On Jul 27, 2012, at 10:45 AM, Anders Holm wrote:
Dear list members
I need a function that calculates the bivariate normal distribution
for each observation. It is part of a likelihood function and I have
1000's of cases. As I understand it I cannot use packages like
"mvtnorm" because it requres a covariance matrix of the same
dimension as the number of observations. Basically what I need is a
function that takes as arguments a n*2 matrix of bivariate values
given a common mean and covariance matrix, where n is the number of
cases and which returns a n*1 vector of the probabilities of the
bivariate normal distribution of the n*2 vector of values.
I do not think you are reading the documentation for the d- and p-
functions in mvtnorm correctly:
Here is the 2-dimensional case using pmvnorn (since you asked for
probabilities) and the result is as expected:
> n <- 2
> mean <- rep(0, 2)
> corr <- diag(2)
> corr[lower.tri(corr)] <- 0
> corr[upper.tri(corr)] <- 0
Half of the xy plane of a 2d-mvnorm with 0 covariances should give 0.5
> prob <- pmvnorm( lower= c(-Inf,-Inf), upper= c( 0, Inf), mean, corr)
> prob
[1] 0.5
attr(,"error")
[1] 2e-16
attr(,"msg")
[1] "Normal Completion"
And a single quadrant should give 0.25.
> prob <- pmvnorm(lower=c(-Inf,-Inf), upper=c( 0, 0), mean, corr)
> prob
[1] 0.25
attr(,"error")
[1] 1e-15
attr(,"msg")
[1] "Normal Completion"
I guessing that you want to provide the data to pmvnorm with apply()
using -Inf as the 'lower' limits and your datapoints as the 'upper'
values:
Perhaps:
apply(n_x_2_values,
>
all the best
Anders Holm
Department of Education
Aarhus University
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