Univariate or Multivariate Normal Fit

Computes the mean, covariance, and log-likelihood from fitting a single Gaussian to given data (univariate or multivariate normal).

Usage

mvn( modelName, data, prior = NULL, warn = NULL, ...)

Arguments

modelName

A character string representing a model name. This can be either "Spherical", "Diagonal", or "Ellipsoidal" or else
"X" for one-dimensional data,
"XII" for a spherical Gaussian,
"XXI" for a diagonal Gaussian
"XXX" for a general ellipsoidal Gaussian

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.

prior

Specification of a conjugate prior on the means and variances. The default assumes no prior.

warn

A logical value indicating whether or not a warning should be issued whenever a singularity is encountered. The default is given by mclust.options("warn").

...

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

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.

loglik

The log likelihood for the data in the mixture model.

Attributes:

"WARNING" An appropriate warning if problems are encountered in the computations.

See also

mvnX, mvnXII, mvnXXI, mvnXXX, mclustModelNames

Examples

n <- 1000

set.seed(0)
x <- rnorm(n, mean = -1, sd = 2)
mvn(modelName = "X", x) 
#> $modelName
#> [1] "X"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 1
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#> [1] -1.031659
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "X"
#> 
#> $parameters$variance$d
#> [1] 1
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$sigmasq
#> [1] 3.980071
#> 
#> 
#> 
#> $loglik
#> [1] -2109.588
#> 
#> attr(,"returnCode")
#> [1] 0

mu <- c(-1, 0, 1)

set.seed(0)
x <- sweep(matrix(rnorm(n*3), n, 3) %*% (2*diag(3)), 
           MARGIN = 2, STATS = mu, FUN = "+")
mvn(modelName = "XII", x) 
#> $modelName
#> [1] "XII"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.03165915
#> [2,] -0.04957289
#> [3,]  1.13628546
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XII"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$sigmasq
#> [1] 3.963291
#> 
#> $parameters$variance$Sigma
#>          [,1]     [,2]     [,3]
#> [1,] 3.963291 0.000000 0.000000
#> [2,] 0.000000 3.963291 0.000000
#> [3,] 0.000000 0.000000 3.963291
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>          [,1]     [,2]     [,3]
#> [1,] 3.963291 0.000000 0.000000
#> [2,] 0.000000 3.963291 0.000000
#> [3,] 0.000000 0.000000 3.963291
#> 
#> 
#> $parameters$variance$scale
#> [1] 3.963291
#> 
#> 
#> 
#> $loglik
#> [1] -6322.428
#> 
#> attr(,"returnCode")
#> [1] 0
mvn(modelName = "Spherical", x) 
#> $modelName
#> [1] "XII"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.03165915
#> [2,] -0.04957289
#> [3,]  1.13628546
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XII"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$sigmasq
#> [1] 3.963291
#> 
#> $parameters$variance$Sigma
#>          [,1]     [,2]     [,3]
#> [1,] 3.963291 0.000000 0.000000
#> [2,] 0.000000 3.963291 0.000000
#> [3,] 0.000000 0.000000 3.963291
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>          [,1]     [,2]     [,3]
#> [1,] 3.963291 0.000000 0.000000
#> [2,] 0.000000 3.963291 0.000000
#> [3,] 0.000000 0.000000 3.963291
#> 
#> 
#> $parameters$variance$scale
#> [1] 3.963291
#> 
#> 
#> 
#> $loglik
#> [1] -6322.428
#> 
#> attr(,"returnCode")
#> [1] 0

set.seed(0)
x <- sweep(matrix(rnorm(n*3), n, 3) %*% diag(1:3), 
           MARGIN = 2, STATS = mu, FUN = "+")
mvn(modelName = "XXI", x)
#> $modelName
#> [1] "XXI"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.01582957
#> [2,] -0.04957289
#> [3,]  1.20442820
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XXI"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$Sigma
#>           [,1]    [,2]     [,3]
#> [1,] 0.9950176 0.00000 0.000000
#> [2,] 0.0000000 4.27032 0.000000
#> [3,] 0.0000000 0.00000 8.188836
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>           [,1]    [,2]     [,3]
#> [1,] 0.9950176 0.00000 0.000000
#> [2,] 0.0000000 4.27032 0.000000
#> [3,] 0.0000000 0.00000 8.188836
#> 
#> 
#> $parameters$variance$scale
#> [1] 3.264659
#> 
#> $parameters$variance$shape
#> [1] 0.3047846 1.3080448 2.5083282
#> 
#> 
#> 
#> $loglik
#> [1] -6031.548
#> 
#> attr(,"returnCode")
#> [1] 0
mvn(modelName = "Diagonal", x)
#> $modelName
#> [1] "XXI"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.01582957
#> [2,] -0.04957289
#> [3,]  1.20442820
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XXI"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$Sigma
#>           [,1]    [,2]     [,3]
#> [1,] 0.9950176 0.00000 0.000000
#> [2,] 0.0000000 4.27032 0.000000
#> [3,] 0.0000000 0.00000 8.188836
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>           [,1]    [,2]     [,3]
#> [1,] 0.9950176 0.00000 0.000000
#> [2,] 0.0000000 4.27032 0.000000
#> [3,] 0.0000000 0.00000 8.188836
#> 
#> 
#> $parameters$variance$scale
#> [1] 3.264659
#> 
#> $parameters$variance$shape
#> [1] 0.3047846 1.3080448 2.5083282
#> 
#> 
#> 
#> $loglik
#> [1] -6031.548
#> 
#> attr(,"returnCode")
#> [1] 0

