Description Usage Arguments Details Value References See Also Examples
Computes maximum likelihood estimators (MLE) for finite mixtures of unrestricted multivariate skew t (FM-MST) model via the EM algorithm.
1 2 3 4 5 6 |
object, x |
an object class of class |
g |
a scalar specifying the number of components in the mixture model |
dat |
the data matrix giving the coordinates of the point(s) where the density is evaluated.
This is either a vector of length |
initial |
(optional) a list containing the initial parameters of the mixture model.
See the 'Details' section. The default is |
known |
(optional) a list containing parameters of the mixture model that are known
and not required to be estimated. See the 'Details' section. The default is |
itmax |
(optional) a positive integer specifying the maximum number of EM iterations
to perform. The default is |
eps |
(optional) a numeric value used to control the termination criteria for the EM loops.
It is the maximum tolerance for the absolute difference between the log-likelihood value
and the asymptotic log likelihood value. The default is |
clust |
(optional) a numeric value of length |
nkmeans |
(optional) a numeric value indicating how many k-means trials to be used
when searching for initial values. The default is |
print |
(optional) a logical value. If |
tmethod |
(optional) an integer indicating which method to use when computing t distribution function values.
See |
... |
not used. |
The arguments init
and known
, if specified, is a list structure containing
at least one of mu
, sigma
, delta
, dof
, pro
(See dfmmst
for the structure of each of these elements).
If init=FALSE
(default), the program uses an automatic approach based on
k-means clustering to generate an initial value for the model parameters.
Note that this may not provide the best results.
As the EM algorithm is sensitive to the starting value,
it is highly recommended to apply a wide range different initializations.
A simple strategy is implemented in fmmst.init
.
mu |
a list of |
sigma |
a list of |
delta |
a list of |
dof |
a numeric vector of length |
pro |
a vector of length of |
tau |
an |
clusters |
a vector of length n of final partition. |
loglik |
the final log likelihood value. |
lk |
a vector of log likelihood values at each EM iteration. |
iter |
number of iterations performed. |
eps |
the final absolute difference between the log likelihood value and the asymptotic log likelihood value. |
aic, bic |
Akaike Information Criterion (AIC), Bayes Information Criterion (BIC) |
Lee S, McLachlan G (2011). On the fitting of mixtures of multivariate skew t-distributions via the EM algorithm. arXiv:1109.4706 [stat.ME]
Lee, S. and McLachlan, G.J. (2014) Finite mixtures of multivariate skew t-distributions: some recent and new results. Statistics and Computing, 24, 181-202.
Lee, S. and McLachlan, G.J. (2013) EMMIXuskew: An R
package for
fitting mixtures of multivariate skew t-distributions via the EM algorithm.
Journal of Statistical Software, 55(12), 1-22.
URL http://www.jstatsoft.org/v55/i12/.
