R: M-step for a parameterized Gaussian mixture model.

mstepE {mclust} | R Documentation

## M-step for a parameterized Gaussian mixture model.

### Description

Maximization step in the EM algorithm for a parameterized Gaussian mixture model.

### Usage

    mstepE( data, z, prior = NULL, warn = NULL, ...)
    mstepV( data, z, prior = NULL, warn = NULL, ...)
    mstepEII( data, z, prior = NULL, warn = NULL, ...)
    mstepVII( data, z, prior = NULL, warn = NULL, ...)
    mstepEEI( data, z, prior = NULL, warn = NULL, ...)
    mstepVEI( data, z, prior = NULL, warn = NULL, control = NULL, ...)
    mstepEVI( data, z, prior = NULL, warn = NULL, ...)
    mstepVVI( data, z, prior = NULL, warn = NULL, ...)
    mstepEEE( data, z, prior = NULL, warn = NULL, ...)
    mstepEEV( data, z, prior = NULL, warn = NULL, ...)
    mstepVEV( data, z, prior = NULL, warn = NULL, control = NULL,...)
    mstepVVV( data, z, prior = NULL, warn = NULL, ...)
    mstepEVE( data, z, prior = NULL, warn = NULL, control = NULL, ...)
    mstepEVV( data, z, prior = NULL, warn = NULL, ...)
    mstepVEE( data, z, prior = NULL, warn = NULL, control = NULL, ...)
    mstepVVE( data, z, prior = NULL, warn = NULL, control = NULL, ...)

### 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.
`z` | A matrix whose `[i,k]`th entry is the conditional probability of the ith observation belonging to the kth component of the mixture. In analyses involving noise, this should not include the conditional probabilities for the noise component.
`prior` | Specification of a conjugate prior on the means and variances. The default assumes no prior.
`warn` | A logical value indicating whether or not certain warnings (usually related to singularity) should be issued when the estimation fails. The default is given by `mclust.options("warn")`.
`control` | Values controlling termination for models `"VEI"` and `"VEV"` that have an iterative M-step. This should be a list with components named itmax and tol. These components can be of length 1 or 2; in the latter case, `mstep` will use the second value, under the assumption that the first applies to an outer iteration (as in the function `me`). The default uses the default values from the function `emControl`, which sets no limit on the number of iterations, and a relative tolerance of `sqrt(.Machine$double.eps)` on successive iterates.
`...` | Catches unused arguments in indirect or list calls via `do.call`.

### Value

A list including the following components:

`modelName` | A character string identifying the model (same as the input argument).
`parameters` | `pro` A vector whose kth component is the mixing proportion for the kth component of the mixture model. If the model includes a Poisson term for noise, there should be one more mixing proportion than the number of Gaussian components. `mean` The mean for each component. If there is more than one component, this is a matrix whose kth column is the mean of the kth component of the mixture model. `variance` A list of variance parameters for the model. The components of this list depend on the model specification. See the help file for `mclustVariance` for details.
`Attributes:` | `"info"` For those models with iterative M-steps (`"VEI"` and `"VEV"`), information on the iteration. `"WARNING"` An appropriate warning if problems are encountered in the computations.

### References

C. Fraley and A. E. Raftery (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97:611-631.

C. Fraley, A. E. Raftery, T. B. Murphy and L. Scrucca (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597, Department of Statistics, University of Washington.

### Note

This function computes the M-step only for MVN mixtures, so in analyses involving noise, the conditional probabilities input should exclude those for the noise component.

In contrast to `me` for the EM algorithm, computations in `mstep` are carried out unless failure due to overflow would occur. To impose stricter tolerances on a single `mstep`, use `me` with the itmax component of the `control` argument set to 1.

### See Also

`mstep`, `me`, `estep`, `mclustVariance`, `priorControl`, `emControl`.

### Examples

    ## Not run:
    mstepVII(data = iris[,-5], z = unmap(iris[,5]))
    ## End(Not run)

[Package mclust version 5.3 Index]