Rmixmod (version 2.1.10)

mixmodCompositeModel: 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
)

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

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 \(j\). Optional.

component.independency

logical to include models where \([\varepsilon_k^j]\) is independent of the component \(k\). Optional.

Author

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

Details

In heterogeneous case, Gaussian model can only belong to the diagonal family. We assume that the variance matrices \(\Sigma_{k}\) are diagonal. In the parameterization, it means that the orientation matrices \(D_{k}\) are permutation matrices. We write \(\Sigma_{k}=\lambda_{k}B_{k}\) where \(B_{k}\) is a diagonal matrix with \(| B_{k}|=1\). This particular parameterization gives rise to 4 models: \([\lambda B]\), \([\lambda_{k}B]\), \([\lambda B_{k}]\) and \([\lambda_{k}B_{k}]\). The multinomial distribution is associated to the \(j\)th variable of the \(k\)th 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.

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"))