fmmst.init
, rfmmst
, dfmmst
, fmmst.contour.2d
1 2 3 4 5 |
Loading required package: MASS
Finite Mixture of Multivariate Skew t-distribution
with 2 components
----------------------------------------------------
Iteration 0 : loglik = -1375.755
Iteration 1 : loglik = -1372.719
Iteration 2 : loglik = -1370.503
Iteration 3 : loglik = -1368.776
Iteration 4 : loglik = -1367.395
Iteration 5 : loglik = -1366.256
----------------------------------------------------
Iteration 5: loglik = -1366.256
Component means:
[,1] [,2]
[1,] 182.126977 181.094629
[2,] 5.725095 8.418986
Component scale matrices:
[[1]]
[,1] [,2]
[1,] 11.4682797 0.7770157
[2,] 0.7770157 2.6873680
[[2]]
[,1] [,2]
[1,] 9.967333 7.325116
[2,] 7.325116 10.900295
Component skewness parameters:
[,1] [,2]
[1,] 7.931061 -9.187155
[2,] 6.298261 8.926576
Component degrees of freedom:
38.77001 41.18913
Component mixing proportions:
0.4263113 0.5736887
Finite Mixture of Multivarate Skew t-distributions
with 2 components
Component means:
[,1] [,2]
[1,] 182.126977 181.094629
[2,] 5.725095 8.418986
Component scale matrices:
[[1]]
[,1] [,2]
[1,] 11.4682797 0.7770157
[2,] 0.7770157 2.6873680
[[2]]
[,1] [,2]
[1,] 9.967333 7.325116
[2,] 7.325116 10.900295
Component skewness parameters:
[,1] [,2]
[1,] 7.931061 -9.187155
[2,] 6.298261 8.926576
Component degrees of freedom:
38.77001 41.18913
Component mixing proportions:
0.4263113 0.5736887
$pro
[1] 0.4263113 0.5736887
$mu
$mu[[1]]
[,1]
[1,] 182.126977
[2,] 5.725095
$mu[[2]]
[,1]
[1,] 181.094629
[2,] 8.418986
$sigma
$sigma[[1]]
[,1] [,2]
[1,] 11.4682797 0.7770157
[2,] 0.7770157 2.6873680
$sigma[[2]]
[,1] [,2]
[1,] 9.967333 7.325116
[2,] 7.325116 10.900295
$delta
$delta[[1]]
[,1]
[1,] 7.931061
[2,] 6.298261
$delta[[2]]
[,1]
[1,] -9.187155
[2,] 8.926576
$dof
[1] 38.77001 41.18913
$tau
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.9998759186 0.93714322 0.03017676 0.2944467 0.5838414 0.007161885
[2,] 0.0001240814 0.06285678 0.96982324 0.7055533 0.4161586 0.992838115
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.6702328 0.002357614 0.0009523704 0.16948 0.96229317 0.94885165
[2,] 0.3297672 0.997642386 0.9990476296 0.83052 0.03770683 0.05114835
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.0001025849 0.0454367 0.03147941 0.06904956 0.04908538 0.09800578
[2,] 0.9998974151 0.9545633 0.96852059 0.93095044 0.95091462 0.90199422
[,19] [,20] [,21] [,22] [,23] [,24] [,25]
[1,] 0.4244983 0.01556741 0.1093494 0.01405254 0.004247963 0.3307743 0.5835683
[2,] 0.5755017 0.98443259 0.8906506 0.98594746 0.995752037 0.6692257 0.4164317
[,26] [,27] [,28] [,29] [,30] [,31]
[1,] 0.2994598 0.04242444 0.005270056 1.175658e-08 0.05331546 0.1135514
[2,] 0.7005402 0.95757556 0.994729944 1.000000e+00 0.94668454 0.8864486
[,32] [,33] [,34] [,35] [,36] [,37] [,38]
[1,] 0.09793356 0.0244225 0.120719 0.6592509 0.07116022 0.0007452455 0.01318239
[2,] 0.90206644 0.9755775 0.879281 0.3407491 0.92883978 0.9992547545 0.98681761
