[R] DIfference between weights options in lm GLm and gls.
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Thu Mar 23 19:38:24 CET 2006
Spencer Graves <spencer.graves at pdf.com> writes:
> In my tests, "gls" did NOT give the same answers as "lm" and "glm",
> and I don't know why; perhaps someone else will enlighten us both.
The weights argument in gls (&gnls&lme&nlme) specifies the variance,
not the actual weight which is the reciprocal. (This is to my mind a
somewhat curious design decision, as is the fact that varPower and
varConstPower actually specifies the SD rather than the variance).
> I
> got the same answers from "lm" and "glm". Since you report different
> results, please supply a replicatable example.
>
> I tried the following:
> set.seed(1)
> DF <- data.frame(x=1:8, xf=rep(c("a", "b"), 4),
> y=rnorm(8), w=1:8, one=rep(1,8))
> fit.lm.w <- lm(y~x, DF, weights=w)
> fit.glm.w <- glm(y~x, data=DF, weights=w)
> fit.gls.w <- gls(y~x, data=DF,
> weights=varFixed(~w))
>
> > coef(fit.lm.w)
> (Intercept) x
> -0.2667521 0.0944190
> > coef(fit.glm.w)
> (Intercept) x
> -0.2667521 0.0944190
> > coef(fit.gls.w)
> (Intercept) x
> -0.5924727 0.1608727
>
> I also tried several variants of this. I know this does not answer
> your questions, but I hope it will contribute to an answer.
>
> spencer graves
>
> Goeland wrote:
>
> > Dear r-users£¬
> >
> > Can anyone explain exactly the difference between Weights options in lm glm
> > and gls?
> >
> > I try the following codes, but the results are different.
> >
> >
> >
> >>lm1
> >
> >
> > Call:
> > lm(formula = y ~ x)
> >
> > Coefficients:
> > (Intercept) x
> > 0.1183 7.3075
> >
> >
> >>lm2
> >
> >
> > Call:
> > lm(formula = y ~ x, weights = W)
> >
> > Coefficients:
> > (Intercept) x
> > 0.04193 7.30660
> >
> >
> >>lm3
> >
> >
> > Call:
> > lm(formula = ys ~ Xs - 1)
> >
> > Coefficients:
> > Xs Xsx
> > 0.04193 7.30660
> >
> > Here ys= y*sqrt(W), Xs<- sqrt(W)*cbind(1,x)
> >
> > So we can see weights here for lm means the scale for X and y.
> >
> > But for glm and gls I try
> >
> >
> >>glm1
> >
> >
> > Call: glm(formula = y ~ x)
> >
> > Coefficients:
> > (Intercept) x
> > 0.1183 7.3075
> >
> > Degrees of Freedom: 1242 Total (i.e. Null); 1241 Residual
> > Null Deviance: 1049000
> > Residual Deviance: 28210 AIC: 7414
> >
> >>glm2
> >
> >
> > Call: glm(formula = y ~ x, weights = W)
> >
> > Coefficients:
> > (Intercept) x
> > 0.1955 7.3053
> >
> > Degrees of Freedom: 1242 Total (i.e. Null); 1241 Residual
> > Null Deviance: 1548000
> > Residual Deviance: 44800 AIC: 11670
> >
> >>glm3
> >
> >
> > Call: glm(formula = y ~ x, weights = 1/W)
> >
> > Coefficients:
> > (Intercept) x
> > 0.03104 7.31033
> >
> > Degrees of Freedom: 1242 Total (i.e. Null); 1241 Residual
> > Null Deviance: 798900
> > Residual Deviance: 19900 AIC: 5285
> >
> >
> >>glm4
> >
> >
> > Call: glm(formula = ys ~ Xs - 1)
> >
> > Coefficients:
> > Xs Xsx
> > 2.687 6.528
> >
> > Degrees of Freedom: 1243 Total (i.e. Null); 1241 Residual
> > Null Deviance: 4490000
> > Residual Deviance: 506700 AIC: 11000
> >
> > With weights, the glm did not give the same results as lm why?
> >
> > Also for gls, I use varFixed here.
> >
> >
> >>gls3
> >
> > Generalized least squares fit by REML
> > Model: y ~ x
> > Data: NULL
> > Log-restricted-likelihood: -3737.392
> >
> > Coefficients:
> > (Intercept) x
> > 0.03104214 7.31032540
> >
> > Variance function:
> > Structure: fixed weights
> > Formula: ~W
> > Degrees of freedom: 1243 total; 1241 residual
> > Residual standard error: 4.004827
> >
> >>gls4
> >
> > Generalized least squares fit by REML
> > Model: ys ~ Xs - 1
> > Data: NULL
> > Log-restricted-likelihood: -5500.311
> >
> > Coefficients:
> > Xs Xsx
> > 2.687205 6.527893
> >
> > Degrees of freedom: 1243 total; 1241 residual
> > Residual standard error: 20.20705
> >
> > We can see the relation between glm and gls with weight as what
> >
> > I think, but what's the difference between lm wit gls and glm? why?
> >
> > Thanks so much.!
> >
> > Goeland
> >
> >
> >
> > Goeland
> > goeland at gmail.com
> > 2006-03-16
> >
> >
> >
> > ------------------------------------------------------------------------
> >
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>
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--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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