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Rmixmod (version 2.1.10)

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
)

Value

an object of [MultinomialModel] containing some of the 10 Binary Models:

ModelProp.Var.Comp.
Binary_p_EEqualTRUETRUE
Binary_p_EjFALSETRUE
Binary_p_EkTRUEFALSE
Binary_p_EkjFALSEFALSE
Binary_p_EkjhFALSEFALSE
Binary_pk_EFreeTRUETRUE
Binary_pk_EjFALSETRUE
Binary_pk_EkTRUEFALSE
Binary_pk_EkjFALSEFALSE
Binary_pk_EkjhFALSEFALSE

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 \(j\). 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 contact@mixmod.org

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

Run this code
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)

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