[,39] [,40] [,41] [,42] [,43] [,44]
[1,] 0.0002742872 0.1503655 0.06000756 0.01841932 0.001407294 0.004064201
[2,] 0.9997257128 0.8496345 0.93999244 0.98158068 0.998592706 0.995935799
[,45] [,46] [,47] [,48] [,49] [,50]
[1,] 0.001476746 0.02764118 0.5535145 0.006438722 0.0008751984 0.0001377015
[2,] 0.998523254 0.97235882 0.4464855 0.993561278 0.9991248016 0.9998622985
[,51] [,52] [,53] [,54] [,55] [,56]
[1,] 0.001349252 0.007137324 0.0002775852 0.5341756 0.02567962 0.002787439
[2,] 0.998650748 0.992862676 0.9997224148 0.4658244 0.97432038 0.997212561
[,57] [,58] [,59] [,60] [,61] [,62]
[1,] 0.1379046 0.0009479905 0.0005136197 0.0007421358 0.1449849 0.00312072
[2,] 0.8620954 0.9990520095 0.9994863803 0.9992578642 0.8550151 0.99687928
[,63] [,64] [,65] [,66] [,67] [,68]
[1,] 0.009630327 0.324631 0.01961144 0.0008834766 1.191931e-05 0.0006111342
[2,] 0.990369673 0.675369 0.98038856 0.9991165234 9.999881e-01 0.9993888658
[,69] [,70] [,71] [,72] [,73] [,74]
[1,] 0.01469694 0.00560461 0.0005947097 0.0008388549 0.01083147 0.000898157
[2,] 0.98530306 0.99439539 0.9994052903 0.9991611451 0.98916853 0.999101843
[,75] [,76] [,77] [,78] [,79] [,80]
[1,] 0.0008722512 0.004022883 0.1391564 1.206697e-06 5.787954e-05 1.550174e-06
[2,] 0.9991277488 0.995977117 0.8608436 9.999988e-01 9.999421e-01 9.999984e-01
[,81] [,82] [,83] [,84] [,85] [,86]
[1,] 0.0007660721 3.922871e-06 2.629853e-05 0.05309207 5.807131e-06 0.005914419
[2,] 0.9992339279 9.999961e-01 9.999737e-01 0.94690793 9.999942e-01 0.994085581
[,87] [,88] [,89] [,90] [,91] [,92]
[1,] 0.09209575 0.00018962 0.003676475 5.742299e-05 0.0272106 1.334660e-06
[2,] 0.90790425 0.99981038 0.996323525 9.999426e-01 0.9727894 9.999987e-01
[,93] [,94] [,95] [,96] [,97] [,98]
[1,] 0.002782172 5.862402e-05 0.01920249 7.683559e-08 1.340007e-07 2.535098e-08
[2,] 0.997217828 9.999414e-01 0.98079751 9.999999e-01 9.999999e-01 1.000000e+00
[,99] [,100] [,101] [,102] [,103] [,104]
[1,] 1.542307e-10 1.359515e-10 0.009577232 0.1355241 0.98457527 1.000000e+00
[2,] 1.000000e+00 1.000000e+00 0.990422768 0.8644759 0.01542473 4.181028e-08
[,105] [,106] [,107] [,108] [,109] [,110]
[1,] 1.000000e+00 0.5032857 0.90601565 0.97376261 9.999991e-01 0.99003427
[2,] 3.027051e-08 0.4967143 0.09398435 0.02623739 9.066937e-07 0.00996573
[,111] [,112] [,113] [,114] [,115] [,116]
[1,] 0.97300274 9.999997e-01 9.999986e-01 9.999882e-01 0.4901118 0.9997055107
[2,] 0.02699726 2.949209e-07 1.433555e-06 1.177044e-05 0.5098882 0.0002944893
[,117] [,118] [,119] [,120] [,121] [,122]
[1,] 1.000000e+00 0.98957485 9.999965e-01 0.990605161 1.964559e-05 0.994833664
[2,] 6.732545e-11 0.01042515 3.548511e-06 0.009394839 9.999804e-01 0.005166336
[,123] [,124] [,125] [,126] [,127] [,128]
[1,] 0.9998049168 9.999999e-01 0.98700544 1.00000e+00 9.999742e-01 0.995442311
[2,] 0.0001950832 5.166193e-08 0.01299456 4.93555e-08 2.580767e-05 0.004557689
[,129] [,130] [,131] [,132] [,133]
