Rmixmod (version 2.0.3)

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)

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.

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	Model	Prop.	Var.	Comp.

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") )