cdensE {mclust} | R Documentation

## Component Density for a Parameterized MVN Mixture Model

### Description

Computes component densities for points in a parameterized MVN mixture model.

### Usage

    cdensE(data, mu, sigmasq, eps, warnSingular, logarithm = FALSE, ...)
    cdensV(data, mu, sigmasq, eps, warnSingular, logarithm = FALSE, ...)
    cdensEII(data, mu, sigmasq, eps, warnSingular, logarithm = FALSE, ...)
    cdensVII(data, mu, sigmasq, eps, warnSingular, logarithm = FALSE, ...)
    cdensEEI(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensVEI(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensEVI(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensVVI(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensEEE(data, mu, eps, warnSingular, logarithm = FALSE, ...)
    cdensEEV(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensVEV(data, mu, decomp, eps, warnSingular, logarithm = FALSE, ...)
    cdensVVV(data, mu, eps, warnSingular, logarithm = FALSE, ...)

### Arguments

`data` | A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.
`mu` | The mean for each component. If there is more than one component, `mu` is a matrix whose columns are the means of the components.
`sigmasq` | for the one-dimensional models ("E", "V") and spherical models ("EII", "VII"). This is either a vector whose kth component is the variance for the kth component in the mixture model ("V" and "VII"), or a scalar giving the common variance for all components in the mixture model ("E" and "EII").
`decomp` | for the diagonal models ("EEI", "VEI", "EVI", "VVI") and some ellipsoidal models ("EEV", "VEV"). This is a list described in more detail in `cdens`.
`logarithm` | A logical value indicating whether or not the logarithm of the component densities should be returned. The default is to return the component densities, obtained from the log component densities by exponentiation.
`...` | An argument giving the variance that takes one of the following forms: decomp for models "EII" and "VII"; see above. cholSigma see Sigma, for "EEE". Sigma for the equal variance model "EEE". A d by d matrix giving the common covariance for all components of the mixture model. cholsigma see sigma, for "VVV". sigma for the unconstrained variance model "VVV". A d by d by G matrix array whose `[,,k]`th entry is the covariance matrix for the kth component of the mixture model. The form of the variance specification is the same as for the output for the `em`, `me`, or `mstep` methods for the specified mixture model. Also used to catch unused arguments from a `do.call` call.
`eps` | A scalar tolerance for deciding when to terminate computations due to computational singularity in covariances. Smaller values of `eps` allow computations to proceed nearer to singularity. The default is `.Mclust\$eps`.
`warnSingular` | A logical value indicating whether or not a warning should be issued whenever a singularity is encountered. The default is `.Mclust\$warnSingular`.

### Value

A numeric matrix whose `[i,j]`th entry is the density of observation i in component j. The densities are not scaled by mixing proportions.

### 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

`cdens`, `dens`, `EMclust`, `mstep`, `mclustOptions`, `do.call`

### Examples

    n <- 100 ## create artificial data

    set.seed(0)
    x <- rbind(matrix(rnorm(n*2), n, 2) %*% diag(c(1,9)),
               matrix(rnorm(n*2), n, 2) %*% diag(c(1,9))[,2:1])
    xclass <- c(rep(1,n),rep(2,n))
    clPairs(x, cl = xclass, sym = c("1","2")) ## display the data

    modelVII <- meVII(x, z = unmap(xclass))
    modelVVI <- meVVI(x, z = unmap(xclass))
    modelVVV <- meVVV(x, z = unmap(xclass))

    names(modelVII)
    args(cdensVII)
    cdenVII <- cdensVII(data = x, mu = modelVII$mu, pro = modelVII$pro,
                        decomp = modelVII$decomp)
    names(modelVVI)
    args(cdensVVI)
    cdenVVI <- cdensVII(data = x, mu = modelVVI$mu, pro = modelVVI$pro,
                        decomp = modelVVI$decomp)
    names(modelVVV)
    args(cdensVVV)
    cdenVVV <- cdensVVV( data = x, mu = modelVVV$mu, pro = modelVVV$pro,
                         cholsigma = modelVVV$cholsigma)

    cbind(class=xclass,VII=map(cdenVII),VVI=map(cdenVVI),VVV=map(cdenVVV))

    ## alternative call

    cdenVII <- do.call("cdensVII", c(list(data = x), modelVII))
    cdenVVI <- do.call("cdensVVI", c(list(data = x), modelVVI))
    cdenVVV <- do.call("cdensVVV", c(list(data = x), modelVVV))

    cbind(class=xclass,VII=map(cdenVII),VVI=map(cdenVVI),VVV=map(cdenVVV))

[Package Contents]