[1,] 1.000000e+00 1.000000e+00 9.999999e-01 0.9992008099 1.000000e+00
[2,] 4.712247e-12 2.894134e-09 7.980299e-08 0.0007991901 2.015846e-13
[,134] [,135] [,136] [,137] [,138]
[1,] 1.000000e+00 1.000000e+00 0.9997818289 1.000000e+00 0.998438284
[2,] 4.015469e-13 1.145899e-09 0.0002181711 2.816621e-09 0.001561716
[,139] [,140] [,141] [,142] [,143] [,144]
[1,] 9.999992e-01 1.000000e+00 0.0009658014 0.9998606357 0.995784807 0.9984406
[2,] 7.882494e-07 3.412483e-09 0.9990341986 0.0001393643 0.004215193 0.0015594
[,145] [,146] [,147] [,148] [,149] [,150]
[1,] 0.8392222 0.95296893 0.997912154 0.06336282 0.9991606436 0.874618
[2,] 0.1607778 0.04703107 0.002087846 0.93663718 0.0008393564 0.125382
[,151] [,152] [,153] [,154] [,155] [,156]
[1,] 0.1395799 0.1503868 0.03380488 9.999995e-01 0.004376436 0.03929143
[2,] 0.8604201 0.8496132 0.96619512 4.961904e-07 0.995623564 0.96070857
[,157] [,158] [,159] [,160] [,161] [,162]
[1,] 0.7746092 0.4517992 9.999967e-01 0.990797748 9.999677e-01 0.08394098
[2,] 0.2253908 0.5482008 3.304827e-06 0.009202252 3.227918e-05 0.91605902
[,163] [,164] [,165] [,166] [,167] [,168] [,169]
[1,] 0.9946992 0.97719045 0.99870494 0.03310229 0.8570636 0.4211694 0.0191177
[2,] 0.0053008 0.02280955 0.00129506 0.96689771 0.1429364 0.5788306 0.9808823
[,170] [,171] [,172] [,173] [,174] [,175]
[1,] 0.6626237 0.05496518 0.4165535 0.2883269 0.003099098 0.3787094
[2,] 0.3373763 0.94503482 0.5834465 0.7116731 0.996900902 0.6212906
[,176] [,177] [,178] [,179] [,180] [,181]
[1,] 0.9998490858 1.000000e+00 0.08335613 0.1155384 0.3675864 0.04901295
[2,] 0.0001509142 6.976888e-09 0.91664387 0.8844616 0.6324136 0.95098705
[,182] [,183] [,184] [,185] [,186] [,187]
[1,] 0.997946589 0.3075857 9.999859e-01 0.3552272 9.999611e-01 0.9996194701
[2,] 0.002053411 0.6924143 1.410759e-05 0.6447728 3.888396e-05 0.0003805299
[,188] [,189] [,190] [,191] [,192] [,193]
[1,] 0.4558908 9.999993e-01 9.999694e-01 9.999997e-01 9.999500e-01 0.999800337
[2,] 0.5441092 7.291228e-07 3.063712e-05 3.242120e-07 5.001844e-05 0.000199663
[,194] [,195] [,196] [,197] [,198] [,199] [,200]
[1,] 0.990449995 9.999425e-01 0.8132804 0.3816304 0.8370515 0.8989452 0.9407401
[2,] 0.009550005 5.745154e-05 0.1867196 0.6183696 0.1629485 0.1010548 0.0592599
[,201] [,202]
[1,] 0.1550315 9.999993e-01
[2,] 0.8449685 6.905201e-07
$clusters
[1] 1 1 2 2 1 2 1 2 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 1 2 2
[38] 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
[75] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1
[112] 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2
[149] 1 1 2 2 2 1 2 2 1 2 1 1 1 2 1 1 1 2 1 2 2 1 2 2 2 2 2 1 1 2 2 2 2 1 2 1 2
[186] 1 1 2 1 1 1 1 1 1 1 1 2 1 1 1 2 1
$loglik
[1] -1366.256
$lk
[1] -1375.755 -1372.719 -1370.503 -1368.776 -1367.395 -1366.256
$iter
[1] 5
$eps
[1] 1.138409
$aic
[1] 2766.512
$bic
[1] 2822.753
attr(,"class")
[1] "fmmst"
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