Estimating model parameters for system of equations
Dear Louise
On 15 November 2011 19:03, lstevenson <louise.stevenson at lifesci.ucsb.edu> wrote:
Hi all, I'm trying to estimate model parameters in R for a pretty simple system of equations, but I'm having trouble. ?Here is the system of equations (all derivatives): eqAlgae <- (u_Amax * C_A) * (1 - (Q_Amin / Q_A)) eqQuota <- (p_max * R_V) / (K_p + R_V) - ((Q_A-Q_Amin)*u_Amax) eqResource <- -C_A * (p_max * R_V) / (K_p + R_V) eqSystem <- list(C_A = eqAlgae, Q_A = eqQuota, R_V = eqResource) I want to estimate u_Amax, Q_Amin, p_max and Q_Amin with the data I've collected using least squares. I've tried using systemfit but I'm not sure how to write out the equations (my attempt is above but that doesn't work since I haven't given values to the parameters I'm trying to estimate - should I give those parameters initial values?). I've looked into the other functions to get least squares estimates (e.g. lm() ) but I'm not sure how to use that for a system of equations. I have some experience with R but I'm a novice when it comes to parameter estimation, so any help would be much appreciated! Thank you!
Your system of equations is non-linear in parameters. As lm() and systemfit() can only estimate models that are linear in parameters, you cannot use these commands to estimate your model. The "systemfit" package includes the function nlsystemfit() that is intended to estimate systems of non-linear equations. However, nlsystemfit() is still under development and often has convergence problems. Therefore, I wouldn't use it for "serious" applications. You can estimate your non-linear equations separately with nls(). If you want to estimate your equations jointly, I am afraid that you either have to switch to another software or have to implement the estimation yourself. You could, e.g., minimize the determinant of the residual covariance matrix with optim(), nlm(), nlminb(), or another optimizer or you could maximize the likelihood function of the FIML model using maxLik(). Sorry that I (and R) cannot present you a simple solution! Best wishes from Copenhagen, Arne
Arne Henningsen http://www.arne-henningsen.name