PGMM_dfree {IMIFA}

Estimate the Number of Free Parameters in Finite Factor Analytic Mixture Models (PGMM)

Description

Estimates the dimension of the 'free' parameters in fully finite factor analytic mixture models, otherwise known as Parsimonious Gaussian Mixture Models (PGMM), typically necessary for the penalty term of various model selection criteria.

Usage

PGMM_dfree(Q,
           P,
           G = 1L,
           method = c("UUU", "UUC", "UCU", "UCC", "CUU", "CUC",
                      "CCU", "CCC", "CCUU", "UCUU", "CUCU", "UUCU"),
           equal.pro = FALSE)

Arguments

Q

The number of latent factors (which can be 0, corresponding to a model with diagonal covariance). This argument is vectorised.

P

The number of variables. Must be a single strictly positive integer.

G

The number of clusters. This defaults to 1. Must be a single strictly positive integer.

method

By default, calculation assumes the UUU model with unconstrained loadings and unconstrained diagonal uniquesseses (i.e. the factor analysis model). The seven other models detailed in McNicholas and Murphy (2008) are given too (of which currently the first four are accommodated within mcmc_IMIFA). The first letter denotes whether loadings are constrained/unconstrained across clusters; the second letter denotes the same for the uniquenesses; the final letter denotes whether uniquenesses are in turn constrained to be isotropic. Finally, the 4 extra 4-letter models from the EPGMM family (McNicholas and Murphy, 2010), are also included.

equal.pro

Logical variable indicating whether or not the mixing mixing proportions are equal across clusters in the model (default = FALSE).

Value

A vector of length length(Q) giving the total number of parameters, including means and mixing proportions, and not only covariance parameters. Set equal.pro to FALSE and subtract G * P from the result to determine the number of covariance parameters only.

Note

This function is used to calculate the penalty terms for the aic.mcmc and bic.mcmc model selection criteria implemented in get_IMIFA_results for finite factor models (though mcmc_IMIFA currently only implements the UUU, UUC, UCU, and UCC covariance structures). The function is vectorised with respect to the argument Q.

Though the function is available for standalone use, note that no checks take place, in order to speed up repeated calls to the function inside mcmc_IMIFA.

Author(s)

Keefe Murphy - <[e-mail]>

References

McNicholas, P. D. and Murphy, T. B. (2008) Parsimonious Gaussian mixture models, Statistics and Computing, 18(3): 285-296.

McNicholas, P. D. and Murphy, T. B. (2010) Model-Based clustering of microarray expression data via latent Gaussian mixture models, Bioinformatics, 26(21): 2705-2712.

See Also

get_IMIFA_results, mcmc_IMIFA

Examples

(UUU <- PGMM_dfree(Q=0:5, P=50, G=3, method="UUU"))
(CCC <- PGMM_dfree(Q=0:5, P=50, G=3, method="CCC", equal.pro=TRUE))