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,

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