[R] Generate bivariate binomial data

[Charles C. Berry]

On Fri, 17 Apr 2009, ONKELINX, Thierry wrote:

> Dear all,
>
> Could someone point me to a function or algorithm to generate random
> bivariate binomial data?
>
> Some details about what I'm trying to do. I have a dataset of trees who
> were categorised as not damaged or damaged. Each tree is measured twice
> (once in two consecutive years). The trees can recover from the damage
> but the data is clearly correlated. As a (un)damaged tree is more likely
> to stay (un)damaged. A GEE-model indicates a correlation of about 0.6
> between the measures on the same tree.

The commonly used sampling models for such count data (see Bishop, 
Fienberg, and Holland, Discrete Multivariate Analysis, 1975.) involve four 
parameters. There are various parameterizations.

In your case, the total sample size (N), the proportion of 
undamaged trees at the first (pr.undam.1), and the proportions at the 
second time conditional on the first (p.undam.2.undam.1, p.undam.2.dam.1) 
seems like reasonable way to parameterize the problem to do your 
simulation.

If you have the marginal counts and the correlation, you can transform 
them to the above parameterization by hacking through the algebra to find 
the expected 2 by 2 table of counts as a function of the latter 
parameters.

Then

y <- rbinom( N, 1, pr.undam.1 )
x <- rbinom( N, 1, ifelse(y==1, pr.undam.2.undam.1, pr.undam.2.dam.1 )

table(x,y)

should get you started

HTH,

Chuck

> I need to simulate similar dataset to do some power calculations.
>
> Best regards,
>
> Thierry
>
> ------------------------------------------------------------------------
> ----
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and Forest
> Cel biometrie, methodologie en kwaliteitszorg / Section biometrics,
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> Thierry.Onkelinx at inbo.be
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Charles C. Berry                            (858) 534-2098
                                             Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	            UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901