[R] Problem with lm.resid() when weights are provided
Fox, John
j|ox @end|ng |rom mcm@@ter@c@
Mon Sep 17 19:16:19 CEST 2018
Dear Hamed,
> -----Original Message-----
> From: Hamed Ha [mailto:hamedhaseli using gmail.com]
> Sent: Monday, September 17, 2018 3:56 AM
> To: Fox, John <jfox using mcmaster.ca>
> Cc: r-help using r-project.org
> Subject: Re: [R] Problem with lm.resid() when weights are provided
>
> H i John,
>
>
> Thank you for your reply.
>
>
> I see your point, thanks. I checked lm.wfit() and realised that there is a tol
> parameter that is already set to 10^-7. This is not even the half decimal to the
> machine precision. Furthermore, plying with tol parameter does not solve the
> problem, as far as I checked.
tol plays a different role in lm.wfit(). It's for the QR decomposition (done in C code), I suppose to determine the rank of the weighted model matrix. Generally in this kind of context, you'd use something like the square root of the machine double epsilon to define a number that's effectively 0, and the tolerance used here isn't too far off that -- about an order of magnitude larger.
I'm not an expert in computer arithmetic or numerical linear algebra, so I don't have anything more to say about this.
>
>
> I still see this issue as critical and we should report it to the R core team to be
> investigated more. What do you think?
I don't think that it's a critical issue because it isn't sensible to specify nonzero weights so close to 0. A simple solution is to change these weights to 0 in your code calling lm().
That said, I suppose that it might be better to make lm.wfit() more robust to near-zero weights. If you feel strongly about this, you can file a bug report, but I'm not interested in pursuing it.
Best,
John
>
>
> Regards,
> Hamed.
>
>
> On Fri, 14 Sep 2018 at 22:46, Fox, John <jfox using mcmaster.ca
> <mailto:jfox using mcmaster.ca> > wrote:
>
>
> Dear Hamed,
>
> When you post a question to r-help, generally you should cc
> subsequent messages there as well, as I've done to this response.
>
> The algorithm that lm() uses is much more numerically stable than
> inverting the weighted sum-of-squares-and-product matrix. If you want to see
> how the computations are done, look at lm.wfit(), in which the residuals and
> fits are computed as
>
> z$residuals <- z$residuals/wts
> z$fitted.values <- y - z$residuals
>
> Zero weights are handled specially, and your tiny weights are thus the
> source of the problem. When you divide by a number less than the machine
> double-epsilon, you can't expect numerically stable results. I suppose that
> lm.wfit() could check for 0 weights to a tolerance rather than exactly.
>
> John
>
> > -----Original Message-----
> > From: Hamed Ha [mailto:hamedhaseli using gmail.com
> <mailto:hamedhaseli using gmail.com> ]
> > Sent: Friday, September 14, 2018 5:34 PM
> > To: Fox, John <jfox using mcmaster.ca <mailto:jfox using mcmaster.ca> >
> > Subject: Re: [R] Problem with lm.resid() when weights are provided
> >
> > Hi John,
> >
> > Thank you for your reply.
> >
> > I agree that the small weights are the potential source of the
> instability in the
> > result. I also suspected that there are some failure/bugs in the actual
> > algorithm that R uses for fitting the model. I remember that at some
> points I
> > checked the theoretical estimation of the parameters, solve(t(x)
> %*% w %*%
> > x) %*% t(x) %*% w %*% y, (besides the point that I had to set tol
> parameter in
> > solve() to a super small value) and realised that lm() and the
> theoretical
> > results match together. That is the parameter estimation is right in
> R.
> > Moreover, I checked the predictions, predict(lm.fit), and it was right.
> Then the
> > only source of error remained was resid() function. I further checked
> this
> > function and it is nothing more than calling a sub-element from and
> lm() fit.
> > Putting all together, I think that there is something wrong/bug/miss-
> > configuration in the lm() algorithm and I highly recommend the R
> core team to
> > fix that.
> >
> > Please feel free to contact me for more details if required.
> >
> > Warm regards,
> > Hamed.
