R help - Aug 2019 - Simulate I x J contingency tables using correlation coefficient using bivariate normal distribution

Dear R Users,

I am interested in generating contingency tables from bivariate normal
distribution using different correlation coefficient values.

I am experimenting numerous ways of generating contingency tables, and one
possible way is to generate from multinomial distribution.

I wonder how to generate the count variables from a continuous distribution
using correlation structure. Generating bivariate normal variables can be
easily done using mvrnorm() in R. I am struggling to write R code for
generating count from continuous variables.

Any suggestions is very much appreciated.

Thanks.
Sripriya.

	[[alternative HTML version deleted]]

Dear Sripriya,

Step 1. generate random values from a multivariate normal distribution
Step 2. convert the random values into probabilities
Step 3. convert the probabilities into values from the target distribution

library(mvtnorm)
n <- 1e3
correl <- 0.9
lambda <- c(10, 50)
sigma <- matrix(correl, ncol = length(lambda), nrow = length(lambda))
diag(sigma) <- 1
binorm <- rmvnorm(n, sigma = sigma)
bip <- apply(binorm, 2, pnorm)
bipois <- sapply(
  seq_along(lambda),
  function(i) {
    qpois(bip[, i], lambda = lambda[i])
  }
)
plot(bipois)
table(data.frame(bipois))

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
To call in the statistician after the experiment is done may be no more
than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does not
ensure that a reasonable answer can be extracted from a given body of data.
~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////

<https://www.inbo.be>


Op ma 19 aug. 2019 om 10:29 schreef Sri Priya <sri.chocho at gmail.com>:
> Dear R Users,
>
> I am interested in generating contingency tables from bivariate normal
> distribution using different correlation coefficient values.
>
> I am experimenting numerous ways of generating contingency tables, and one
> possible way is to generate from multinomial distribution.
>
> I wonder how to generate the count variables from a continuous distribution
> using correlation structure. Generating bivariate normal variables can be
> easily done using mvrnorm() in R. I am struggling to write R code for
> generating count from continuous variables.
>
> Any suggestions is very much appreciated.
>
> Thanks.
> Sripriya.
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
	[[alternative HTML version deleted]]

Dear Thierry,

Thank you very much for your answer.  I got some idea about generating
tables from bivariate normal from your code. But still there will be an
argument to choose the lambda value. So, I am thinking whether to generate
count data using margial CDF? Because one may wish to test the independence
from any contingency table. I am planning to test the same for this kind of
table versus multinomial tables.

Once again thank you for your timely response.

Regards
Sripriya

On Mon, Aug 19, 2019 at 2:53 PM Thierry Onkelinx <thierry.onkelinx at
inbo.be>
wrote:
> Dear Sripriya,
>
> Step 1. generate random values from a multivariate normal distribution
> Step 2. convert the random values into probabilities
> Step 3. convert the probabilities into values from the target distribution
>
> library(mvtnorm)
> n <- 1e3
> correl <- 0.9
> lambda <- c(10, 50)
> sigma <- matrix(correl, ncol = length(lambda), nrow = length(lambda))
> diag(sigma) <- 1
> binorm <- rmvnorm(n, sigma = sigma)
> bip <- apply(binorm, 2, pnorm)
> bipois <- sapply(
>   seq_along(lambda),
>   function(i) {
>     qpois(bip[, i], lambda = lambda[i])
>   }
> )
> plot(bipois)
> table(data.frame(bipois))
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
> FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality
Assurance
> thierry.onkelinx at inbo.be
> Havenlaan 88 bus 73, 1000 Brussel
> www.inbo.be
>
>
>
///////////////////////////////////////////////////////////////////////////////////////////
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
>
///////////////////////////////////////////////////////////////////////////////////////////
>
> <https://www.inbo.be>
>
>
> Op ma 19 aug. 2019 om 10:29 schreef Sri Priya <sri.chocho at
gmail.com>:
>
>> Dear R Users,
>>
>> I am interested in generating contingency tables from bivariate normal
>> distribution using different correlation coefficient values.
>>
>> I am experimenting numerous ways of generating contingency tables, and
one
>> possible way is to generate from multinomial distribution.
>>
>> I wonder how to generate the count variables from a continuous
>> distribution
>> using correlation structure. Generating bivariate normal variables can
be
>> easily done using mvrnorm() in R. I am struggling to write R code for
>> generating count from continuous variables.
>>
>> Any suggestions is very much appreciated.
>>
>> Thanks.
>> Sripriya.
>>
>>         [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
	[[alternative HTML version deleted]]

> Step 1. generate random values from a multivariate normal distribution
> Step 2. convert the random values into probabilities
> Step 3. convert the probabilities into values from the target distribution
This requires a cautionary note.
The method above is simple in the univariate case (where people would
usually start with a uniform distribution), however, generalizing it
to the multivariate case, is not as simple as Thierry as suggested.

That doesn't necessarily mean that his solution is wrong.
(Because there's more than one way of defining a bivariate Poisson
distribution).