R help - Apr 2009 - Generate bivariate binomial data

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.
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,
methodology and quality assurance
Gaverstraat 4
9500 Geraardsbergen
Belgium 
tel. + 32 54/436 185
Thierry.Onkelinx at inbo.be 
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

Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver weer 
en binden het INBO onder geen enkel beding, zolang dit bericht niet bevestigd is
door een geldig ondertekend document. The views expressed in  this message 
and any annex are purely those of the writer and may not be regarded as stating 
an official position of INBO, as long as the message is not confirmed by a duly 
signed document.

Hi Thierry,

I think it should be possible to generate such correlated data using a mixed
model approach:


1) Generate pairs of correlated linear predictor values using an ordinary linear
mixed
model setup (for example using rnorm() repeatedly)

2) Back-transform these values using the inverse logit (or similar link
function) to
obtain probabilities

3) Draw binomial responses using the probabilities from 2) (using rbinom())


You may need to use trial-and-error to get the right amount of correlation.


Christian

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,
> methodology and quality assurance
> Gaverstraat 4
> 9500 Geraardsbergen
> Belgium
> tel. + 32 54/436 185
> Thierry.Onkelinx at inbo.be
> 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
>
> Dit bericht en eventuele bijlagen geven enkel de visie van de schrijver
weer
> en binden het INBO onder geen enkel beding, zolang dit bericht niet
bevestigd is
> door een geldig ondertekend document. The views expressed in  this message
> and any annex are purely those of the writer and may not be regarded as
stating
> an official position of INBO, as long as the message is not confirmed by a
duly
> signed document.
>
> ______________________________________________
> R-help at r-project.org mailing list
> 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.
>
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