The following is the code for the model.matrix. But it still doesn't
answer why A:B is interpreted differently in Y~A+B+A:B and Y~A:B. By
'why', I mean how R internally does it and what is the rational behind
the way of doing it?
And it didn't answer why in the model.matrix of Y~A, there are a-1
terms from A plus the intercept, but in the model.matrix of Y~A:B,
there are a*b terms (rather than a*b-1 terms) plus the intercept.
Since the one coefficient of the lm of Y~A:B is going to be NA, why
bother to include the corresponding term in the model matrix?
############code below
set.seed(0)
a=3
b=4
AB_effect=data.frame(
name=paste(
unlist(
do.call(
rbind
, rep(list(paste('A', letters[1:a],sep='')), b)
)
)
, unlist(
do.call(
cbind
, rep(list(paste('B', letters[1:b],sep='')), a)
)
)
, sep=':'
)
, value=rnorm(a*b)
, stringsAsFactors=F
)
max_n=10
n=sample.int(max_n, a*b, replace=T)
AB=mapply(function(name, n){rep(name,n)}, AB_effect$name, n)
Y=AB_effect$value[match(unlist(AB), AB_effect$name)]
Y=Y+a*b*rnorm(length(Y))
sub_fr=as.data.frame(do.call(rbind, strsplit(unlist(AB), ':')))
rownames(sub_fr)=NULL
colnames(sub_fr)=c('A', 'B')
fr=data.frame(Y=Y,sub_fr)
my_subset=function(amm) {
coding=apply(
amm
,1
, function(x) {
paste(x, collapse='')
}
)
amm[match(unique(coding), coding),]
}
my_subset(model.matrix(Y ~ A*B,fr))
my_subset(model.matrix(Y ~ (A+B)^2,fr))
my_subset(model.matrix(Y ~ A + B + A:B,fr))
my_subset(model.matrix(Y ~ A:B - 1,fr))
my_subset(model.matrix(Y ~ A:B,fr))
On Fri, Mar 5, 2010 at 8:45 AM, Gabor Grothendieck
<ggrothendi...@gmail.com> wrote:
The way to understand this is to look at the output of model.matrix:
model.matrix(fo, fr)
for each formula you tried. If your data is large you will have to
use a subset not to be overwhelmed with output.
On Fri, Mar 5, 2010 at 9:08 AM, blue sky <bluesky...@gmail.com> wrote:
Suppose, 'fr' is data.frame with columns 'Y', 'A' and 'B'. 'A' has
levels 'Aa'
'Ab' and 'Ac', and 'B' has levels 'Ba', 'Bb', 'Bc' and 'Bd'. 'Y'
columns are numbers.
I tried the following three sets of commands. I understand that A*B is
equivalent to A+B+A:B. However, A:B in A+B+A:B is different from A:B
just by itself (see the 3rd and 4th set of commands). Would you please
help me understand why the meanings of A:B are different in different
contexts?
I also see the coefficient of AAc:BBd is NA (the last set of
commands). I'm wondering why this coefficient is not removed from the
'coefficients' vector. Since lm(Y~A) has coefficients for (intercept),
Ab, Ac (there are no NA's), I think that it is reasonable to make sure
that there are no NA's when there are interaction terms, namely, A:B
in this case.
Thank you for answering my questions!
alm=lm(Y ~ A*B,fr)
alm$coefficients
(Intercept) AAb AAc BBb BBc
BBd
-3.548176 -2.086586 7.003857 4.367800 11.887356 -3.470840
AAb:BBb AAc:BBb AAb:BBc AAc:BBc AAb:BBd AAc:BBd
5.160865 -11.858425 -12.853116 -20.289611 6.727401 -2.327173
alm=lm(Y ~ A + B + A:B,fr)
alm$coefficients
(Intercept) AAb AAc BBb BBc
BBd
-3.548176 -2.086586 7.003857 4.367800 11.887356 -3.470840
AAb:BBb AAc:BBb AAb:BBc AAc:BBc AAb:BBd AAc:BBd
5.160865 -11.858425 -12.853116 -20.289611 6.727401 -2.327173
alm=lm(Y ~ A:B - 1,fr)
alm$coefficients
AAa:BBa AAb:BBa AAc:BBa AAa:BBb AAb:BBb AAc:BBb
AAa:BBc
-3.5481765 -5.6347625 3.4556808 0.8196231 3.8939016 -4.0349449
8.3391795
AAb:BBc AAc:BBc AAa:BBd AAb:BBd AAc:BBd
-6.6005222 -4.9465744 -7.0190168 -2.3782017 -2.3423322
alm=lm(Y ~ A:B,fr)
alm$coefficients
(Intercept) AAa:BBa AAb:BBa AAc:BBa AAa:BBb
AAb:BBb
-2.34233221 -1.20584424 -3.29243033 5.79801305 3.16195534
6.23623377
AAc:BBb AAa:BBc AAb:BBc AAc:BBc AAa:BBd AAb:BBd
-1.69261273 10.68151168 -4.25819000 -2.60424217 -4.67668454
-0.03586951
AAc:BBd
NA
