Your terminology is confused. At least it confuses me. I think you are
mixing up ``bivariate distributions'' and ``mixture'' (of two)
distributions.
What you get by rbinding x.1 and x.2 is a sample from a mixture of
two *bivariate*
(Gaussian) distributions, one with mean c(0,0), and one with mean c
(3,4).
Of course x.3 is a sample from a single *bivariate* Gaussian
distribution with
mean c(0,0).
In both cases the covariance matrix is presumably the identity, since
no covariance
matrix is specified.
So your final result X.1 has columns which are independent samples
from univariate
distributions, the first of which is a mixture of N(0,1) and N(3,1),
the second
of which is a mixture of N(0,1) and N(4,1), and the third and fourth
of which are
both N(0,1).
Are you really interested in
* bivariate distributions?
* mixtures of (two) univariate distributions?
* mixtures of (two) bivariate distributions?
If the latter option, why are you talking about the columns of X.1
individually?
If the middle option, why are you using rmvnorm() at all?
If the first option, what exactly is your question?
Your thinking seems to be very muddy. You will need to clarify it
considerably.
If you do so, you may be able to pose a meaningful question, and
perhaps answer
it yourself.
cheers,
Rolf Turner
On 23/10/2008, at 11:59 AM, Tom.O wrote:
This might not be the correct forum for this question for there
might be some
flaws in my logic so the R function I'm looking for might not be the
correct, but I know there’s a lot of smart people in this forum so
please
correct me if I'm wrong. I have been googling and searching in this
forum
for something useful but so far I'm out of luck.
This is the background to my problem. I have a set of samples that
I know
are either from a normal distribution or a bivariate normal
distribution and
my goal is to find the combination of samples that would give the
best fit
of a bivariate distribution.
I'm currently using maximum likelihood estimation to fit the bivariate
normal model but this is where my problems start. How do I find in an
efficient way the best combination, is there a function would do
the trick
for me?
One solution is to run an exhaustive search, but this would take a
while
since the possible combinations is huge. So hopefully this is my last
option.
My other problem is what test should I use to rank the models,
WALD, F-test
or likelihood ratio-test (LR-test)? My colleague thought that the
LR-test
would be the best to use, but he was not sure. And in that case which
function is best to use. I have found some LR tests but they use
fits from
glm models etc.
Here is an example of my problem.
library(mixtools)
x.1<-rmvnorm(40, c(0, 0))
x.2<-rmvnorm(60, c(3, 4))
x.3<-rmvnorm(100, c(0, 0))
X.1<-cbind(rbind(x.1, x.2),x.3)
colnames(X.1) =LETTERS[1:4]
sample A and B is bivariate and C and D is not, so theoretically
the best
combination would be to use A and B in the model since they change
at the
same time, but other combinations with a bivariate and non bivariate
combinations would also work but should give a worse fit than A and
B. And
the worst case would be to fit a bivariate distribution to C and D.
So this is the case...
Regards Tom
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