise component are facilitated here too.

Author(s)

Keefe Murphy - <[e-mail]>

See Also

MoE_estep, MoE_cstep, MoE_clust, mclustVariance

Examples

data(ais)
hema  <- ais[,3:7]
model <- MoE_clust(hema, G=3, gating= ~ BMI + sex, modelNames="EEE", network.data=ais)
Dens  <- MoE_dens(data=hema, mus=model$parameters$mean,
                  sigs=model$parameters$variance, log.tau=log(model$parameters$pro))

# Construct the z matrix and compute the log-likelihood
Estep <- MoE_estep(Dens=Dens)
(ll   <- Estep$loglik)

# Check that the z matrix & classification are the same as those from the model
identical(max.col(Estep$z), as.integer(unname(model$classification))) #TRUE
identical(Estep$z, model$z)                                           #TRUE

# The same can be done for models with expert covariates &/or a noise component
# Note for models with expert covariates that the mean has to be supplied as 0,
# and the data has to be supplied as "resid.data"
m2    <- MoE_clust(hema, G=2, expert= ~ sex, modelNames="EVE", network.data=ais, tau0=0.1)
Dens2 <- MoE_dens(data=m2$resid.data, sigs=m2$parameters$variance, mus=0, 
                  log.tau=log(m2$parameters$pro), Vinv=m2$parameters$Vinv)

MoEClust documentation built on May 29, 2024, 6:44 a.m.