mixmodCompositeModel {Rmixmod} | R Documentation

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

### Description

Define a list of heterogeneous model to test in MIXMOD.

### Usage

    mixmodCompositeModel(listModels = NULL, free.proportions = TRUE,
      equal.proportions = TRUE, variable.independency = NULL,
      component.independency = NULL)

### Arguments

`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.
`variable.independency` | logical to include models where [\varepsilon_k^j] is independent of the variable j. Optionnal.
`component.independency` | logical to include models where [\varepsilon_k^j] is independent of the component k. Optionnal.

### Details

In heterogeneous case, Gaussian model can only belong to the 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}]. The multinomial distribution is associated to the jth variable of the kth component is reparameterized by a center a_k^j and the dispersion \varepsilon_k^j around this center. Thus, it allows us to give an interpretation similar to the center and the variance matrix used for continuous data in the Gaussian mixture context. In the following, this model will be denoted by [\varepsilon_k^j]. In this context, three other models can be easily deduced. We note [\varepsilon_k] the model where \varepsilon_k^j is independent of the variable j, [\varepsilon^j] the model where \varepsilon_k^j is independent of the component k and, finally, [\varepsilon] the model where \varepsilon_k^j is independent of both the variable $j$ and the component k. In order to maintain some unity in the notation, we will denote also [\varepsilon_k^{jh}] the most general model introduced at the previous section.

### Value

an object of [`CompositeModel`] which contains some of the 40 heterogeneous Models:

Model | Prop. | Var. | Comp. | Volume | Shape
Heterogeneous_p_E_L_B | Equal | TRUE | TRUE | Equal | Equal
Heterogeneous_p_E_Lk_B |  | TRUE | TRUE | Free | Equal
Heterogeneous_p_E_L_Bk |  | TRUE | TRUE | Equal | Free
Heterogeneous_p_E_Lk_Bk |  | TRUE | TRUE | Free | Free
Heterogeneous_p_Ek_L_B |  | TRUE | FALSE | Equal | Equal
Heterogeneous_p_Ek_Lk_B |  | TRUE | FALSE | Free | Equal
Heterogeneous_p_Ek_L_Bk |  | TRUE | FALSE | Equal | Free
Heterogeneous_p_Ek_Lk_Bk |  | TRUE | FALSE | Free | Free
Heterogeneous_p_Ej_L_B |  | FALSE | TRUE | Equal | Equal
Heterogeneous_p_Ej_Lk_B |  | FALSE | TRUE | Free | Equal
Heterogeneous_p_Ej_L_Bk |  | FALSE | TRUE | Equal | Free
Heterogeneous_p_Ej_Lk_Bk |  | FALSE | TRUE | Free | Free
Heterogeneous_p_Ekj_L_B |  | FALSE | FALSE | Equal | Equal
Heterogeneous_p_Ekj_Lk_B |  | FALSE | FALSE | Free | Equal
Heterogeneous_p_Ekj_L_Bk |  | FALSE | FALSE | Equal | Free
Heterogeneous_p_Ekj_Lk_Bk |  | FALSE | FALSE | Free | Free
Heterogeneous_p_Ekjh_L_B |  | FALSE | FALSE | Equal | Equal
Heterogeneous_p_Ekjh_Lk_B |  | FALSE | FALSE | Free | Equal
Heterogeneous_p_Ekjh_L_Bk |  | FALSE | FALSE | Equal | Free
Heterogeneous_p_Ekjh_Lk_Bk |  | FALSE | FALSE | Free | Free
Heterogeneous_pk_E_L_B | Free | TRUE | TRUE | Equal | Equal
Heterogeneous_pk_E_Lk_B |  | TRUE | TRUE | Free | Equal
Heterogeneous_pk_E_L_Bk |  | TRUE | TRUE | Equal | Free
Heterogeneous_pk_E_Lk_Bk |  | TRUE | TRUE | Free | Free
Heterogeneous_pk_Ek_L_B |  | TRUE | FALSE | Equal | Equal
Heterogeneous_pk_Ek_Lk_B |  | TRUE | FALSE | Free | Equal
Heterogeneous_pk_Ek_L_Bk |  | TRUE | FALSE | Equal | Free
Heterogeneous_pk_Ek_Lk_Bk |  | TRUE | FALSE | Free | Free
Heterogeneous_pk_Ej_L_B |  | FALSE | TRUE | Equal | Equal
Heterogeneous_pk_Ej_Lk_B |  | FALSE | TRUE | Free | Equal
Heterogeneous_pk_Ej_L_Bk |  | FALSE | TRUE | Equal | Free
Heterogeneous_pk_Ej_Lk_Bk |  | FALSE | TRUE | Free | Free
Heterogeneous_pk_Ekj_L_B |  | FALSE | FALSE | Equal | Equal
Heterogeneous_pk_Ekj_Lk_B |  | FALSE | FALSE | Free | Equal
Heterogeneous_pk_Ekj_L_Bk |  | FALSE | FALSE | Equal | Free
Heterogeneous_pk_Ekj_Lk_Bk |  | FALSE | FALSE | Free | Free
Heterogeneous_pk_Ekjh_L_B |  | FALSE | FALSE | Equal | Equal
Heterogeneous_pk_Ekjh_Lk_B |  | FALSE | FALSE | Free | Equal
Heterogeneous_pk_Ekjh_L_Bk |  | FALSE | FALSE | Equal | Free
Heterogeneous_pk_Ekjh_Lk_Bk |  | FALSE | FALSE | Free | Free

### 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

      mixmodCompositeModel()
      # composite models with equal proportions
      mixmodCompositeModel(free.proportions=FALSE)
      # composite models with equal proportions and independent of the variable
      mixmodCompositeModel(free.proportions=FALSE, variable.independency=TRUE)
      # composite models with a pre-defined list
      mixmodCompositeModel( listModels=c("Heterogeneous_pk_Ekjh_L_Bk","Heterogeneous_pk_Ekjh_Lk_B") )

[Package Rmixmod version 2.1.2.2 Index]