PGMM_dfree: 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). This 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 UUU and UUC covariance structures).

Usage

PGMM_dfree(Q, P, G = 1, method = c("UUU", "UUC", "UCU", "UCC", "CUU", "CUC",
  "CCU", "CCC"))

Arguments

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

The number of variables.

The number of groups. This defaults to 1.

method

By default, calculation assumes the UUU model with unconstrained loadings and unconstrained isotropic uniquesses. The other seven models detailed in McNicholas and Murphy (2008) are also given. The first letter denotes whether loadings are constrained/unconstrained across groups; the second letter denotes the same for the uniquenesses; the final letter denotes whether uniquenesses are in turn constrained to be isotropic.

Value

A vector of length length(Q).

References

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

Examples

Run this code

# NOT RUN {
UUU <- PGMM_dfree(Q=4:5, P=50, G=3, method="UUU")
CCC <- PGMM_dfree(Q=4:5, P=50, G=3, method="CCC")
# }