[R] Weighted SUR/NSUR

[Arne Henningsen]

Dear Ariel

Thank you for your detailed explanations and the example. Indeed, it
should be rather straightforward to implement observation-specific
weights in systemfit (i.e. in the estimation of systems of linear or
non-linear equations). As you indicated that many people are looking
for this feature, I wonder if I should start a crowd-funding
campaign...

Best regards,
Arne


On 16 August 2013 18:23, Ariel <ariel.muldoon at oregonstate.edu> wrote:
> Arne Henningsen-3 wrote
>>> Is it possible
>>> to run SUR with weights using systemfit? I mean weighted seemingly
>> unrelated
>>> regression (weighted SUR)
>>
>> Currently, systemfit cannot estimate (SUR) models with
>> observation-specific
>> weights :-(
>>
>>> or weighted nonlinear unrelated regression (weighted NSUR).
>>
>> We are still not yet finished with implementing nonlinear models in
>> systemfit (see http://www.systemfit.org/) :-(
>
> I recently had a student come to me with a very similar (okay, identical)
> problem as the OP.  I had to learn PROC MODEL, anyway, so I thought I’d poke
> around in R while I was at it.  I have nothing to add about any problems
> with or the lack of maturity of the estimation procedure for nlsystemfit(),
> but I do have some ideas about observation-level weights.
>
> It took me awhile to make the leap from the fairly straightforward linear
> weighted least squares (for example, see  Weisberg's Applied Linear
> Regression textbook equation 5.8) to understanding how weighting worked in
> nonlinear least squares.  The R help forum certainly came in handy:
> https://stat.ethz.ch/pipermail/r-help/2004-November/060424.html.  I can add
> weights into a nonlinear regression by simply multiplying both the response
> and the nonlinear function by the square root of the desired weights.
> Here’s a toy example, where I compare a model fit using the “weights”
> argument in nls() with a model where I put the weights in “by hand” :
>
> DNase1 = subset(DNase, Run == 1)
> fit2 = nls(density ~ Asym/(1 + exp((xmid - log(conc))/scal)),
>                  data = DNase1,
>                  start = list(Asym = 3, xmid = 0, scal = 1), weights =
> rep(1:8, each = 2))
> summary(fit2)
>
> # Take the square root of the weights for fitting “by hand”
> sw = sqrt(rep(1:8, each = 2) )
> fit3 = nls(sw*density ~ sw*(Asym/(1 + exp((xmid - log(conc))/scal))),
> DNase1,
>                  start = list(Asym = 3, xmid = 0, scal = 1) )
> summary(fit3)
>
> # The predicted values for fit3 need to be divided by the weights
>         # but the residuals are weighted residuals
> predict(fit2)
> predict(fit3)/sw
>
> It seems like this weighted approach could be easily extended to the model
> formulas for a system of nonlinear equations (it would be similar for linear
> equations) to be fit with systemfit.
>
>>  Parresol (2001) in his paper
>> titled Additivity of nonlinear biomass
>> equations has run weighted NSUR using PROC MODEL (SAS institute Inc.1993).
>> I was wondering if r can do that.
>
> It turned out I had to use this weighting approach in PROC MODEL, as well,
> when each equation in the system had a different set of weights.  The
> estimates I get when fitting the Parresol example mentioned by the OP using
> nlsystemfit and PROC MODEL are within spitting distance of each other, so I
> feel like I am at least making the same mistakes in both software packages.
>
> I'm wondering if my logic is sound or if I'm missing some complication that
> occurs when working with systems of equations.  I’ve seen several folks
> looking to fit weighted systems of equations in R with systemfit, and this
> approach might get them what they need.
>
> Ariel
>
>
>
> --
> View this message in context: http://r.789695.n4.nabble.com/Weighted-SUR-NSUR-tp4670602p4673973.html
> Sent from the R help mailing list archive at Nabble.com.
>
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-- 
Arne Henningsen
http://www.arne-henningsen.name