Marginal parameters from fitted GMMs via mclust

Function to compute the marginal parameters from a fitted Gaussian mixture models.

Usage

mclustMarginalParams(object, ...)

gmm2margParams(pro, mu, sigma, ...)

Arguments

object

An object of class Mclust or densityMclust.

...

Further arguments passed to or from other methods.

pro

A vector of mixing proportions for each mixture component.

mu

A matrix of mean vectors for each mixture component. For a \(d\)-variate dataset on \(G\) components, the matrix has dimension \((d \times G)\).

sigma

An array of covariance matrices for each mixture component. For a \(d\)-variate dataset on \(G\) components, the array has dimension \((d \times d \times G)\).

Value

Returns a list of two components for the mean and covariance of the marginal distribution.

Details

Given a \(G\)-component GMM with estimated mixture weight \(\pi_k\), mean vector \(\mu_{k}\), and covariance matrix \(\Sigma_{k}\), for mixture component \(k = 1, \dots, G\), then the marginal distribution has:

• mean vector $$\mu = \sum_{k=1}^G \pi_k \mu_k$$

• covariance matrix $$\Sigma = \sum_{k=1}^G \pi_k \Sigma_k + \pi_k (\mu_k - \mu)'(\mu_k - \mu)$$

References

Frühwirth-Schnatter S. (2006) Finite Mixture and Markov Switching Models, Springer, Sec. 6.1.1

See also

mclust::Mclust(), mclust::densityMclust().

Author

Luca Scrucca

Examples

x = iris[,1:4]
mod = Mclust(x, G = 3)
mod$parameters$pro
#> [1] 0.3333333 0.3005423 0.3661243
mod$parameters$mean
#>               [,1]     [,2]     [,3]
#> Sepal.Length 5.006 5.915044 6.546807
#> Sepal.Width  3.428 2.777451 2.949613
#> Petal.Length 1.462 4.204002 5.482252
#> Petal.Width  0.246 1.298935 1.985523
mod$parameters$variance$sigma
#> , , 1
#> 
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.13320850  0.10938369  0.019191764 0.011585649
#> Sepal.Width    0.10938369  0.15495369  0.012096999 0.010010130
#> Petal.Length   0.01919176  0.01209700  0.028275400 0.005818274
#> Petal.Width    0.01158565  0.01001013  0.005818274 0.010695632
#> 
#> , , 2
#> 
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.22572159  0.07613348   0.14689934  0.04335826
#> Sepal.Width    0.07613348  0.08024338   0.07372331  0.03435893
#> Petal.Length   0.14689934  0.07372331   0.16613979  0.04953078
#> Petal.Width    0.04335826  0.03435893   0.04953078  0.03338619
#> 
#> , , 3
#> 
#>              Sepal.Length Sepal.Width Petal.Length Petal.Width
#> Sepal.Length   0.42943106  0.10784274   0.33452389  0.06538369
#> Sepal.Width    0.10784274  0.11596343   0.08905176  0.06134034
#> Petal.Length   0.33452389  0.08905176   0.36422115  0.08706895
#> Petal.Width    0.06538369  0.06134034   0.08706895  0.08663823
#> 
mclustMarginalParams(mod)
#> $mean
#>          [,1]     [,2]  [,3]     [,4]
#> [1,] 5.843333 3.057333 3.758 1.199333
#> 
#> $variance
#>             [,1]        [,2]       [,3]       [,4]
#> [1,]  0.68590753 -0.03840722  1.2675722  0.5115543
#> [2,] -0.03840722  0.19181382 -0.3304093 -0.1210532
#> [3,]  1.26757218 -0.33040933  3.0982006  1.2879867
#> [4,]  0.51155432 -0.12105317  1.2879867  0.5775488
#>