mixmodCompositeModel: Create an instance of the ['CompositeModel'] class In Rmixmod: Classification with Mixture Modelling

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

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 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"))


Rmixmod documentation built on May 29, 2024, 7:32 a.m.