You are not offering example of real codings but are rather showing something1 that you think looks like something2 (in R) that looks like something3 (in a textbook?). My guess is that the something2 might be contrast matrices or model matrices.

If you want a contrast matrix whose columns sum to zero (which is one possible situation that some people might call "centered" then look at the documentation for sum and poly contrasts. If you want to see a situation where model matrices are constructed which compare to the overall mean (another possible interpretation of "centered"), then look at the documentation for model.matrix and run the examples on that page with a -1 in the formula.

--
David.
On Jan 11, 2011, at 3:18 PM, Christofer Bogaso wrote:

Dear all, I would like to ask one question related to statistics, for
specifically on defining dummy variables. As of now, I have come across 3
different kind of dummy variables (assuming I am working with Seasonal
dummy, and number of season is 4):

dummy1 <- diag(4)
for(i in 1:3) dummy1 <- rbind(dummy1, diag(4))
dummy1 <- dummy1[,-4]

dummy2 <- dummy1
dummy2[dummy2 == 0] = -1/(4-1)

dummy3 <- dummy1 - 1/4

head(dummy1)
    [,1] [,2] [,3]
[1,]    1    0    0
[2,]    0    1    0
[3,]    0    0    1
[4,]    0    0    0
[5,]    1    0    0
[6,]    0    1    0
head(dummy2)
          [,1]       [,2]       [,3]
[1,]  1.0000000 -0.3333333 -0.3333333
[2,] -0.3333333  1.0000000 -0.3333333
[3,] -0.3333333 -0.3333333  1.0000000
[4,] -0.3333333 -0.3333333 -0.3333333
[5,]  1.0000000 -0.3333333 -0.3333333
[6,] -0.3333333  1.0000000 -0.3333333
head(dummy3)
     [,1]  [,2]  [,3]
[1,]  0.75 -0.25 -0.25
[2,] -0.25  0.75 -0.25
[3,] -0.25 -0.25  0.75
[4,] -0.25 -0.25 -0.25
[5,]  0.75 -0.25 -0.25
[6,] -0.25  0.75 -0.25
Now I want to know which type of dummy definition is called Centered dummy
and why it is called so? Is it equivalent to use any of the above
definitions (atleast 2nd and 3rd?) It would really be very helpful if
somebody point any suggestion and clarification.

Thanks and regards,

        [[alternative HTML version deleted]]

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