Dear All,
I have a questions I would like to ask about and wonder if you have any thoughts
to make it work in R.
1. I work in the field of medicine where physiologic variables are often
simulated, and they can not have negative values. Most often the assumption is
made to simulate this parameters with a normal distribution but in the
"log-domain" to avoid from negative values to be generated. Since the
expected mean and SD is usually known from the normal domain, using the methods
described in the wikipedia article "Arithmetric moments" I generate
μand σ and simulate with rlnorm(). At times though the following issue comes up:
I have the mean and SD for the parameters available from the normal domain, and
the covariance matrix from the normal domain. Then I would like to simulate the
values, but to avoid from negative values being generated I have to fall back on
rlnorm in {compositions}. My issue is though that my covariance matrix is
representing the covariance of the parameters in the normal domain, as opposed
to in the lognormal domain. Any thoughts on how
to work around this?
apreciate the help,
Andras
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On 11-Oct-2012 17:22:44 Andras Farkas wrote:> Dear All, > I have a questions I would like to ask about and wonder if you > have any thoughts to make it work in R. > > 1. I work in the field of medicine where physiologic variables > are often simulated, and they can not have negative values. > Most often the assumption is made to simulate this parameters > with a normal distribution but in the "log-domain" to avoid from > negative values to be generated. Since the expected mean and SD > is usually known from the normal domain, using the methods described > in the wikipedia article "Arithmetric moments" I generate ??and ?? > and simulate with rlnorm(). At times though the following issue > comes up: I have the mean and SD for the parameters available > from the normal domain, and the covariance matrix from the normal > domain. Then I would like to simulate the values, but to avoid > from negative values being generated I have to fall back on rlnorm > in {compositions}. My issue is though that my covariance matrix is > representing the covariance of the parameters in the normal domain, > as opposed to in the lognormal domain. Any thoughts on how to work > around this? > > apreciate the help, > AndrasIf I understand your question correctly, if Y is the variable being simulated then you know the mean (M, say) and the variance (V, say) of log(Y). So you can simulate X from a normal distribution with mean M and variance V = S^2 (S = SD of X), and then Y = exp(X): Y <- exp(rnorm(n,M,S)) where n is the number of sampled values you want. When Y is multivariate, with M the vector of means and V the covariance matrix of log(Y), then use a similar approach with the function mvrnorm() from the MASS package: library(MASS) Y <- mvrnorm(n,M,V) Does this help? Ted. ------------------------------------------------- E-Mail: (Ted Harding) <Ted.Harding at wlandres.net> Date: 11-Oct-2012 Time: 18:51:47 This message was sent by XFMail
(I made a slip with the mulstivariate case below: see at [***]) On 11-Oct-2012 17:51:51 Ted Harding wrote:> On 11-Oct-2012 17:22:44 Andras Farkas wrote: >> Dear All, >> I have a questions I would like to ask about and wonder if you >> have any thoughts to make it work in R. >> >> 1. I work in the field of medicine where physiologic variables >> are often simulated, and they can not have negative values. >> Most often the assumption is made to simulate this parameters >> with a normal distribution but in the "log-domain" to avoid from >> negative values to be generated. Since the expected mean and SD >> is usually known from the normal domain, using the methods described >> in the wikipedia article "Arithmetric moments" I generate ??and ?? >> and simulate with rlnorm(). At times though the following issue >> comes up: I have the mean and SD for the parameters available >> from the normal domain, and the covariance matrix from the normal >> domain. Then I would like to simulate the values, but to avoid >> from negative values being generated I have to fall back on rlnorm >> in {compositions}. My issue is though that my covariance matrix is >> representing the covariance of the parameters in the normal domain, >> as opposed to in the lognormal domain. Any thoughts on how to work >> around this? >> >> apreciate the help, >> Andras >If I understand your question correctly, if Y is the variable being simulated then you know the mean (M, say) and the variance (V, say) of log(Y). So you can simulate X from a normal distribution with mean M and variance V = S^2 (S = SD of X), and then Y = exp(X): Y <- exp(rnorm(n,M,S)) where n is the number of sampled values you want. When Y is multivariate, with M the vector of means and V the covariance matrix of log(Y), then use a similar approach with the function mvrnorm() from the MASS package: [***] ## library(MASS) ## Y <- mvrnorm(n,M,V) library(MASS) Y <- exp(mvrnorm(n,M,V)) Does this help? Ted.> ------------------------------------------------- > E-Mail: (Ted Harding) <Ted.Harding at wlandres.net> > Date: 11-Oct-2012 Time: 18:51:47 > This message was sent by XFMail > > ______________________________________________ > 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.------------------------------------------------- E-Mail: (Ted Harding) <Ted.Harding at wlandres.net> Date: 11-Oct-2012 Time: 19:44:02 This message was sent by XFMail