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Intercept in lm and in library(car): Anova

2 messages · Stefan Th. Gries, John Fox

Original
Stefan Th. Gries
# 
Hi

I have two questions regarding the meaning of intercept outputs of lm.

Question 1: In data set 1 (a fully-balanced design), the line with
(Intercept) contains the overall mean, and the estimates contain the
differences from the overall mean (matching those from model.tables).
But in data set 2, the line with the intercept does not correspond to
the overall mean and the estimates don't correspond to the differences
outputted by model.tables. What does the output contain here?

#####
rm(list=ls(all=TRUE))
options(contrasts=c("contr.sum", "contr.poly"))

# data set 1
Y1<-c(43, 23, 88, 45, 2, 68, 39, 41, 55, 64, 91, 9, 90, 37, 88, 41)
M1<-factor(c("k", "g", "k", "g", "k", "k", "g", "g", "g", "g", "k",
"k", "g", "g", "k", "k"))
N1<-factor(c("k", "g", "g", "k", "k", "g", "k", "g", "k", "g", "g",
"k", "g", "k", "g", "k"))

# linear model 1
model1<-lm(Y1~M1*N1); summary(model1)
model.tables(aov(Y1~M1*N1), "means")
model.tables(aov(Y1~M1*N1))

# data set 2
Y2<-c(34, 16, 46, 5, 2, 78, 31, 39, 25, 64, 45, 92, 65, 91, 60, 12,
33, 40, 72, 61, 49, 59)
M2<-factor(c(rep("a", 10), rep("b", 12)))
N2<-factor(c(rep("d", 4), rep("e", 6), rep("d", 8), rep("e", 4)))

# linear model 2
model2<-lm(Y2~M2*N2); summary(model2)
model.tables(aov(Y2~M2*N2), "means")
model.tables(aov(Y2~M2*N2))
#####


Question 2: what does the line with (Intercept) mean that the
following lines produce?

#####
library(car)
Anova(model, type=c("III"))
#####

Any help would be much appreciated. Thx,
STG
John Fox
# 
Dear Stefan,
In both datasets, the intercept is the "grand mean", which in a two-way
ANOVA (parametrized with sum-to-zero contrasts) is the mean of the cell
means. In the first case, because the data are balanced, the mean of the
cell means corresponds to the mean of Y1. In the second case, where there
are unequal cell counts, the mean of the cell means is different from the
mean of Y2 (but equal to the estimated intercept):
[1] 45.02083

The line in the output from Anova() in the package for the intercept tests
the null hypothesis that the intercept parameter is different from 0, which
rarely would be of interest.

I hope this helps,
 John