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

[Spencer Graves]

	  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.  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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