[R] DIfference between weights options in lm GLm and gls.

[Peter Dalgaard]

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
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