dgmcm.loglik: Probability, density, and likelihood functions of the...
In GMCM: Fast Estimation of Gaussian Mixture Copula Models

Description Usage Arguments Details Value Author(s) Examples

Marginal and simultaneous cumulative distribution, log probability density, and log-likelihood functions of the Gaussian mixture model (GMM) and Gaussian mixture copula model (GMCM) and the relevant inverse marginal quantile functions.

dgmcm.loglik(theta, u, marginal.loglik = FALSE, ...)

dgmm.loglik(theta, z, marginal.loglik = FALSE)

dgmm.loglik.marginal(theta, x, marginal.loglik = TRUE)

pgmm.marginal(z, theta)

qgmm.marginal(u, theta, res = 1000, spread = 5, rule = 2)

`theta`	A list parameters as described in `rtheta`.
`u`	A matrix of (estimates of) realizations from the GMCM where each row corresponds to an observation.
`marginal.loglik`	Logical. If `TRUE`, the marginal log-likelihood functions for each multivariate observation (i.e. the log densities) are returned. In other words, if `TRUE` the sum of the marginal likelihoods is not computed.
`...`	Arguments passed to `qgmm.marginal`.
`z`	A matrix of realizations from the latent process where each row corresponds to an observation.
`x`	A matrix where each row corresponds to an observation.
`res`	The resolution at which the inversion of `qgmm.marginal` is done. Default is 1000.
`spread`	The number of marginal standard deviations from the marginal means the `pgmm.marginal` is to be evaluated on.
`rule`	The extrapolation rule used in `approxfun`.

qgmm.marginal distributes approximately res points around the cluster centers according to the mixture proportions in theta$pie and evaluates pgmm.marginal on these points. An approximate inverse of pgmm.marginal function is constructed by linear interpolation of the flipped evaluated coordinates.

The returned value depends on the value of marginal.loglik. If TRUE, the non-summed marginal likelihood values are returned. If FALSE, the scalar sum log-likelihood is returned.

dgmcm.loglik: As above, with the GMCM density.

dgmm.loglik: As above, with the GMM density.

dgmm.loglik.marginal: As above, where the j'th element is evaluated in the j'th marginal GMM density.

pgmm.marginal: A matrix where the (i,j)'th entry is the (i,j)'th entry of z evaluated in the jth marginal GMM density.

qgmm.marginal: A matrix where the (i,j)'th entry is the (i,j)'th entry of u evaluated in the inverse jth marginal GMM density.

Anders Ellern Bilgrau <anders.ellern.bilgrau@gmail.com>

set.seed(1)
data <- SimulateGMCMData(n = 10)
u <- data$u
z <- data$z
print(theta <- data$theta)

GMCM:::dgmcm.loglik(theta, u, marginal.loglik = FALSE)
GMCM:::dgmcm.loglik(theta, u, marginal.loglik = TRUE)

GMCM:::dgmm.loglik(theta, z, marginal.loglik = FALSE)
GMCM:::dgmm.loglik(theta, z, marginal.loglik = TRUE)

GMCM:::dgmm.loglik.marginal(theta, z, marginal.loglik = FALSE)
GMCM:::dgmm.loglik.marginal(theta, z, marginal.loglik = TRUE)

GMCM:::pgmm.marginal(z, theta)
GMCM:::qgmm.marginal(u, theta)

$m
[1] 3

$d
[1] 2

$pie
     pie1      pie2      pie3 
0.2193406 0.3074170 0.4732425 

$mu
$mu$comp1
[1] 13.29799 12.72429

$mu$comp2
[1]   4.146414 -15.399500

$mu$comp3
[1] -9.285670 -2.947204


$sigma
$sigma$comp1
          [,1]     [,2]
[1,] 13.348429 8.850678
[2,]  8.850678 5.934935

$sigma$comp2
           [,1]       [,2]
[1,]  3.0665824 -0.3895294
[2,] -0.3895294  2.6192252

$sigma$comp3
          [,1]      [,2]
[1,] 1.9840226 0.4433423
[2,] 0.4433423 2.8292856


[1] 13.59121
           [,1]
 [1,] 3.7357739
 [2,] 0.8021746
 [3,] 0.2719414
 [4,] 0.8672774
 [5,] 0.6881781
 [6,] 0.8119559
 [7,] 1.1731392
 [8,] 0.9476444
 [9,] 0.7314841
[10,] 3.5616420
          [,1]
[1,] -43.74253
           [,1]
 [1,] -3.653635
 [2,] -4.037537
 [3,] -6.198597
 [4,] -4.256785
 [5,] -3.879436
 [6,] -3.802766
 [7,] -4.805304
 [8,] -5.308502
 [9,] -4.146636
[10,] -3.653327
          [,1]      [,2]
[1,] -28.94221 -28.39174
           [,1]      [,2]
 [1,] -3.878353 -3.511683
 [2,] -2.048666 -2.791043
 [3,] -3.554761 -2.915783
 [4,] -2.166867 -2.957184
 [5,] -2.112156 -2.455467
 [6,] -2.355797 -2.258921
 [7,] -3.228134 -2.750316
 [8,] -3.082020 -3.174180
 [9,] -2.690093 -2.188029
[10,] -3.825364 -3.389137
            [,1]       [,2]
 [1,] 0.84505432 0.84019072
 [2,] 0.18455949 0.37171423
 [3,] 0.45460398 0.36120747
 [4,] 0.33718720 0.72988747
 [5,] 0.15397511 0.67091502
 [6,] 0.09592262 0.47416290
 [7,] 0.74791295 0.08598483
 [8,] 0.73595788 0.26505301
 [9,] 0.05758476 0.55218465
[10,] 0.85356669 0.85999327
            [,1]        [,2]
 [1,]  11.314478  11.2413720
 [2,]  -9.679158  -4.7958888
 [3,]  -6.809556  -4.9778080
 [4,]  -8.495785  -0.8596063
 [5,]  -9.923474  -1.7148287
 [6,] -10.457700  -3.5847277
 [7,]   6.163773 -16.3443181
 [8,]   5.884038 -13.6349242
 [9,] -10.928869  -2.8746333
[10,]  11.714836  11.8618236