Typo/edit in MARK book p. 6-52

[trrobbin]

4th sentence of section 6.9, "The number of columns used to characterize group differences (eg. belonging to one group or not) will always equal the number of dummy variables (coded "0" or "1") that you need to characterize group differences"

The next sentence states that it is k-1, so should the prior sentence read "The number of columns used to characterize group differences (eg. belonging to one group or not) will always equal one less than the number of dummy variables (coded "0" or "1") that you need to characterize group differences".

Don't mean to be pestering you, but I really just want to make sure that I am understanding things correctly.

Thank you!

[cooch]

4th sentence of section 6.9, "The number of columns used to characterize group differences (eg. belonging to one group or not) will always equal the number of dummy variables (coded "0" or "1") that you need to characterize group differences"

The next sentence states that it is k-1, so should the prior sentence read "The number of columns used to characterize group differences (eg. belonging to one group or not) will always equal one less than the number of dummy variables (coded "0" or "1") that you need to characterize group differences".

Don't mean to be pestering you, but I really just want to make sure that I am understanding things correctly.

Thank you!

No the text is correct. If you have k groups, you need k-1 columns to code for it in the design matrix. So, as stated, the number of columns used to characterize group differences is always equal to the number of dummy variables codes. So, if you have 2 levels of a group (k=2), you need k-1=1 columns. 3 levels, of a group (k=3), then k-1=2 columns. The number of columns used to characterize the group differences is the number of columns of dummy variables, which (as noted in the next part of the text) is simply k-1.

So, if anything, the first part of the text you quote is superfluous, given the second. But, it is laid out as it is to prevent confusion. If it helps, though, you simply need k-1 columns to code for a given group, where k is the number of levels of the group.

[trrobbin]

No the text is correct. If you have k groups, you need k-1 columns to code for it in the design matrix. So, as stated, the number of columns used to characterize group differences is always equal to the number of dummy variables codes. So, if you have 2 levels of a group (k=2), you need k-1=1 columns. 3 levels, of a group (k=3), then k-1=2 columns. The number of columns used to characterize the group differences is the number of columns of dummy variables, which (as noted in the next part of the text) is simply k-1.

So, if anything, the first part of the text you quote is superfluous, given the second. But, it is laid out as it is to prevent confusion. If it helps, though, you simply need k-1 columns to code for a given group, where k is the number of levels of the group.[/quote]

So, should it be the number of dummy variable codes, then, and not just dummy variables? Or dummy variables are the beta not the "0" and "1" per se? And, there could be dummy variable codes of "0", "1", "2", etc. right?

I understand the logic of the k-1, I'm just trying to fully comprehend the specifics, that I apparently don't as of yet.

[cooch]

So, should it be the number of dummy variable codes, then, and not just dummy variables? Or dummy variables are the beta not the "0" and "1" per se? And, there could be dummy variable codes of "0", "1", "2", etc. right?

No, dummies are binary (i.e., 0, or 1). So, you need k-1 columns of 0/1 dummies to code for k unique levels of a classification variable. This is what imposes the k-1 constraint. This is actually covered in the first 2 sections of the chapter. The assumption by this point in the chapter is that you recognize that dummy variables are binary 0/1. Not sure what you mean by a dummy variable 'code'. The dummy variables are what you use to 'code' the group associations. See in particular section 6.2 (p. 8 in particular).

[trrobbin]

No, dummies are binary (i.e., 0, or 1). So, you need k-1 columns of 0/1 dummies to code for k unique levels of a classification variable. This is what imposes the k-1 constraint. This is actually covered in the first 2 sections of the chapter. The assumption by this point in the chapter is that you recognize that dummy variables are binary 0/1. Not sure what you mean by a dummy variable 'code'. The dummy variables are what you use to 'code' the group associations. See in particular section 6.2 (p. 8 in particular).

What is my dummy variable now? Sorry for drinking on the job.

Thank you!