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A question on dummy variable

6 messages · Bert Gunter, David Winsemius, Gabor Grothendieck +2 more

Bert Gunter
# 
R does not use dummy variables. Models and contrasts are specified in
more natural, model formula based ways. See

?arima

 and/or CRAN's Time Series task view for numerous packages that fit time series.

-- Bert

On Tue, Jan 11, 2011 at 12:18 PM, Christofer Bogaso
<bogaso.christofer at gmail.com> wrote:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      David Winsemius
    

    

      
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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.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
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On Tue, Jan 11, 2011 at 3:18 PM, Christofer Bogaso

        
<bogaso.christofer at gmail.com> wrote:

            

      
      
      
    

        
The contrasts of your dummy1 matrix are contr.SAS contrasts in R.
(The default contrasts in R are contr.treatment which are the same as
contr.SAS except contr.SAS uses the last level as the base whereas
treatment contrasts use the first level as the base.)

   options(contrasts = c("contr.SAS", "contr.poly"))
   f <- gl(4, 1, 16)
   M <- model.matrix( ~ f )
   all( M[, -1] == dummy1) # TRUE

Centered contrasts are ones which have been centered -- i.e. the mean
of each column has been subtracted from that column.  This is
equivalent to saying that the column sums are zero.

The means of the three columns of dummy1 are c(1/4, 1/4, 1/4) so if we
subtract 1/4 from dummy1 we get a centered contrasts matrix. That is
precisely what you did to get dummy3.  We can check that dummy3 is
centered:

   colSums(dummy3) # 0 0 0

dummy2 is just a scaled version of dummy3.  In fact dummy2 equals
dummy3 / .75 so its not fundamentally different.  Its columns still
sum to zero so its still centered.

   all( dummy2 == dummy3 / .75) # TRUE
   colSums(dummy2) # 0 0 0 except for floating point error

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      John Sorkin
    

    

      
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Christofer,
I am not sure I understand how you are using your dummy variables. Generally if you have n categories you need n-1 dummy variables. Thus if you have three categories, low, medium, high and want to compare two of the levels to a reference level (a coding scheme sometimes called reference cell coding) you could use the following coding which medium and high to the reference level, low:

level   dummy1 dummy2
low        0     0        
medium     0     1
high       1     0

You will notice that for three categories, my dummy variables from  an 3 by 2 matrix. In general the dummy variable matrix for n categories will be an n by n-1 matrix. You say your have four seasons. I would expect your dummy variable matrix to be of size 4 by 3. Your matrices are 6 by 3. Am I not understanding what you are trying to do?
John

John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC,
University of Maryland School of Medicine Claude D. Pepper OAIC,
University of Maryland Clinical Nutrition Research Unit, and
Baltimore VA Center Stroke of Excellence

University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524

(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
jsorkin at grecc.umaryland.edu

            

      
      
      
    

        
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):

            

      
      
      
    

        
[,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

            

      
      
      
    

        
[,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

            

      
      
      
    

        
[,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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      Christofer Bogaso
    

    

      
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Thanks Gabor and other for their input. I admit that I must have placed some
reproducible codes on what I wanted. However it was actually in my mind
however I restrained because it was not any R related query rather a general
Statistics related.

Here I am using dummy variables in ***Time series context***. Please assume
following artificial TS along with the quarterly dummies:

library(zoo)
# my time series
MyTimeSeries <- zooreg(101:126, start=as.yearqtr(as.Date("2005-01-01")),
frequency=4)
# creation of quarterly dummy
### dummy1
dummy1 <- zooreg(Reduce("rbind", rep(list(diag(4)), 7)),
start=as.yearqtr(as.Date("2005-01-01")), frequency=4) 
dummy1 <- merge(dummy1, MyTimeSeries, all=F)[,1:4]
colnames(dummy1) <- paste("dummy", 1:4, sep="")
### dummy2
dummy2 <- dummy1 - 1/4
### dummy3
dummy3 <- dummy1
dummy3[dummy3 ==0] = -1/(4-1)
# Time series with quarterly dummy
TS_with_dummy1 <- cbind(MyTimeSeries, dummy1[,-4])
TS_with_dummy2 <- cbind(MyTimeSeries, dummy2[,-4])
TS_with_dummy3 <- cbind(MyTimeSeries, dummy3[,-4])
TS_with_dummy1
TS_with_dummy2
TS_with_dummy3

Here you see, as my previous post, there are 3 types of dummies: dummy1,
dummy2, and dummy3 (quarterly dummies). I used to use dummy1 declaration for
all my time series analysis. However later in the "vars" package I noticed
the 2nd type of definition for dummy. And 3rd definition I have come across
from somewhere in net (which I cant just recall at this time.) Here my
question was: which is the centred dummy variable (according to help page of
vars package 2nd one is the centred dummy)?

However I am searching for the definition of centred dummy variables in time
series analysis context. Therefore I would want to know, why 2nd one is
called centred dummy? Why people prefer for it, not the Standard dummy
definition (i.e. dummy1).

Can you please explain?

Thanks and regards,

-----Original Message-----
From: Gabor Grothendieck [mailto:ggrothendieck at gmail.com] 
Sent: 12 January 2011 05:47
To: Christofer Bogaso
Cc: r-help at r-project.org
Subject: Re: [R] A question on dummy variable

On Tue, Jan 11, 2011 at 3:18 PM, Christofer Bogaso

        
<bogaso.christofer at gmail.com> wrote:

            

      
      
      
    

        
The contrasts of your dummy1 matrix are contr.SAS contrasts in R.
(The default contrasts in R are contr.treatment which are the same as
contr.SAS except contr.SAS uses the last level as the base whereas treatment
contrasts use the first level as the base.)

   options(contrasts = c("contr.SAS", "contr.poly"))
   f <- gl(4, 1, 16)
   M <- model.matrix( ~ f )
   all( M[, -1] == dummy1) # TRUE

Centered contrasts are ones which have been centered -- i.e. the mean of
each column has been subtracted from that column.  This is equivalent to
saying that the column sums are zero.

The means of the three columns of dummy1 are c(1/4, 1/4, 1/4) so if we
subtract 1/4 from dummy1 we get a centered contrasts matrix. That is
precisely what you did to get dummy3.  We can check that dummy3 is
centered:

   colSums(dummy3) # 0 0 0

dummy2 is just a scaled version of dummy3.  In fact dummy2 equals
dummy3 / .75 so its not fundamentally different.  Its columns still sum to
zero so its still centered.

   all( dummy2 == dummy3 / .75) # TRUE
   colSums(dummy2) # 0 0 0 except for floating point error

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