MoEClust (version 1.4.1)

MoE_compare: Choose the best MoEClust model

Description

Takes one or more sets of MoEClust models fitted by MoE_clust (or MoE_stepwise) and ranks them according to the BIC, ICL, or AIC. It's possible to respect the internal ranking within each set of models, or to discard models within each set which were already deemed sub-optimal. This function can help with model selection via exhaustive or stepwise searches.

Usage

MoE_compare(...,
            criterion = c("bic", "icl", "aic"),
            pick = 10L,
            optimal.only = FALSE)
# S3 method for MoECompare
print(x,
      index = seq_len(x$pick),
      posidens = TRUE,
      rerank = FALSE,
      digits = 3L,
      details = TRUE, 
      maxi = length(index),
      ...)

Arguments

...

One or more objects of class "MoEClust" outputted by MoE_clust. All models must have been fit to the same data set. A single named list of such objects can also be supplied. Additionally, objects of class "MoECompare" outputted by this very function can also be supplied here.

This argument is only relevant for the MoE_compare function and will be ignored for the associated print function.

criterion

The criterion used to determine the ranking. Defaults to "bic".

pick

The (integer) number of models to be ranked and compared. Defaults to 10L. Will be constrained by the number of models within the "MoEClust" objects supplied via ... if optimal.only is FALSE, otherwise constrained simply by the number of "MoEClust" objects supplied. Setting pick=Inf is a valid way to select all models.

optimal.only

Logical indicating whether to only rank models already deemed optimal within each "MoEClust" object (TRUE), or to allow models which were deemed suboptimal enter the final ranking (FALSE, the default). See details.

x, index, posidens, rerank, digits, details, maxi

Arguments required for the associated print function:

x

An object of class "MoECompare" resulting from a call to MoE_compare.

index

A logical or numeric vector giving the indices of the rows of the table of ranked models to print. This defaults to the full set of ranked models. It can be useful when the table of ranked models is large to examine a subset via this index argument, for display purposes. See rerank.

posidens

A logical indicating whether models which have been flagged for having positive log-densities should be included in the comparison (defaults to TRUE). Such models may correspond to spurious solutions and can be discarded by specifying posidens=FALSE. Only relevant if any of the "MoEClust" objects being compared were themselves run with posidens=TRUE.

rerank

A logical indicating whether the ranks should be recomputed when subsetting using index. Defaults to FALSE. Only relevant when details=TRUE.

digits

The number of decimal places to round model selection criteria to (defaults to 3).

details

Logical indicating whether some additional details should be printed, defaults to TRUE. Exists to facilitate MoE_stepwise printing.

maxi

A number specifying the maximum number of rows/models to print. Defaults to length(index).

Value

A list of class "MoECompare", for which a dedicated print function exists, containing the following elements (each of length pick, and ranked according to criterion, where appropriate):

data

The name of the data set to which the models were fitted.

optimal

The single optimal model (an object of class "MoEClust") among those supplied, according to the chosen criterion.

pick

The final number of ranked models. May be different (i.e. less than) the supplied pick value.

MoENames

The names of the supplied "MoEClust" objects.

modelNames

The mclustModelNames.

G

The optimal numbers of components.

df

The numbers of estimated parameters.

iters

The numbers of EM/CEM iterations.

bic

BIC values, ranked according to criterion.

icl

ICL values, ranked according to criterion.

aic

AIC values, ranked according to criterion.

loglik

Maximal log-likelihood values, ranked according to criterion.

gating

The gating formulas.

expert

The expert formulas.

algo

The algorithm used for fitting the model - either "EM", "CEM", "cemEM".

equalPro

Logical indicating whether mixing proportions were constrained to be equal across components.

hypvol

Hypervolume parameters for the noise component if relevant, otherwise set to NA (see MoE_control).

noise

The type of noise component fitted (if any). Only displayed if at least one of the compared models has a noise component.

noise.gate

Logical indicating whether gating covariates were allowed to influence the noise component's mixing proportion. Only printed for models with a noise component, when at least one of the compared models has gating covariates.

equalNoise

Logical indicating whether the mixing proportion of the noise component for equalPro models is also equal (TRUE) or estimated (FALSE).

Details

The purpose of this function is to conduct model selection on "MoEClust" objects, fit to the same data set, with different combinations of gating/expert network covariates or different initialisation settings.

Model selection will have already been performed in terms of choosing the optimal number of components and GPCM/mclust model type within each supplied set of results, but MoE_compare will respect the internal ranking of models when producing the final ranking if optimal.only is FALSE: otherwise only those models already deemed optimal within each "MoEClust" object will be ranked.

As such if two sets of results are supplied when optimal.only is FALSE, the 1st, 2nd and 3rd best models could all belong to the first set of results, meaning a model deemed suboptimal according to one set of covariates could be superior to one deemed optimal under another set of covariates.

References

Murphy, K. and Murphy, T. B. (2020). Gaussian parsimonious clustering models with covariates and a noise component. Advances in Data Analysis and Classification, 14(2): 293-325. <10.1007/s11634-019-00373-8>.

See Also

See MoE_stepwise for identifying the optimal model and its covariates via greedy forward stepwise selection.

MoE_clust, mclustModelNames, plot.MoEClust, as.Mclust

Examples

# NOT RUN {
data(CO2data)
CO2   <- CO2data$CO2
GNP   <- CO2data$GNP

# Fit a range of models 
m1    <- MoE_clust(CO2, G=1:3)
m2    <- MoE_clust(CO2, G=2:3, gating= ~ GNP)
m3    <- MoE_clust(CO2, G=1:3, expert= ~ GNP)
m4    <- MoE_clust(CO2, G=2:3, gating= ~ GNP, expert= ~ GNP)
m5    <- MoE_clust(CO2, G=2:3, equalPro=TRUE)
m6    <- MoE_clust(CO2, G=2:3, expert= ~ GNP, equalPro=TRUE)
m7    <- MoE_clust(CO2, G=2:3, expert= ~ GNP, tau0=0.1)

# Rank only the optimal models and examine the best model
(comp <- MoE_compare(m1, m2, m3, m4, m5, m6, m7, optimal.only=TRUE))
(best <- comp$optimal)
(summ <- summary(best, classification=TRUE, parameters=TRUE, networks=TRUE))

# Examine all models visited, including those already deemed suboptimal
# Only print models with expert covariates & more than one component
comp2 <- MoE_compare(m1, m2, m3, m4, m5, m6, m7, pick=Inf)
print(comp2, index=comp2$expert != "None" & comp2$G > 1)

# Conduct a stepwise search on the same data
(mod1 <- MoE_stepwise(CO2, GNP))

# Conduct another stepwise search considering models with a noise component
(mod2 <- MoE_stepwise(CO2, GNP, noise=TRUE))

# Compare both sets of results to choose the optimal model
(best <- MoE_compare(mod1, mod2, optimal.only=TRUE)$optimal)
# }