Dear R users,

I'm having trouble with calculating pvalues for my 2d dataset. First I
performed clustering and I would like to get some info about the strength
of cluster membership for each point. I've calculated (thanks to nice
people help) the multivariate normal densities (mnd) using dmvnorm function:

pd11=mvtnorm::dmvnorm(dataset1,mean=dataset1MC$parameters$mean[,1],sigma=dataset1MC$parameters$variance$sigma[,,1])

I've obtained a vector of mnds for each cluster:

NA12043      NA12249      NA12264      NA12707      NA12716      NA12717
   NA12751      NA12762      NA12864      NA12873      NA07034      NA07048
     NA07055      NA07345      NA07348      NA07357      NA10830
 NA10835
8.627681e+00 8.465797e+00 1.522724e+01 2.047262e+01 1.780368e+01
2.443946e+01 8.687642e+00 5.024366e+00 2.163811e+01 6.093326e-01
1.503374e+00 2.263341e+00 2.177880e+01 2.851877e+01 1.240402e+01
7.498245e+00 1.186389e+01 1.229760e+01
     NA12154      NA12234      NA12236      NA12763      NA12801
 NA12812      NA12813      NA12878      NA10851      NA10854      NA10857
   NA10859      NA10861      NA10863      NA11839      NA11840      NA11881
     NA11882
8.293616e+00 4.019101e-19 2.733848e+01 2.623284e+01 2.320810e+01
5.112927e-01 1.432336e+01 1.000314e+01 1.675454e+01 8.239816e+00
2.449679e+01 2.655419e+01 2.294064e+01 2.218329e-17 8.844933e+00
2.911991e+00 2.170381e+01 3.089883e+00
     NA11994      NA12044      NA12056      NA12057      NA12891
 NA12892
1.668749e+01 1.588963e+01 5.913443e+00 2.924297e+01 1.765777e+01
7.935129e+00

Next, what I would like to do is to calculate the pvalue for each point,
which was assigned to particular cluster. In order to do this i'm using
pmvnorm function, but I found it difficult to set the region of
integration. As I understand to get the probability of cluster membership I
should define how 'far' from the cluster mean is my point. However, I've
got 2d dataset and my mean is also 2d:

       [1,]         [2,]
 1.348992  1.269590

but I've got only one density value for each point.

Using:

pmvnorm(mean=dataset1MC$parameters$mean[,1],sigma=dataset1MC$parameters$variance$sigma[,,1],
lower=2.218329e-17, upper=as.vector(dataset1MC$parameters$mean[,1]))

gives strange results, since for 2.218329e-17 the output is:

 [1] 0.348126
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"

and

pmvnorm(mean=dataset1MC$parameters$mean[,1],sigma=dataset1MC$parameters$variance$sigma[,,1],
lower= as.vector(dataset1MC$parameters$mean[,1]) , upper=2.924297e+01)

gives:

[1] 0.348126
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"

If it is possible I would like to get some info about:

Is my idea of calculating  the probability of cluster membership is
correct? How I can set properly the region of integration?

I would be grateful for any help.

Best Wishes,

Bas.

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