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:hamedhas...@gmail.com]
> Sent: Friday, September 14, 2018 5:34 PM
> To: Fox, John <j...@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 <j...@mcmaster.ca
> <mailto:j...@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-boun...@r-project.org <mailto:r-help-
> boun...@r-project.org> ] On Behalf Of Hamed Ha
> > Sent: Tuesday, September 11, 2018 8:39 AM
> > To: r-help@r-project.org <mailto:r-help@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@r-project.org <mailto:R-help@r-project.org> mailing list --
> To UNSUBSCRIBE and more, see
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> > PLEASE do read the posting guide http://www.R-project.org/posting-
> > guide.html
> > and provide commented, minimal, self-contained, reproducible
> code.
>
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