Re: generating data with specified spearman correlation

From: David Jones (dajxxx_at_ceh.ac.uk)
Date: 11/25/04 

Date: Thu, 25 Nov 2004 09:59:14 -0000

Glen wrote:
> "David Jones" <dajxxx@ceh.ac.uk> wrote in message
> news:<41a46e2a$1@news.nwl.ac.uk>...
>> (ii) use a bivariate uniform distribution for which the correlation
>> can be evaluated: the correation here is both the population
Spearman
>> and Pearson correlation. Fix the dependence parameter to get the
>> required correlation, then transform to the required marginal
>> distributions. Chapter 8 of "Families of Bivarite Distributions" by
>> KV Mardia (Griffin,1970) discusses one possibility for this.
>
> A bivariate distribution with uniform marginals is a bivariate
copula.
>
> See for example the books
>
> Joe, H., (1997), Multivariate Models and Dependence Concepts,
Chapman
> & Hall.
>
> Nelsen, R. B., (1999), An Introduction to Copulas, Springer-Verlag.
>
> There are a number of copulas (families of distributions with
uniform
> marginals) for which the Spearman correlation can be specified by
the
> choice of a parameter.

But, in this context, an additional important question may be the ease
of generating r.v.'s from the joint distribution. Some have a
reasonably simple expression for the conditional distribution of one
margin given the other, which proves a route to generation.

>
>> (iii) If specific marginal distributions are required, of the same
>> type, there may be one or more families of multivariate distibution
>> specific to that type. Then either use a theoretical derivation of
>> the Spearman correlation, or use simulations to estimate the
Spearman
>> correlation, and adjust the dependence parameter to get the
required
>> correlation.
>
> Since the spearman correlation is unaffected by monotonic
transforms,
> you can get arbitrary marginals by taking a bivariate copula from
(ii)
> and transforming the uniform marginals by the inverse cdf transform
> X=F^{-1}(U)

Yes, but it may be that one of a "natural" family of multivariate
distributions with specific margins seems particularly appropriate.

In the OP's context, it might well be most convenient computationally
(programming-wise) to base things on generating multivariate normals
(since progs for these are easy to find) and starting from there.

David Jones

Relevant Pages

  • Re: generating data with specified spearman correlation
    ... > use a bivariate uniform distribution for which the correlation ... the correation here is both the population Spearman ... A bivariate distribution with uniform marginals is a bivariate copula. ...
    (sci.stat.math)
  • Re: Bayesian estimation of structured correlation/covariance
    ... correlation between a pair of paths. ... >> should formulate this as covariance matrix estimation with the ... > large step of using the Wishart/ inverse Wishart distribution for the ... > switch from viewing your problem as one of estimating the covarince ...
    (sci.stat.math)
  • Re: How to ensure data correlation
    ... Based upon the goodness of fit tests, ... distribution for each variable seperately. ... was present in the original sample data. ... See the recent thread "Data Simulation from Correlation matrix" ...
    (sci.stat.math)
  • Re: distribution of sample correlation coefficient
    ... I am wanting to use the measured correlation ... coefficient rho is known and deterministic. ... distribution might be a reasonable model as it is ... A large-sample approximation for the sampling distribution of r can be obtained from Fisher's z. ...
    (sci.stat.math)
  • Re: distribution of sample correlation coefficient
    ... wanting to use the measured correlation coefficient r between two ... thinking a Beta distribution might be a reasonable model as it is ... something by looking at large-sample approximations based on assuming ... for the cumulants of either the sample correlation ...
    (sci.stat.math)
Loading