bic {mclust} | R Documentation

## BIC for Parameterized MVN Mixture Models

### Description

Compute the BIC (Bayesian Information Criterion) for parameterized mixture models given the loglikelihood, the dimension of the data, and number of mixture components in the model.

### Usage

    bic(modelName, loglik, n, d, G, ...)

### Arguments

`modelName` | A character string indicating the model. Possible models: "E" for spherical, equal variance (one-dimensional) "V" for spherical, variable variance (one-dimensional) "EII": spherical, equal volume "VII": spherical, unequal volume "EEI": diagonal, equal volume, equal shape "VEI": diagonal, varying volume, equal shape "EVI": diagonal, equal volume, varying shape "VVI": diagonal, varying volume, varying shape "EEE": ellipsoidal, equal volume, shape, and orientation "EEV": ellipsoidal, equal volume and equal shape "VEV": ellipsoidal, equal shape "VVV": ellipsoidal, varying volume, shape, and orientation
`loglik` | The loglikelihood for a data set with respect to the MVN mixture model specified in the `modelName` argument.
`n` | The number of observations in the data use to compute `loglik`.
`d` | The dimension of the data used to compute `loglik`.
`G` | The number of components in the MVN mixture model used to compute `loglik`.
`...` | Arguments for diagonal-specific methods, in particular equalPro A logical variable indicating whether or not the components in the model are assumed to be present in equal proportion. The default is `.Mclust\$equalPro`. noise A logical variable indicating whether or not the model includes and optional Poisson noise component. The default is to assume that the model does not include a noise component.

### Value

The BIC or Bayesian Information Criterion for the given input arguments.

### References

C. Fraley and A. E. Raftery (2002a). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611:631. See http://www.stat.washington.edu/mclust.

C. Fraley and A. E. Raftery (2002b). MCLUST:Software for model-based clustering, density estimation and discriminant analysis. Technical Report, Department of Statistics, University of Washington. See http://www.stat.washington.edu/mclust.

### See Also

`bicE`, ..., `bicVVV`, `EMclust`, `estep`, `mclustOptions`, `do.call`.

### Examples

    data(iris)
    irisMatrix <- as.matrix(iris[,1:4])
    irisClass <- iris[,5]

    n <- nrow(irisMatrix)
    d <- ncol(irisMatrix)
    G <- 3

    emEst <- me(modelName="VVI",data=irisMatrix, unmap(irisClass))
    names(emEst)

    args(bic)
    bic(modelName="VVI",loglik=emEst$loglik,n=n,d=d,G=G)
    do.call("bic", emEst)    ## alternative call

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