Sigma <- matrix(c(9,-4,1,-4,9,4,1,4,9), 3, 3)
set.seed(0)
x <- sweep(matrix(rnorm(n*3), n, 3) %*% chol(Sigma), 
           MARGIN = 2, STATS = mu, FUN = "+")
mvn(modelName = "XXX", x) 
#> $modelName
#> [1] "XXX"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.04748872
#> [2,] -0.04550547
#> [3,]  1.12277306
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XXX"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$Sigma
#>           [,1]      [,2]     [,3]
#> [1,]  8.955159 -4.084953 1.015574
#> [2,] -4.084953  9.572449 4.417112
#> [3,]  1.015574  4.417112 8.800769
#> 
#> $parameters$variance$cholSigma
#>          [,1]      [,2]       [,3]
#> [1,] 2.992517 -1.365056  0.3393713
#> [2,] 0.000000 -2.776521 -1.7577291
#> [3,] 0.000000  0.000000 -2.3655833
#> 
#> $parameters$variance$cholsigma
#>          [,1]      [,2]       [,3]
#> [1,] 2.992517 -1.365056  0.3393713
#> [2,] 0.000000 -2.776521 -1.7577291
#> [3,] 0.000000  0.000000 -2.3655833
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>           [,1]      [,2]     [,3]
#> [1,]  8.955159 -4.084953 1.015574
#> [2,] -4.084953  9.572449 4.417112
#> [3,]  1.015574  4.417112 8.800769
#> 
#> 
#> 
#> 
#> $loglik
#> [1] -7235.154
#> 
#> attr(,"returnCode")
#> [1] 0
mvn(modelName = "Ellipsoidal", x) 
#> $modelName
#> [1] "XXX"
#> 
#> $prior
#> NULL
#> 
#> $n
#> [1] 1000
#> 
#> $d
#> [1] 3
#> 
#> $G
#> [1] 1
#> 
#> $parameters
#> $parameters$pro
#> [1] 1
#> 
#> $parameters$mean
#>             [,1]
#> [1,] -1.04748872
#> [2,] -0.04550547
#> [3,]  1.12277306
#> 
#> $parameters$variance
#> $parameters$variance$modelName
#> [1] "XXX"
#> 
#> $parameters$variance$d
#> [1] 3
#> 
#> $parameters$variance$G
#> [1] 1
#> 
#> $parameters$variance$Sigma
#>           [,1]      [,2]     [,3]
#> [1,]  8.955159 -4.084953 1.015574
#> [2,] -4.084953  9.572449 4.417112
#> [3,]  1.015574  4.417112 8.800769
#> 
#> $parameters$variance$cholSigma
#>          [,1]      [,2]       [,3]
#> [1,] 2.992517 -1.365056  0.3393713
#> [2,] 0.000000 -2.776521 -1.7577291
#> [3,] 0.000000  0.000000 -2.3655833
#> 
#> $parameters$variance$cholsigma
#>          [,1]      [,2]       [,3]
#> [1,] 2.992517 -1.365056  0.3393713
#> [2,] 0.000000 -2.776521 -1.7577291
#> [3,] 0.000000  0.000000 -2.3655833
#> 
#> $parameters$variance$sigma
#> , , 1
#> 
#>           [,1]      [,2]     [,3]
#> [1,]  8.955159 -4.084953 1.015574
#> [2,] -4.084953  9.572449 4.417112
#> [3,]  1.015574  4.417112 8.800769
#> 
#> 
#> 
#> 
#> $loglik
#> [1] -7235.154
#> 
#> attr(,"returnCode")
#> [1] 0