On Thu, 15 Jun 2000 13:01:08 ARG, Eduardo Sendra <[log in to unmask]>
wrote:
> We are trying to compare growth curves from several populations of
> Argentine silversides from nearby localities (lakes). We have estimates
> of von
> Bertalanfy's parameteres for all of them and would like to compare
> overall
> growth or growth performance for the stocks.
>        I would appreciate any suggestions or literature citations that
> might
>help us solve the problem.

The literature specific to the von Bert is not as rich as the
statistical literature on more general nonlinear models.  For the
case where one has repeated measurements (for example, body size)
from individual subjects (fish), the following presents a good
overview of Bayesian and frequentist modeling strategies:

  Davidian, M., and Giltinan.  1995.  Nonlinear models for repeated
     measurement data.  Chapman and Hall, London.

The case for single measurements from individual fish is conceptually
simpler because those are usually statistically independent.

To "compare curves", one formulates an extension of the response
function that includes parameters for the groups to be compared.
For the von Bert, one might start with the general case where
t-zero, k and L-infinity all have a component that is common to
all fish, and another component that quantifies the contribution
of the group effect.  One may find tbat only one or two of the
parameters show an important group effect, and in those cases
the model can be simplified.  For repeated measurements on
individual fish, it is also useful to include a random effect for
individuals; in that case, look for information on "random
coefficient" or "hierarchical" regression models.

If the primary data are not available, and all one has are parameter
estimates and their standard errors, inference is problematic.
The covariances among the parameters contain relevant information
and, without them, comparisons among groups can be misleading.
See the literature on meta analysis (e.g.:

  DuMouchel, W.H., and J.E. Harris.  1983.  Bayes methods for
     combining the results of cancer studies in humans and other
     species.  Journal of the American Statistical Association
     78:293-315.

  Cooper, H., and L. Hedges, editors.  1994.  The handbook of
     research synthesis.  Russell Sage Foundation, New York.)

><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>
       To leave the Fish-Sci list, Send blank message to:
        mailto:[log in to unmask]
      Need help? Contact  [log in to unmask]
><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><> ><>