Hi All, in a paper (which I can't locate now...) which I read recently it was stated that restraints do not reduce the number of parameters, rather they augment the number of data points (so strong restraints are like strong data, weak restraints weak data...). Only strict NCS constraints, where the copies have to stay exactly the same, would reduce the number of parameters. Both augment the data to parameter ratio, of course. I really liked this explanation. Mark
On 9 April 2010 21:54, Ian Tickle <ianj...@gmail.com> wrote: > Hi Ed > > It's very difficult to deal theoretically with NCS because, unlike > bond lengths where the uncertainties are known a priori (at least in > principle), with NCS you don't know the uncertainties a priori, if you > see what I mean (rather like unknown unknowns!). In other words the > optimal weights and hence the effective number of parameters will > depend on the exactness of the NCS. In practice you can of course > determine the weights by minimising Rfree w.r.t.them. So I think it > would be quite difficult to do what you are proposing, i.e. to > disentangle the effects of the obs/param ratio and any effect of > correlation of the working & test sets. Interesting problem though! > > BTW I think you are mis-quoting the formula in the paper, it should be > <Rfree/R> = sqrt((Nobs+Nparam)/(Nobs-Nparam)). > > In other words R is reduced below its expected value in the absence of > random error, by overfitting the errors in the working set, but people > tend to forget that the test set also has, on average, random errors > of the same magnitude which tend to increase Rfree *above* its > expected value. > > Cheers > > -- Ian > > > On Fri, Apr 9, 2010 at 8:25 PM, Edward A. Berry <ber...@upstate.edu> > wrote: > > Has anyone looked theoretically at how ncs-restraints affect > > the expected Rfree/R ratio? > > > > Tickle et al., Acta Cryst. (1998). D54, 547-557 > > concluded Rfree/R = sqrt(Nobs/(Nobs-Nparam)) . > > He suggested that, with restrained refinement of coordinates > > plus individual isotropic B-factors, the effective number > > of parameters per atom is two. If we add strong N-fold NCS > > restraints on coordinates and B-factor, does that effectively > > reduce the number of parameters by a factor of N? > > Giving 2/N for parameters per atom? > > > > I'm curious how much of the drop in the r-free ratio observed > > on enforcing NCS is due to the reduction in the effective > > number of parameters, and how much is due to linking reflections > > in the free set with the working set. Given an expression to > > predict the effect of reducing number of parameters, seeing > > how much of the actual drop in Rfree/R it accounts for > > would let us see how severe the linkage problem is. > > > > Ed > > > -- Mark J van Raaij http://webspersoais.usc.es/mark.vanraaij http://www.ibmb.csic.es
