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 ***
grupo16.0174 0.7083 8.496 3.67e-06 ***
grupo20.9420 0.6987 1.3480.205
---
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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