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > On Fri, 14 Sep 2018 at 13:35, Fox, John <jfox using mcmaster.ca
> <mailto:jfox using mcmaster.ca>
> > <mailto:jfox using mcmaster.ca <mailto:jfox using mcmaster.ca> > > wrote:
> >
> >
> > Dear Hamed,
> >
> > I don't think that anyone has picked up on this problem.
> >
> > What's peculiar about your weights is that several are 0 within
> > rounding error but not exactly 0:
> >
> > > head(df)
> > y x weight
> > 1 1.5115614 0.5520924 2.117337e-34
> > 2 -0.6365313 -0.1259932 2.117337e-34
> > 3 0.3778278 0.4209538 4.934135e-31
> > 4 3.0379232 1.4031545 2.679495e-24
> > 5 1.5364652 0.4607686 2.679495e-24
> > 6 -2.3772787 -0.7396358 6.244160e-21
> >
> > I can reproduce the results that you report:
> >
> > > (mod.1 <- lm(y ~ x, data=df))
> >
> > Call:
> > lm(formula = y ~ x, data = df)
> >
> > Coefficients:
> > (Intercept) x
> > -0.04173 2.03790
> >
> > > max(resid(mod.1))
> > [1] 1.14046
> > > (mod.2 <- lm(y ~ x, data=df, weights=weight))
> >
> > Call:
> > lm(formula = y ~ x, data = df, weights = weight)
> >
> > Coefficients:
> > (Intercept) x
> > -0.05786 1.96087
> >
> > > max(resid(mod.2))
> > [1] 36.84939
> >
> > But the problem disappears when the tiny nonzero weight are set
> to 0:
> >
> > > df2 <- df
> > > df2$weight <- zapsmall(df2$weight)
> > > head(df2)
> > y x weight
> > 1 1.5115614 0.5520924 0
> > 2 -0.6365313 -0.1259932 0
> > 3 0.3778278 0.4209538 0
> > 4 3.0379232 1.4031545 0
> > 5 1.5364652 0.4607686 0
> > 6 -2.3772787 -0.7396358 0
> > > (mod.3 <- update(mod.2, data=df2))
> >
> > Call:
> > lm(formula = y ~ x, data = df2, weights = weight)
> >
> > Coefficients:
> > (Intercept) x
> > -0.05786 1.96087
> >
> > > max(resid(mod.3))
> > [1] 1.146663
> >
> > I don't know exactly why this happens, but suspect numerical
> > instability produced by the near-zero weights, which are smaller
> than the
> > machine double-epsilon
> >
> > > .Machine$double.neg.eps
> > [1] 1.110223e-16
> >
> > The problem also disappears, e.g., if the tiny weight are set to 1e-
> 15
> > rather than 0.
> >
> > I hope this helps,
> > John
> >
> > -----------------------------------------------------------------
> > John Fox
> > Professor Emeritus
> > McMaster University
> > Hamilton, Ontario, Canada
> > Web: https://socialsciences.mcmaster.ca/jfox/
> >
> >
> >
> > > -----Original Message-----
> > > From: R-help [mailto:r-help-bounces using r-project.org <mailto:r-
> help-bounces using r-project.org> <mailto:r-help- <mailto:r-help->
> > bounces using r-project.org <mailto:bounces using r-project.org> > ] On
> Behalf Of Hamed Ha
> > > Sent: Tuesday, September 11, 2018 8:39 AM
> > > To: r-help using r-project.org <mailto:r-help using r-project.org>
> <mailto:r-help using r-project.org <mailto:r-help using r-project.org> >
> > > Subject: [R] Problem with lm.resid() when weights are provided
> > >
> > > Dear R Help Team.
> > >
> > > I get some weird results when I use the lm function with weight.
