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 [εkj][\varepsilon_k^j] is independent of the variable jj. optional.

component.independency

logical to include models where [εkj][\varepsilon_k^j] is independent of the component kk. optional.

Details

In the multinomial mixture model, the multinomial distribution is associated to the jjth variable of the kkth component is reparameterized by a center akja_k^j and the dispersion εkj\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 [εkj][\varepsilon_k^j]. In this context, three other models can be easily deduced. We note [εk][\varepsilon_k] the model where εkj\varepsilon_k^j is independent of the variable jj, [εj][\varepsilon^j] the model where εkj\varepsilon_k^j is independent of the component kk and, finally, [ε][\varepsilon] the model where εkj\varepsilon_k^j is independent of both the variable $j$ and the component kk. In order to maintain some unity in the notation, we will denote also [εkjh][\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 2.1.10 Index]