mixmodGaussianModel {Rmixmod} | R Documentation

## Create an instance of the [`GaussianModel`] class

### Description

Define a list of Gaussian model to test in MIXMOD.

### Usage

    mixmodGaussianModel(family = "all", listModels = NULL,
      free.proportions = TRUE, equal.proportions = TRUE)

### Arguments

`family` | character defining a family of models. "general" for the general family, "diagonal" for the diagonal family, "spherical" for the spherical family and "all" for all families. Default is "general".
`listModels` | a list of characters containing a list of models. It is optional.
`free.proportions` | logical to include models with free proportions. Default is TRUE.
`equal.proportions` | logical to include models with equal proportions. Default is TRUE.

### Details

In the Gaussian mixture model, following Banfield and Raftery (1993) and Celeux and Govaert (1995), we consider a parameterization of the variance matrices of the mixture components consisting of expressing the variance matrix Σ_{k} in terms of its eigenvalue decomposition

Σ_{k}= λ_{k} D_{k} A_{k}D'_{k}

where λ_{k}=|Σ_{k}|^{1/d}, D_{k} is the matrix of eigenvectors of Σ_{k} and A_{k} is a diagonal matrix, such that | A_{k} |=1, with the normalized eigenvalues of Σ_{k} on the diagonal in a decreasing order. The parameter λ_{k} determines the volume of the kth cluster, D_{k} its orientation and A_{k} its shape. By allowing some but not all of these quantities to vary between clusters, we obtain parsimonious and easily interpreted models which are appropriate to describe various clustering situations.

In general family, we can allow the volumes, the shapes and the orientations of clusters to vary or to be equal between clusters. Variations on assumptions on the parameters λ_{k}, D_{k} and A_{k} (1 ≤q k ≤q K) lead to 8 general models of interest. For instance, we can assume different volumes and keep the shapes and orientations equal by requiring that A_{k}=A (A unknown) and D_{k}=D (D unknown) for k=1,…,K. We denote this model [λ_{k}DAD']. With this convention, writing [λ D_{k}AD'_{k}] means that we consider the mixture model with equal volumes, equal shapes and different orientations. In diagonal family, we assume that the variance matrices Σ_{k} are diagonal. In the parameterization, it means that the orientation matrices D_{k} are permutation matrices. We write Σ_{k}=λ_{k}B_{k} where B_{k} is a diagonal matrix with | B_{k}|=1. This particular parameterization gives rise to 4 models: [λ B], [λ_{k}B], [λ B_{k}] and [λ_{k}B_{k}].

In spherical family, we assume spherical shapes, namely A_{k}=I, I denoting the identity matrix. In such a case, two parsimonious models are in competition: [λ I] and [λ_{k}I].

### Value

an object of [`GaussianModel`] which contains some of the 28 Gaussian Models:

Model | Family | Prop. | Volume | Shape | Orient.
Gaussian_p_L_C | General | Equal | Equal | Equal | Equal
Gaussian_p_Lk_C |  |  | Free | Equal | Equal
Gaussian_p_L_D_Ak_D |  |  | Equal | Free | Equal
Gaussian_p_Lk_D_Ak_D |  |  | Free | Free | Equal
Gaussian_p_L_Dk_A_Dk |  |  | Equal | Equal | Free
Gaussian_p_Lk_Dk_A_Dk |  |  | Free | Equal | Free
Gaussian_p_L_Ck |  |  | Equal | Free | Free
Gaussian_p_Lk_Ck |  |  | Free | Free | Free
Gaussian_p_L_B | Diagonal | Equal | Equal | Equal | Axes
Gaussian_p_Lk_B |  |  | Free | Equal | Axes
Gaussian_p_L_Bk |  |  | Equal | Free | Axes
Gaussian_p_Lk_Bk |  |  | Free | Free | Axes
Gaussian_p_L_I | Spherical | Equal | Equal | Equal | NA
Gaussian_p_Lk_I |  |  | Free | Equal | NA
Gaussian_pk_L_C | General | Free | Equal | Equal | Equal
Gaussian_pk_Lk_C |  |  | Free | Equal | Equal
Gaussian_pk_L_D_Ak_D |  |  | Equal | Free | Equal
Gaussian_pk_Lk_D_Ak_D |  |  | Free | Free | Equal
Gaussian_pk_L_Dk_A_Dk |  |  | Equal | Equal | Free
Gaussian_pk_Lk_Dk_A_Dk |  |  | Free | Equal | Free
Gaussian_pk_L_Ck |  |  | Equal | Free | Free
Gaussian_pk_Lk_Ck |  |  | Free | Free | Free
Gaussian_pk_L_B | Diagonal | Free | Equal | Equal | Axes
Gaussian_pk_Lk_B |  |  | Free | Equal | Axes
Gaussian_pk_L_Bk |  |  | Equal | Free | Axes
Gaussian_pk_Lk_Bk |  |  | Free | Free | Axes
Gaussian_pk_L_I | Spherical | Free | Equal | Equal | NA
Gaussian_pk_Lk_I |  |  | Free | Equal | NA

### Author(s)

Florent Langrognet and Remi Lebret and Christian Poli ans Serge Iovleff, with contributions from C. Biernacki and G. Celeux and G. Govaert contact@mixmod.org

### References

C. Biernacki, G. Celeux, G. Govaert, F. Langrognet. "Model-Based Cluster and Discriminant Analysis with the MIXMOD Software". Computational Statistics and Data Analysis, vol. 51/2, pp. 587-600. (2006)

### Examples

      mixmodGaussianModel()
      # all Gaussian models with equal proportions
      mixmodGaussianModel(family="all",free.proportions=FALSE)
      # Diagonal and Spherical Gaussian models
      mixmodGaussianModel(family=c("diagonal","spherical"))
      # Gaussian models with a pre-defined list
      mixmodGaussianModel(listModels=c("Gaussian_p_L_C","Gaussian_p_L_Ck","Gaussian_pk_L_I"))

[Package Rmixmod version 2.1.2.2 Index]