> The
> > issue can
> > > be reproduced by the example below:
> > >
> > >
> > > The input data is (weights are intentionally designed to reflect
> some
> > > structures in the data)
> > >
> > >
> > > > df
> > > y x weight
> > > 1.51156139 0.55209240 2.117337e-34
> > > -0.63653132 -0.12599316 2.117337e-34
> > > 0.37782776 0.42095384 4.934135e-31
> > > 3.03792318 1.40315446 2.679495e-24
> > > 1.53646523 0.46076858 2.679495e-24
> > > -2.37727874 -0.73963576 6.244160e-21
> > > 0.37183065 0.20407468 1.455107e-17
> > > -1.53917553 -0.95519361 1.455107e-17
> > > 1.10926675 0.03897129 3.390908e-14
> > > -0.37786333 -0.17523593 3.390908e-14
> > > 2.43973603 0.97970095 7.902000e-11
> > > -0.35432394 -0.03742559 7.902000e-11
> > > 2.19296613 1.00355263 4.289362e-04
> > > 0.49845532 0.34816207 4.289362e-04
> > > 1.25005260 0.76306225 5.000000e-01
> > > 0.84360691 0.45152356 5.000000e-01
> > > 0.29565993 0.53880068 5.000000e-01
> > > -0.54081334 -0.28104525 5.000000e-01
> > > 0.83612836 -0.12885659 9.995711e-01
> > > -1.42526769 -0.87107631 9.999998e-01
> > > 0.10204789 -0.11649899 1.000000e+00
> > > 1.14292898 0.37249631 1.000000e+00
> > > -3.02942081 -1.28966997 1.000000e+00
> > > -1.37549764 -0.74676145 1.000000e+00
> > > -2.00118016 -0.55182759 1.000000e+00
> > > -4.24441674 -1.94603608 1.000000e+00
> > > 1.17168144 1.00868008 1.000000e+00
> > > 2.64007761 1.26333069 1.000000e+00
> > > 1.98550114 1.18509599 1.000000e+00
> > > -0.58941683 -0.61972416 9.999998e-01
> > > -4.57559611 -2.30914920 9.995711e-01
> > > -0.82610544 -0.39347576 9.995711e-01
> > > -0.02768220 0.20076910 9.995711e-01
> > > 0.78186399 0.25690215 9.995711e-01
> > > -0.88314153 -0.20200148 5.000000e-01
> > > -4.17076452 -2.03547588 5.000000e-01
> > > 0.93373070 0.54190626 4.289362e-04
> > > -0.08517734 0.17692491 4.289362e-04
> > > -4.47546619 -2.14876688 4.289362e-04
> > > -1.65509103 -0.76898087 4.289362e-04
> > > -0.39403030 -0.12689705 4.289362e-04
> > > 0.01203300 -0.18689898 1.841442e-07
> > > -4.82762639 -2.31391121 1.841442e-07
> > > -0.72658380 -0.39751171 3.397282e-14
> > > -2.35886866 -1.01082109 0.000000e+00
> > > -2.03762707 -0.96439902 0.000000e+00
> > > 0.90115123 0.60172286 0.000000e+00
> > > 1.55999194 0.83433953 0.000000e+00
> > > 3.07994058 1.30942776 0.000000e+00
> > > 1.78871462 1.10605530 0.000000e+00
> > >
> > >
> > >
> > > Running simple linear model returns:
> > >
> > > > lm(y~x,data=df)
> > >
> > > Call:
> > > lm(formula = y ~ x, data = df)
> > >
> > > Coefficients:
> > > (Intercept) x
> > > -0.04173 2.03790
> > >
> > > and
> > > > max(resid(lm(y~x,data=df)))
> > > [1] 1.14046
> > >
> > >
> > > *HOWEVER if I use the weighted model then:*
> > >
> > > lm(formula = y ~ x, data = df, weights = df$weights)
> > >
> > > Coefficients:
> > > (Intercept) x
> > > -0.05786 1.96087
> > >
> > > and
> > > > max(resid(lm(y~x,data=df,weights=df$weights)))
> > > [1] 60.91888
> > >
> > >
> > > as you see, the estimation of the coefficients are nearly the
> same
> > but the
> > > resid() function returns a giant residual (I have some cases
> where
> > the value is
> > > much much higher). Further, if I calculate the residuals by
> simply
> > > predict(lm(y~x,data=df,weights=df$weights))-df$y then I get the
> true
> > value for
> > > the residuals.
> > >
> > >
> > > Thanks.
> > >
> > > Please do not hesitate to contact me for more details.
> > > Regards,
> > > Hamed.
> > >
> > > [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
> > > R-help using r-project.org <mailto:R-help using r-project.org>
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