On Mon, 2007-10-22 at 06:24 -0700, privalan wrote: > Dear R-users, > > I would like to calculate elasticities and sensitivities of each parameters > involved in the following transition matrix: > > A <- matrix(c( > sigma*s0*f1, sigma*s0*f2, > s, v > ), nrow=2, byrow=TRUE,dimnames=list(stage,stage)) > > > The command "eigen.analysis" avaliable in package "popbio" provides > sensibility matrix and elasticity matrix (same dimension than A). I would > like to know if there is a way to calculate separetely the elasticity of > sigma, s0, f1, f2, s and v ?
You should first calculate the matrix element sensitivities, then calculate the derivatives of the elements of your matrix with respect to the parameter of interest. Then for each element in the matrix, the sensitivity of the parameter is just the product of the derivative and the appropriate element sensitivity, by the chain rule. Then add up all the sensitivities, multiply by your parameter and divide by lambda. ie plot(1:10, 1:10, type="n") text(5,6, expression(e[s[0]] == over(s[0], lambda)~sum(~over(paste(partialdiff,~lambda),paste(partialdiff,~a[ij])) %.% over(paste(partialdiff, ~a[ij]), paste(partialdiff, ~s[0])), ij)), cex=2) Be aware that these elasticities will in general not sum to unity, and cannot be interpreted as "contributions" to lambda. See Caswell (2001), page 232. Cheers, Simon. > > Thanks and regards, > > privalan -- Simon Blomberg, BSc (Hons), PhD, MAppStat. Lecturer and Consultant Statistician Faculty of Biological and Chemical Sciences The University of Queensland St. Lucia Queensland 4072 Australia Room 320 Goddard Building (8) T: +61 7 3365 2506 email: S.Blomberg1_at_uq.edu.au Policies: 1. I will NOT analyse your data for you. 2. Your deadline is your problem. 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. ______________________________________________ R-help@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.
