Rmixmod (version 2.1.1)

mixmodMultinomialModel: Create an instance of the ['>MultinomialModel] class

Description

Define a list of multinomial model to test in MIXMOD.

Usage

mixmodMultinomialModel(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 FALSE.

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 ['>MultinomialModel] containing some of the 10 Binary Models:

Model	Prop.	Var.	Comp.
Binary_p_E	Equal	TRUE	TRUE
Binary_p_Ej		FALSE	TRUE
Binary_p_Ek		TRUE	FALSE
Binary_p_Ekj		FALSE	FALSE
Binary_p_Ekjh		FALSE	FALSE
Binary_pk_E	Free	TRUE	TRUE
Binary_pk_Ej		FALSE	TRUE
Binary_pk_Ek		TRUE	FALSE
Binary_pk_Ekj		FALSE	FALSE
Binary_pk_Ekjh		FALSE	FALSE

Details

In the multinomial mixture model, 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

# NOT RUN {
mixmodMultinomialModel()
  # multinomial models with equal proportions
  mixmodMultinomialModel(equal.proportions=TRUE,free.proportions=FALSE)
  # multinomial models with a pre-defined list
  mixmodMultinomialModel( listModels=c("Binary_pk_E","Binary_p_E") )
  # multinomial models with equal proportions and independent of the variable
  mixmodMultinomialModel(free.proportions=FALSE, variable.independency=TRUE)
# }