mixmodMultinomialModel {Rmixmod} | R Documentation

## 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.

### Details

In the multinomial mixture model, 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 [`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

### 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

      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)

[Package Rmixmod version 2.1.2.2 Index]