BIC of estimated marginal gaussian mixture densities

Estimates the density of each covariates with gaussian mixture models and then gives the associated BIC.

density_estimation(
  X = X,
  nbclustmax = 10,
  nbclustmin = 1,
  verbose = FALSE,
  detailed = FALSE,
  max = TRUE,
  package = c("mclust", "Rmixmod"),
  nbini = 20,
  matshape = FALSE,
  ...
)

Arguments

X	the dataset (matrix)
nbclustmax	max number of clusters in the gaussian mixtures
nbclustmin	min number of clusters in the gaussian mixtures
verbose	verbose or not
detailed	boolean to give the details of the mixtures found
max	boolean. Use an heuristic to shrink nbclustmax according to the number of individuals in the dataset
package	package to use ("mclust","Rmixmod" )
nbini	number of initial points for Rmixmod
matshape	boolean to give the detail in matricial shape
...	additional parameters

Value

a list that contains:

BIC_vect

vector of the BIC (one per variable)

BIC

global value of the BIC (=sum(BIC_vect))

nbclust

vector of the numbers of components

details

list of matrices that describe each Gaussian Mixture (proportions, means and variances)

Examples

# dataset generation
base = mixture_generator(n = 150, p = 10, valid = 0, ratio = 0.4, tp1 = 1, tp2 = 1, tp3 = 1, 
                         positive = 0.5, R2Y = 0.8, R2 = 0.9, scale = TRUE, max_compl = 3, 
                         lambda = 1)
X_appr = base$X_appr # learning sample
density = density_estimation(X = X_appr, detailed = TRUE) # estimation of the marginal densities
density$BIC_vect # vector of the BIC (one per variable)
#>  [1] 449.3303 168.6177 428.1307 426.0546 421.3208 437.8150 427.5890 248.5422
#>  [9] 184.2984 210.7557
density$BIC # global value of the BIC (sum of the BICs)
#> [1] 3402.455
density$nbclust # vector of the numbers of components.
#>  [1] 1 1 1 1 1 1 2 1 1 1
density$details # matrices that describe each Gaussian Mixture (proportions, means and variances)
#> [[1]]
#>      prop   meansvect  varvect i
#> [1,]    1 -0.08230836 1.095105 1
#> 
#> [[2]]
#>      prop meansvect   varvect i
#> [1,]    1 0.9437429 0.1685425 2
#> 
#> [[3]]
#>      prop   meansvect   varvect i
#> [1,]    1 -0.04690112 0.9507723 3
#> 
#> [[4]]
#>      prop meansvect   varvect i
#> [1,]    1 0.0600327 0.9377036 4
#> 
#> [[5]]
#>      prop  meansvect  varvect i
#> [1,]    1 0.02855939 0.908573 5
#> 
#> [[6]]
#>      prop meansvect varvect i
#> [1,]    1 -0.012416 1.01418 6
#> 
#> [[7]]
#>        prop  meansvect   varvect i
#> 1 0.4131431 -1.0517942 0.3308719 7
#> 2 0.5868569  0.7863755 0.2319227 7
#> 
#> [[8]]
#>      prop meansvect   varvect i
#> [1,]    1 -0.874094 0.2871537 8
#> 
#> [[9]]
#>      prop meansvect   varvect i
#> [1,]    1 0.8705975 0.1871154 9
#> 
#> [[10]]
#>      prop meansvect   varvect  i
#> [1,]    1 0.9177486 0.2232089 10
#>