Hi Pete Not sure what you mean by 'which parameters'. We're talking here about the total parameter _count_ and its effect on the statistics, i.e. R factors etc. You can't relate a specific parameter to a specific restraint. The statistics behave in exactly the same way as they would if you did actually reduce the number of parameters (and they certainly don't behave in the same way as they would if you increased the number of observations). That's why I call it the 'effective' no of parameters. In any case I don't think transformation of constraints to parameters is straightforward at all! For example if you constrain all the y co-ordinate parameters to sum to zero by adding an extra equation which y parameter are you 'removing'? Obviously you can remove a parameter explicitly by expressing it in terms of the others, but that's not the only way (or even the best way) of solving a constrained optimisation problem. A better way is usually to _add_ constraint equations using Lagrange multipliers without changing the parameters, then there's no 1-to-1 relationship between constraints and parameters.
Cheers -- Ian On Tue, Feb 1, 2011 at 3:56 PM, Pete Meyer <[email protected]> wrote: > Ian, > >> Now it's still true that Ncon reduces Npar but it's no longer true >> that Ncon increases Nobs. > > This seems counter-intuitive enough for me to ask a stupid question: which > parameters are being removed in restrained refinement? > > For constraints this seems straightforward (transformation of >1 parameters > to 1 parameter); but the same logic doesn't appear to apply to restraints > (at least, I can't figure out how it would). > > Pete >
