Re: st: Statistical/Stata question

[Richard Williams <Richard.A.Williams.5@nd.edu>]

> It isn't silly at all.
>
> In effect, you are forcing the first two categories (1 and 2) to have 
> exactly the same odds (probability) for the event. In other words, you are 
> constraining the odds ratio for category2 vs. category1 to be exactly 
> equal to 1. As a consequence, the comparison of category3 to category1 has 
> the same odds ratio as the comparison of category3 to category2 (and 
> similarly for category4). For the purposes of the model, there are only 3 
> categories: a combined 1/2 category, category3 and category4.
Agreed.  To offer some substantive examples: When you have a categorical 
variable, you may not necessarily want to create and use all possible 
dummies.  The Ns for some categories may be very small, or, for the 
purposes of your analysis, the differences between groups may be small or 
nonexistent.

Suppose, for example, that Race has been coded white, black and other in 
your data.  You might wonder whether (a) you need separate dummies for 
blacks and others, because both groups differ from whites and they also 
differ from each other, or (b) do you just need the dummy for white, in 
which case you'd be saying that the important contrast is white versus 
nonwhite and the differences among nonwhites are not important.

Combining categories may cost you some information, and it may obscure 
important differences by in effect assuming that, say, all minorities are 
the same.  But, combining categories can also make the analysis much more 
manageable and help the most critical points to be clearer.  You can, of 
course, do formal tests to see whether it is legit to combine categories 
together, e.g. if the IVs were black and other and a test reveals that 
their effects do not significantly differ from each other, you could just 
use a dummy var for white/nonwhite instead.  Or, going back to the original 
example, if the IVS were category2, category3, and category4, and category2 
was not significant, that would suggest that you can simplify things by 
just pooling category1 and category2 together (especially if it makes 
logical sense that the groups would differ little if any from each other).


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Richard Williams, Notre Dame Dept of Sociology
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