[R] effects in ANCOVA

[Chuck Cleland]

Tomas Goicoa wrote:
> Dear R users,
> 
> I am trying to fit the following ANCOVA model in R2.4.0
> 
> Y_ij=mu+alpha_i+beta*(X_ij-X..)+epsilon_ij
> 
> Particularly I am interested in obtaining estimates for mu, and the effects 
> alpha_i
> 
> 
> I have this data (from the book Applied Linear Statistical Models by Neter 
> et al (1996), page 1020)
> 
> 
> y<-c(38,43,24,39,38,32,36,38,31,45,27,21,33,34,28)
> x<-c(21,34,23,26,26,29,22,29,30,28,18,16,19,25,29)
> xmean<-x-mean(x)
> grupo<-factor(rep(c(1,2,3),5))
> datos<-data.frame(y,xmean,grupo)
> 
> and I have done the following
> 
> modelo<-lm(y~xmean+grupo,data=datos)
> 
> summary(modelo)
> 
> Call:
> lm(formula = y ~ xmean + grupo, data = datos)
> 
> Residuals:
>      Min      1Q  Median      3Q     Max
> -2.4348 -1.2739 -0.3363  1.6710  2.4869
> 
> Coefficients:
>              Estimate Std. Error t value Pr(>|t|)
> (Intercept)  39.8174     0.8576  46.432 5.66e-14 ***
> xmean         0.8986     0.1026   8.759 2.73e-06 ***
> grupo2       -5.0754     1.2290  -4.130  0.00167 **
> grupo3      -12.9768     1.2056 -10.764 3.53e-07 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> 
> Residual standard error: 1.873 on 11 degrees of freedom
> Multiple R-Squared: 0.9403,     Adjusted R-squared: 0.9241
> F-statistic: 57.78 on 3 and 11 DF,  p-value: 5.082e-07
> 
> 
> In the book, the estimates are
> 
>  From this book,
> 
> mu=33.8
> alpha_1=6.017
> alpha_2=0.942
> beta=0.899
> 
> Is it possible to obtain this estimates and their standard errors from the 
> model I fitted?

  Yes, just change the default contrast for the grupo factor:

y<-c(38,43,24,39,38,32,36,38,31,45,27,21,33,34,28)
x<-c(21,34,23,26,26,29,22,29,30,28,18,16,19,25,29)
xmean<-x-mean(x)
grupo<-factor(rep(c(1,2,3),5))
datos<-data.frame(y,xmean,grupo)

contrasts(datos$grupo) <- contr.sum(3)

modelo<-lm(y~xmean+grupo,data=datos)

summary(modelo)

Call:
lm(formula = y ~ xmean + grupo, data = datos)

Residuals:
    Min      1Q  Median      3Q     Max
-2.4348 -1.2739 -0.3363  1.6710  2.4869

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  33.8000     0.4835  69.908 6.37e-16 ***
xmean         0.8986     0.1026   8.759 2.73e-06 ***
grupo1        6.0174     0.7083   8.496 3.67e-06 ***
grupo2        0.9420     0.6987   1.348    0.205
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.873 on 11 degrees of freedom
Multiple R-Squared: 0.9403,     Adjusted R-squared: 0.9241
F-statistic: 57.78 on 3 and 11 DF,  p-value: 5.082e-07

> Thanks in advance
> 
> Tomas Goicoa
> 
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> 
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-- 
Chuck Cleland, Ph.D.
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